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From: <Saved by Blink>
Snapshot-Content-Location: https://chatgpt.com/c/52dba091-fce2-430e-a57a-3ddb2f9c8b72
Subject: Quantifying Life Pathways
Date: Sat, 8 Jun 2024 20:13:15 -0300
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xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm ml-1"><path fill="currentColor" d="M13 12a1 1 0 1 0-2 0v4a1 1 0 1 0 2 0zM12 9.5A1.25 1.25 0 1 0 12 7a1.25 1.25 0 0 0 0 2.5"></path><path fill="currentColor" fill-rule="evenodd" d="M12 2C6.477 2 2 6.477 2 12s4.477 10 10 10 10-4.477 10-10S17.523 2 12 2M4 12a8 8 0 1 1 16 0 8 8 0 0 1-16 0" clip-rule="evenodd"></path></svg></span></div></div><main class="relative h-full w-full flex-1 overflow-auto transition-width"><div role="presentation" tabindex="0" class="flex h-full flex-col focus-visible:outline-0"><div class="flex-1 overflow-hidden"><div class="react-scroll-to-bottom--css-jqgaj-79elbk h-full"><div class="react-scroll-to-bottom--css-jqgaj-1n7m0yu"><div style="padding: 0px;"><div class="flex flex-col text-sm pb-9"><div class="h-1.5"></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-2" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21af5-5c54-424b-8f0f-eda55975bb9b" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">Quantifying the pathways to life using assembly spaces
Stuart M. Marshall,1 Douglas G. Moore,2 Alastair R. G. Murray,1 Sara I. Walker,2,3* and Leroy
Cronin1*
1 School of Chemistry, University of Glasgow, Glasgow, G12 8QQ, UK.
2 BEYOND Center for Fundamental Concepts in Science, Arizona State University, Tempe,
AZ, USA
3 School of Earth and Space Exploration, Arizona State University, Tempe, AZ, USA
*Corresponding author email: [email protected], [email protected]
Abstract
We have developed the theory of pathway assembly to explore the extrinsic information
required to distinguish a given object from a random ensemble. To quantify the assembly in an
agnostic way, we determine the pathway assembly information contained within such an object
by deconstructing the object into its irreducible parts, and then evaluating the minimum number
of steps to reconstruct the object. The formalisation of this approach uses an assembly space.
By finding the minimal number of steps contained in the route by which the objects can be
assembled within that space, we can compare how much information (������������ ) is gained from
knowing this pathway assembly index (PA) according to ������������������������ ������������= ������������ ������������ ������������
|������������ |
|������������ ������������ ������������| where, for an end
product with ������������ ������������ = ������������ , N is the set of objects possible that can be created from the same
irreducible parts within ������������ steps regardless of PA, and NPA is the subset of those objects with
the precise pathway assembly index ������������ ������������ = ������������ . Applying this theory to objects formed in 1D,
2D and 3D leads to the identification of objects in the world or wider Universe that have high
assembly numbers. We propose that objects with high PA will be uniquely identifiable as those
that must have been produced by biological or technological processes, rather than the
assembly occurring via unbiased random processes alone, thereby defining a new scale of
aliveness. We think this approach is needed to help identify the new physical and chemical
laws needed to understand what life is, by quantifying what life does.<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-3" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="e9035d6d-2322-4e92-93e2-6cf4fa787064" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The article you provided an excerpt from explores a novel theoretical framework called "pathway assembly" which is used to measure the extrinsic information required to differentiate a specific object from a random ensemble. This concept is used to analyze how objects are assembled from their fundamental parts, quantifying the minimal steps needed to reconstruct them within an "assembly space."</p><p>The key metric introduced here is the "pathway assembly index" (PA), which quantifies the information gained from knowing the minimal steps required for the object's assembly. The formula provided (which involves I, N, and N_PA) calculates the information by comparing the size of a set of all possible objects that can be assembled from the same irreducible parts within a given number of steps (N), against a subset of those objects that share the same exact pathway assembly index (N_PA).</p><p>This approach is applied to objects formed in one-dimensional, two-dimensional, and three-dimensional spaces. The researchers propose that objects with high PA values are likely produced through biological or technological processes rather than through random processes. Such a measure could help in identifying objects that have undergone specific assembly pathways that are indicative of life or complex technological processes, thereby aiding in the search for new physical and chemical laws to better understand life itself.</p><p>The implications of this study are profound as they offer a method to quantify "aliveness" and identify objects that require complex assembly processes, which could distinguish biological entities and advanced technologies from simpler, randomly assembled matter. This could potentially redefine our understanding of life and its origins, both on Earth and in the wider universe.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11 4.9099C11 4.47485 10.4828 4.24734 10.1621 4.54132L6.67572 7.7372C6.49129 7.90626 6.25019 8.00005 6 8.00005H4C3.44772 8.00005 3 8.44776 3 9.00005V15C3 15.5523 3.44772 16 4 16H6C6.25019 16 6.49129 16.0938 6.67572 16.2629L10.1621 19.4588C10.4828 19.7527 11 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11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-4" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21c4e-25c3-4296-8cb1-0d24fcd72b0d" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">Introduction
In the thought experiment known as the “infinite monkey theorem”, an infinite number of
monkeys, each having a typewriter, produce strings of text by hitting keys at random (1). Given
infinite resources, it can be deduced that the monkeys will produce all possible strings,
2
including the complete works of Shakespeare. However, when constrained to the bounds of the
physical universe, the likelihood that any particular text is produced by a finite number of
monkeys drops rapidly with the length of the text (2). This can also be extended to physical
objects like cars, aeroplanes, and computers, which must be constructed from a finite set of
objects- just as meaningful text is constructed from a finite set of letters. Even if we were to
convert nearly all matter in the universe to object constructing monkeys, and give them the age
of the universe in which to work, the probability that any monkey would construct any
sufficiently complex physical object is negligible (3). This is an entropic argument – the
number of possible arrangements of the objects of a given composition increases exponentially
with the object size. For example, if the number of possible play-sized strings is sufficiently
large, it would be practically impossible to produce a predetermined Shakespearean string
without the author. This argument implies information external to the object itself is necessary
to construct an object if it is of sufficiently high complexity (4,5): in biology the requisite
information partly comes from DNA, the sequence of which has been acquired through
progressive rounds of evolution. Although Shakespeare’s works are – in the absence of an
appropriate constructor (6) (an author)- as likely to be produced as any other string of the same
length, our knowledge of English, and Shakespeare in particular, allows us to partition the set
of possible strings to generate information about those strings containing meaning, and to
construct them.
Biological systems have access to a lot of information- genetically, epigenetically,
morphologically, and metabolically- and the acquisition of that information occurs via
evolutionary selection over successive cycles of replication and propagation (7). One way to
look at such systems is by comparing the self-dissimilarity between different classes of
complex system, allowing a model free comparison (8). However, it has also been suggested
that much of this information is effectively encrypted, with the heritable information being
encoded with random keys from the environment (9). As such, these random keys are recorded
as frozen accidents and increase the operative information content, as well as help direct the
system during the process of evolution, producing objects that can construct other objects (10).
This is significant since one important characteristic of objects produced autonomously by
machinery (such as life), which itself is instructed in some way, is their relative complexity as
compared to objects that require no information for their assembly beyond what chemistry and
physics alone can provide. This means that for complex objects there is ‘object-assembly’
information that is generated by an evolutionary system, and is not just the product of laws of physics and chemistry alone. Biological systems are the only known source of agency in the
universe (11), and it has been suggested that new physical laws are needed to understand the
phenomenon of life (12). The challenge is how to explore the complexity of objects generated
by evolutionary systems without a priori having a model of the system.
Herein, we present the foundations of a new theoretical approach to agnostically quantify the
amount of potential pathway assembly information contained within an object. This is achieved
by considering how the object can be deconstructed into its irreducible parts, and then
evaluating the minimum number of steps necessary to reconstruct the object along any
pathway. The analysis of pathway assembly is done by the recursive deconstruction of a given
object using shortest paths, and this can be used to evaluate the effective pathway assembly
index for that object (13). In developing pathway assembly, we have been motivated to create
an intrinsic measure of an object forming through random processes, where the only knowledge
required of the system is the basic building blocks and the permitted ways of joining structures
together. This allows determining when an extrinsic agent or evolutionary system is necessary
to construct the object, permitting the search for complexity in the abstract, without any specific
notions of what we are looking for, thus removing the requirement for an external imposition
of meaning, see Figure 1.
Figure 1: The Pathway Assembly process (centre) (13) is compared to implementations of
Shannon Entropy (14) (left) and Kolmogorov Complexity (15) (right) for blue and white
blocks. The Pathway Assembly process leads to a measure of structural complexity that
accounts for the structure of the object and how it could have been constructed, which is in all
cases computable and unambiguous.<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-5" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 25.8215 3.85078C24.8796 2.7893 23.7219 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11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="1b7691f1-632c-4391-9818-386bb5a40aff" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The introduction you provided dives into a theoretical exploration of object complexity and assembly in the context of both biological and non-biological systems. This analysis leans on the "infinite monkey theorem" as a metaphor to discuss the improbability of randomly producing complex structures, such as Shakespearean texts or advanced technological devices like cars and computers, without specific guiding information or instructions.</p><p>The text establishes that complex objects, much like coherent and meaningful texts, require a specific set of information to be assembled correctly. This is contrasted with simpler, random constructs that might arise from basic physical and chemical processes. In biological contexts, this necessary information is often provided by genetic and epigenetic mechanisms, acquired through evolutionary processes that favor the replication of structures capable of supporting their own assembly and propagation.</p><p>The main thrust of the passage is the introduction of a new theoretical approach called "pathway assembly." This approach seeks to quantify the complexity and assembly pathway of objects by deconstructing them into their fundamental parts and analyzing the minimal steps required for their reassembly. This is intended to measure the "pathway assembly information" intrinsic to an object, which helps differentiate between objects formed through random physical processes and those requiring directed, informational input typically associated with biological or technological systems.</p><p>Pathway assembly is contrasted with other complexity measures like Shannon Entropy, which assesses information content without considering structural coherence, and Kolmogorov Complexity, which focuses on the description length of the shortest computer program that can produce the object. Unlike these measures, pathway assembly is designed to provide a clear, computable, and unambiguous measure of structural complexity, focusing on how an object could have been assembled rather than just its informational content or computational generativity.</p><p>This new methodology underscores a broader scientific pursuit to identify and understand complex systems, particularly living systems, which may operate under principles not fully explained by current physical and chemical laws. It suggests a shift towards evaluating systems in terms of their assembly processes, potentially leading to insights into the nature of life and the emergence of complexity in the universe.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11 4.9099C11 4.47485 10.4828 4.24734 10.1621 4.54132L6.67572 7.7372C6.49129 7.90626 6.25019 8.00005 6 8.00005H4C3.44772 8.00005 3 8.44776 3 9.00005V15C3 15.5523 3.44772 16 4 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13V5C17.0045 4.64937 16.9444 4.31278 16.8338 4H18.0045C18.5568 4 19.0045 4.44772 19.0045 5V12C19.0045 12.5523 18.5568 13 18.0045 13H17.0045Z" fill="currentColor"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r56:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-6" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb211cf-22c9-41d3-9c35-02292f04e66f" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">The development of the Pathway Assembly (13) index (PA) was motivated by the desire to
define a biological threshold, such that any object found in abundance with PA above the
threshold would have required the intervention of one or more biological processes to form
(16). The Pathway Assembly index (PA) of an object is the length of the shortest pathway to
construct the object starting from its basic building blocks. It should be noted that this approach
is entirely classical (17), allowing quantifying pathways through assembly space
probabilistically as a way to understand what life does. We construct the object using a
sequence of joining operations, where at each step any structures already created are available
for use in subsequent steps, see Figure 2. The shortest pathway approach is in some ways
analogous to Kolmogorov complexity (15), which in the case of strings is the shortest computer
program that can output a given string. However, Pathway Assembly differs in that we only
allow joining operations as defined in our model. This restriction is intended to allow the
Pathway Assembly process to mimic the natural construction of objects through random
processes, and it also importantly allows the PA of an object to be computable for all finite
objects (see Theorem 4 in the SI).
Figure 2: The basic concept of pathway assembly is shown here. Each of the final structures
can be created from white and blue basic objects in four joining operations, giving a Pathway
Assembly Index of 4. Pathway (a) shows the creation of a structure that can only be formed in
four steps by adding one basic object at a time, while pathway (c) represents the maximum
increase in size per step, by combining the largest object in the pathway with itself at each
stage. Pathway (b) is an intermediate case. 5
Given a system where objects interact randomly and with equal probability, it is intuitively
clear that the likelihood of an object being formed in ������������ steps decreases rapidly with ������������ .
However, it is also true that a highly contrived set of biases could guarantee the formation of
any object. For example, this could occur if we were to model the system such that any
interactions contributing to the formation of the object were certain to be successful, while
other interactions were prohibited. For complex objects, such a serendipitous set of biases
would seem unlikely in the absence of external information about the end products, but physical
systems generally do have biases in their interactions, and we can explore how these affect the
likelihood of formation of objects. However, we expect for any perceived “construction
processes” that requires a large enough set of highly contrived biases, we can deduce that
external information is required in the form of a “machine” that is doing the constructing.<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-7" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 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10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="fa0deedd-9f89-4f07-9258-1750d6248f0f" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The section discusses the motivation and methodology behind the Pathway Assembly (PA) index, a concept developed to measure the complexity of an object's construction from its basic components through a series of joining operations. The PA index quantifies the minimum steps required to assemble an object, aiming to establish a biological threshold that indicates whether an object likely required biological processes for its formation.</p><p>The PA index is analogized with Kolmogorov complexity, which measures the shortest computer program that can produce a given string. However, PA differs significantly because it restricts its operations to those that could plausibly occur through natural processes—specifically, joining operations. This restriction not only ensures that the PA index is computable for all finite objects but also aims to model the natural assembly of objects, emphasizing the feasibility of such constructions in nature or under certain constraints.</p><p>The text also touches on the idea that while random interactions are unlikely to produce complex structures efficiently without biases, certain physical systems do exhibit biases that could influence object formation. This aspect introduces the possibility that even in ostensibly random systems, biases or predefined conditions (akin to a "machine" or directed process) might increase the probability of complex object assembly. Thus, studying these biases helps in understanding the constraints and possibilities within which complex structures can form.</p><p>Overall, the development of the PA index serves as a tool to investigate the underlying processes and requirements for the assembly of complex objects, offering insights into the nature of biological and potentially non-biological systems that produce intricate structures. This approach provides a more structured and measurable way to examine how complex objects arise, suggesting a blend of randomness and specific, perhaps evolutionary, influences that guide their formation.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11 4.9099C11 4.47485 10.4828 4.24734 10.1621 4.54132L6.67572 7.7372C6.49129 7.90626 6.25019 8.00005 6 8.00005H4C3.44772 8.00005 3 8.44776 3 9.00005V15C3 15.5523 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lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-8" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21565-3717-4be4-b487-d70a60f483f1" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">Technological processes are bootstrapped to biological ones, and hence, by extension,
production of technosignatures involves processes that necessarily have a biological origin.
Examples of biosignatures and technosignatures include chemical products produced by the
action of complex molecular systems such as networks of enzymes (18), and also objects whose
creation involved any biological organisms such as technological artefacts (19), complex
chemicals made in the laboratory (20), and the complete works of Shakespeare. Finding the
object in some abundance, or a single object with a large number of complex, but precisely
repeating features, is required in order to distinguish single random occurrences from
deliberately generated objects. For example, a system which produces long random strings will
generate many that have high PA, but not in abundance. Finding the same long string more
than once will tell us that there is a bias in the system towards creating that string, thus
searching for signatures of life should involve looking for objects with high PA found in
relatively high abundance.
Formalism
In this manuscript, we explore the foundations of Pathway Assembly, as well as some of its
properties and variants. We also describe how Pathway Assembly can be incorporated into a
new information measure, Pathway Information, and how this can help identify objects, above
a threshold, that must have been produced by living systems. Finally, we offer some examples
of the use of pathway assembly in systems of varying dimensionality, and describe some
potential real-world applications of this approach. The Pathway Assembly process is formally
defined in the context of an Assembly Space, which comprises an acyclic quiver Γ (a quiver
6
being a directed graph that allows multiple edges between pairs of nodes and has no directed
cycles), where the vertices in the quiver are objects in the space, along with an edge labelling
map ������������ which associates each edge with a vertex in the quiver (see Definition 11 in the SI). The
quiver is associated with a reachability relationship ≤ where for vertices ������������ ,������������ in Γ, ������������ ≤ ������������ if
there is a path from ������������ to ������������ , in other words it is possible reach ������������ starting at ������������ by following a
sequence of edges along their respective directions. If for an edge ������������ from object ������������ to object ������������ ,
������������ (������������ ) = ������������ , then this can be thought of as ������������ being constructed through the combination of ������������ and
������������ . We also require that the symmetric operation exists within the space, i.e. there is an edge ������������
from ������������ to ������������ such that ������������ (������������ ) = ������������ .<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-9" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 25.8215 3.85078C24.8796 2.7893 23.7219 1.94125 22.4257 1.36341C21.1295 0.785575 19.7249 0.491269 18.3058 0.500197C16.1708 0.495044 14.0893 1.16803 12.3614 2.42214C10.6335 3.67624 9.34853 5.44666 8.6917 7.47815C7.30085 7.76286 5.98686 8.3414 4.8377 9.17505C3.68854 10.0087 2.73073 11.0782 2.02839 12.312C0.956464 14.1591 0.498905 16.2988 0.721698 18.4228C0.944492 20.5467 1.83612 22.5449 3.268 24.1293C2.81966 25.4759 2.66413 26.9026 2.81182 28.3141C2.95951 29.7256 3.40701 31.0892 4.12437 32.3138C5.18791 34.1659 6.8123 35.6322 8.76321 36.5013C10.7141 37.3704 12.8907 37.5973 14.9789 37.1492C15.9208 38.2107 17.0786 39.0587 18.3747 39.6366C19.6709 40.2144 21.0755 40.5087 22.4946 40.4998C24.6307 40.5054 26.7133 39.8321 28.4418 38.5772C30.1704 37.3223 31.4556 35.5506 32.1119 33.5179C33.5027 33.2332 34.8167 32.6547 35.9659 31.821C37.115 30.9874 38.0728 29.9178 38.7752 28.684C39.8458 26.8371 40.3023 24.6979 40.0789 22.5748C39.8556 20.4517 38.9639 18.4544 37.5324 16.8707ZM22.4978 37.8849C20.7443 37.8874 19.0459 37.2733 17.6994 36.1501C17.7601 36.117 17.8666 36.0586 17.936 36.0161L25.9004 31.4156C26.1003 31.3019 26.2663 31.137 26.3813 30.9378C26.4964 30.7386 26.5563 30.5124 26.5549 30.2825V19.0542L29.9213 20.998C29.9389 21.0068 29.9541 21.0198 29.9656 21.0359C29.977 21.052 29.9842 21.0707 29.9867 21.0902V30.3889C29.9842 32.375 29.1946 34.2791 27.7909 35.6841C26.3872 37.0892 24.4838 37.8806 22.4978 37.8849ZM6.39227 31.0064C5.51397 29.4888 5.19742 27.7107 5.49804 25.9832C5.55718 26.0187 5.66048 26.0818 5.73461 26.1244L13.699 30.7248C13.8975 30.8408 14.1233 30.902 14.3532 30.902C14.583 30.902 14.8088 30.8408 15.0073 30.7248L24.731 25.1103V28.9979C24.7321 29.0177 24.7283 29.0376 24.7199 29.0556C24.7115 29.0736 24.6988 29.0893 24.6829 29.1012L16.6317 33.7497C14.9096 34.7416 12.8643 35.0097 10.9447 34.4954C9.02506 33.9811 7.38785 32.7263 6.39227 31.0064ZM4.29707 13.6194C5.17156 12.0998 6.55279 10.9364 8.19885 10.3327C8.19885 10.4013 8.19491 10.5228 8.19491 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10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="0749c69f-b142-4486-b45d-74e8f2740a46" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The text you've provided delves into the theoretical framework of Pathway Assembly (PA) and its application to the identification of biosignatures and technosignatures, extending the methodology to differentiate between random occurrences and intentionally created complex objects. The key concept is that technological processes, which produce technosignatures, are ultimately rooted in biological processes, reflecting an evolutionary lineage from natural biological systems to human-made technologies.</p><p><strong>Understanding Pathway Assembly in Assembly Space</strong></p><p>The formalism of Pathway Assembly is set within an assembly space characterized by an acyclic quiver Γ. In this context, a quiver is a directed graph that can include multiple edges between a pair of nodes but does not contain directed cycles. This structure allows for the representation of the assembly process as a network of object interactions where each vertex represents an object, and each directed edge denotes a specific assembly operation between objects.</p><p>The edge labeling map <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.8889em; vertical-align: -0.1944em;"></span><span class="mord mathnormal" style="margin-right: 0.10764em;">f</span></span></span></span> plays a crucial role in this setup. It is used to assign a specific object to each edge, effectively describing how one object contributes to or results from the assembly of another. This setup captures the dynamic and hierarchical relationships inherent in assembly processes, where simpler objects combine in defined ways to form more complex entities.</p><p>The concept of reachability (denoted by ≤) within the quiver is fundamental. It indicates that one object (vertex) can be constructed from another if there exists a directed path in the quiver from the starting object to the target object, adhering to the direction and operations specified along the path. This reachability is essential for understanding the sequential construction of objects and assessing their complexity through the minimal number of steps required in their assembly, as reflected by their PA indices.</p><p><strong>Application and Implications</strong></p><p>The application of Pathway Assembly to the search for biosignatures and technosignatures is particularly intriguing. By analyzing objects with high PA found in significant abundance, scientists can discern patterns indicating deliberate production rather than random generation. This approach is valuable in astrobiology and the search for extraterrestrial intelligence, where distinguishing between naturally occurring and intelligently produced structures can be challenging.</p><p>Furthermore, the formalism of Pathway Assembly and its integration into a broader measure of Pathway Information allow for a refined analysis of how complex systems evolve and are constructed, whether in nature or technology. This methodology not only enhances our understanding of life's underlying processes but also provides a framework for exploring the evolution of technology as an extension of biological development.</p><p>In summary, Pathway Assembly offers a sophisticated tool for exploring the assembly and evolution of complex systems, bridging biological origins and technological advancements, and providing a structured approach to identifying signs of life and intelligent processes in the universe.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" height="24" viewBox="0 0 24 24" 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1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-10" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21ab2-30ad-49c8-a8b3-d07193dfb172" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">calculated the probability of the most likely pathway to assess the impact of the bias. In
the case of zero bias, at assembly index 25, the integer generated along the most probable
pathway will be found has approximately 10−7 probability of being formed. Increasing the bias
to the maximum level ℎ = 5, the integer generated along the most probable pathway at
assembly index 25 will appear approximately 12% of the time, see Figure 5.
10
Figure 5: Left – Minimal addition chains modelled as a decision tree. Right – probability of
the most likely pathway at different levels of bias.
These probabilities will reduce further when considering greater number of choices, such as in
situations of higher dimensionality, like strings, grid structures, and graphs (see “Example
Applications” section below). In the maximum bias case explored here, where ℎ = 5, the
choices with ������������ = 5 will be 10,000 times more likely than those with ������������ = 1. This argument
demonstrates that using a pathway assembly model will result in a threshold above which it is
unlikely that any specific object would be found, with the threshold depending on the system
of objects and joining operations, and the physical limits of the inherent biases present in the
process. Even in a significantly biased system, such a threshold will exist, and any objects
found in abundance with PA above the threshold will require some process inducing specificity
outside of the random (bias) model to form. We consider these additional processes to be
biological. Exploration of the processes and biases of a specific system can then be used, along
with experimental data, to determine this threshold.
In addition to using the assembly index to determine this biological threshold, it is useful to
consider an information measure based on the number of possible structures that can be created
using assembly pathways, see Figure 6. One way to do this is to consider a bounded set of
possible structures ������������ , and then the subset of possible structures with a specified pathway
assembly index, ������������ ������������ ������������ . The "pathway information" is the amount of uncertainty the pathway
assembly index reduces beyond what knowledge of only the size or general composition can
provide. In this case, using the approach of Shannon Information (14), the information provided
by the Pathway Assembly index, ������������������������ ������������, is given by: ������������������������ ������������= ������������ ������������ ������������
|������������ |
|������������ ������������ ������������ |
Figure 6: Pathway Information. The precise definitions of ������������ and ������������ ������������ ������������ will depend on the
specific implementation.
It should be noted that this information measure provides a way of formalizing information
over states (size, composition) and over paths (PA) within a common mathematical framework.
To calculate IPA, there are several possible choices for ������������ , all of which must be finite. In one
option, for an end product with ������������ ������������ = ������������ , N is the set of objects possible that can be created from
the same irreducible parts within ������������ steps regardless of PA, and NPA is the subset of those objects
with the precise pathway assembly index ������������ ������������ = ������������ . This then gives us a measure of the
information provided by learning the assembly index, within the context of all objects that
could be created by traversing that distance in the assembly space. The difference in utility
between the Pathway Assembly index and the pathway information, is that the Assembly Index
provides a simple threshold based on pathway length, whereas pathway information can<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-11" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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20.0378 8.25334 20.2638 8.36823 20.4629C8.48312 20.6619 8.64893 20.8267 8.84863 20.9404L18.5723 26.5542L15.206 28.4979C15.1894 28.5089 15.1703 28.5155 15.1505 28.5173C15.1307 28.5191 15.1107 28.516 15.0924 28.5082L7.04046 23.8557C5.32135 22.8601 4.06716 21.2235 3.55289 19.3046C3.03862 17.3858 3.30624 15.3413 4.29707 13.6194ZM31.955 20.0556L22.2312 14.4411L25.5976 12.4981C25.6142 12.4872 25.6333 12.4805 25.6531 12.4787C25.6729 12.4769 25.6928 12.4801 25.7111 12.4879L33.7631 17.1364C34.9967 17.849 36.0017 18.8982 36.6606 20.1613C37.3194 21.4244 37.6047 22.849 37.4832 24.2684C37.3617 25.6878 36.8382 27.0432 35.9743 28.1759C35.1103 29.3086 33.9415 30.1717 32.6047 30.6641C32.6047 30.5947 32.6047 30.4733 32.6047 30.3889V21.188C32.6066 20.9586 32.5474 20.7328 32.4332 20.5338C32.319 20.3348 32.154 20.1698 31.955 20.0556ZM35.3055 15.0128C35.2464 14.9765 35.1431 14.9142 35.069 14.8717L27.1045 10.2712C26.906 10.1554 26.6803 10.0943 26.4504 10.0943C26.2206 10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="96995dfc-f11d-420c-b4b3-34130bc9f162" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>offer deeper insights into the complexity and specificity of assembly processes by evaluating how much additional information is provided by knowing the pathway assembly index beyond basic structural attributes.</p><p><strong>Delving into Pathway Information (IPA)</strong></p><p>The concept of Pathway Information (IPA) you described is a refined measure that builds on the basic structure of the Pathway Assembly (PA) index. IPA quantifies the additional knowledge gained about an object's complexity and formation process by considering the specific pathways by which the object can be assembled, rather than just its composition or size. This information metric is particularly useful because it encapsulates the uncertainty reduction provided by knowing an object’s assembly pathway, which cannot be gleaned from more general attributes.</p><p>IPA is calculated using a formula similar to that in Shannon Information Theory. The formula considers the total number of possible structures <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6833em;"></span><span class="mord mathnormal" style="margin-right: 0.10903em;">N</span></span></span></span> that can be constructed within a given number of steps and the subset <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mrow><mi>P</mi><mi>A</mi></mrow></msub></mrow><annotation encoding="application/x-tex">N_{PA}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.8333em; vertical-align: -0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right: 0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.3283em;"><span style="top: -2.55em; margin-left: -0.109em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right: 0.13889em;">P</span><span class="mord mathnormal mtight">A</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span></span></span></span></span></span></span></span></span></span> of these structures that have a specific pathway assembly index <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>A</mi></mrow><annotation encoding="application/x-tex">PA</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6833em;"></span><span class="mord mathnormal" style="margin-right: 0.13889em;">P</span><span class="mord mathnormal">A</span></span></span></span>. This differentiation helps in understanding how unique or constrained an assembly process is compared to all possible assembly processes that could be performed under the same conditions:</p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mi>P</mi><mi>A</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">∣</mi><mi>N</mi><mi mathvariant="normal">∣</mi></mrow><mrow><mi mathvariant="normal">∣</mi><msub><mi>N</mi><mrow><mi>P</mi><mi>A</mi></mrow></msub><mi mathvariant="normal">∣</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">IPA = \frac{|N|}{|N_{PA}|}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6833em;"></span><span class="mord mathnormal" style="margin-right: 0.07847em;">I</span><span class="mord mathnormal" style="margin-right: 0.13889em;">P</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.2778em;"></span></span><span class="base"><span class="strut" style="height: 1.53em; vertical-align: -0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.01em;"><span style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∣</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right: 0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.3448em;"><span style="top: -2.3567em; margin-left: -0.109em; margin-right: 0.0714em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right: 0.13889em;">P</span><span class="mord mathnormal mtight">A</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.1433em;"><span></span></span></span></span></span></span><span class="mord mtight">∣</span></span></span></span><span style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span style="top: -3.485em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∣</span><span class="mord mathnormal mtight" style="margin-right: 0.10903em;">N</span><span class="mord mtight">∣</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p><p>This ratio highlights how the knowledge of the specific PA reduces the overall uncertainty or entropy concerning how the object could be assembled.</p><p><strong>Applications and Implications</strong></p><p>The practical application of IPA and PA in systems of varying dimensionality, such as strings, grid structures, and graphs, is crucial for several fields. In astrobiology, for example, determining whether complex molecular structures on other planets are the result of biological processes involves comparing the complexity of these structures against what can be randomly expected given the environment's biases.</p><p>In technology and evolutionary biology, understanding how complex artifacts or biological structures evolve from simpler precursors can shed light on both the history and potential future developments of these systems. By establishing a threshold PA value above which the presence of biological or intentional technological processes is necessary, researchers can more effectively identify and study phenomena that are not merely the product of random or chaotic systems but require a directed, complex series of actions to emerge.</p><p><strong>Thresholds and Biases</strong></p><p>The impact of biases in the system is particularly noteworthy. As demonstrated in your description, even with maximum bias (where certain pathways are exponentially more likely), a threshold still exists where beyond this point, the presence of complex objects almost certainly implies some form of directed, non-random influence. This threshold concept is instrumental in distinguishing between naturally occurring objects and those resulting from specific evolutionary or technological processes.</p><p>In conclusion, the development and application of PA and IPA provide a sophisticated framework for quantifying the complexity and directedness of pathways in natural and technological systems. By extending our understanding of these indices, scientists can better explore the origins and mechanisms of complex systems, potentially leading to significant advances in both theoretical and applied sciences.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11 4.9099C11 4.47485 10.4828 4.24734 10.1621 4.54132L6.67572 7.7372C6.49129 7.90626 6.25019 8.00005 6 8.00005H4C3.44772 8.00005 3 8.44776 3 9.00005V15C3 15.5523 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13.1902V5C15.0045 4.44772 14.5568 4 14.0045 4ZM17.0045 13V5C17.0045 4.64937 16.9444 4.31278 16.8338 4H18.0045C18.5568 4 19.0045 4.44772 19.0045 5V12C19.0045 12.5523 18.5568 13 18.0045 13H17.0045Z" fill="currentColor"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r5r:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 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lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-12" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21bc5-66fe-4cfa-be7b-a25a95ef6ec0" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">Could you give some everyday examples?<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-13" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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20.0378 8.25334 20.2638 8.36823 20.4629C8.48312 20.6619 8.64893 20.8267 8.84863 20.9404L18.5723 26.5542L15.206 28.4979C15.1894 28.5089 15.1703 28.5155 15.1505 28.5173C15.1307 28.5191 15.1107 28.516 15.0924 28.5082L7.04046 23.8557C5.32135 22.8601 4.06716 21.2235 3.55289 19.3046C3.03862 17.3858 3.30624 15.3413 4.29707 13.6194ZM31.955 20.0556L22.2312 14.4411L25.5976 12.4981C25.6142 12.4872 25.6333 12.4805 25.6531 12.4787C25.6729 12.4769 25.6928 12.4801 25.7111 12.4879L33.7631 17.1364C34.9967 17.849 36.0017 18.8982 36.6606 20.1613C37.3194 21.4244 37.6047 22.849 37.4832 24.2684C37.3617 25.6878 36.8382 27.0432 35.9743 28.1759C35.1103 29.3086 33.9415 30.1717 32.6047 30.6641C32.6047 30.5947 32.6047 30.4733 32.6047 30.3889V21.188C32.6066 20.9586 32.5474 20.7328 32.4332 20.5338C32.319 20.3348 32.154 20.1698 31.955 20.0556ZM35.3055 15.0128C35.2464 14.9765 35.1431 14.9142 35.069 14.8717L27.1045 10.2712C26.906 10.1554 26.6803 10.0943 26.4504 10.0943C26.2206 10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="f33665b8-e7af-4d5c-8595-b10c08af5147" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Certainly! Let's explore some everyday examples that illustrate the concepts of the Pathway Assembly (PA) index and Pathway Information (IPA) in a more relatable context:</p><ol><li><p><strong>Building a LEGO Model</strong>:</p><ul><li><strong>PA Index</strong>: When constructing a LEGO model, the PA would represent the minimum number of steps needed to assemble the model from individual LEGO bricks. For a simple model like a small car, the PA might be relatively low, while for a complex model like a replica of the Star Wars Millennium Falcon, the PA would be much higher due to the greater complexity and number of pieces involved.</li><li><strong>IPA</strong>: Knowing the exact sequence of assembly (PA) for the Millennium Falcon reduces the uncertainty compared to just knowing it's made from LEGO bricks. The IPA gives us a measure of how much more we know about the assembly by knowing the specific steps rather than just knowing the final size or the types of bricks used.</li></ul></li><li><p><strong>Cooking a Recipe</strong>:</p><ul><li><strong>PA Index</strong>: Consider making a complex dish like Beef Wellington versus a simple salad. The PA for Beef Wellington would be high because it requires precise assembly of pastry, meat, and seasoning layers, along with specific cooking steps. A salad, in contrast, has a low PA because it involves fewer and simpler preparation steps.</li><li><strong>IPA</strong>: For Beef Wellington, knowing the exact sequence of preparation and cooking steps significantly reduces the uncertainty in how the dish is made, compared to just knowing the ingredients. This is the additional information gained, which is quantified by the IPA.</li></ul></li><li><p><strong>Assembling Furniture</strong>:</p><ul><li><strong>PA Index</strong>: Flat-pack furniture assembly can range from simple (like assembling a stool) to complex (like assembling an entire kitchen). The PA for a kitchen set is higher because it involves more parts and steps.</li><li><strong>IPA</strong>: The instruction manual for assembling a kitchen provides a specific sequence of steps. Knowing these steps through the manual significantly narrows down the possibilities of assembly, unlike when you only know what pieces are included in the box.</li></ul></li><li><p><strong>Creating Artwork</strong>:</p><ul><li><strong>PA Index</strong>: The PA for creating a detailed oil painting is much higher than that for drawing a stick figure with a pencil. The oil painting requires multiple layers, colors, techniques, and steps, each adding to the complexity of the assembly process.</li><li><strong>IPA</strong>: The pathway information in painting could include knowledge about specific techniques (like glazing or impasto) that define how the final artwork is achieved, which is not obvious just from seeing the used colors and canvas size.</li></ul></li><li><p><strong>Software Development</strong>:</p><ul><li><strong>PA Index</strong>: Developing a complex software application involves many steps—from writing individual lines of code to integrating various software modules. The PA would be high for a full-fledged commercial software compared to a simple script.</li><li><strong>IPA</strong>: Detailed documentation of the software's architecture and the development process can significantly clarify how the software is built, much more than knowing just the programming languages used or the final software size.</li></ul></li></ol><p>These examples help illustrate how PA and IPA can be applied to everyday scenarios, highlighting the differences in complexity and the importance of specific assembly pathways in various contexts.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] 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viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-14" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21141-e105-4d1b-a2cf-e561d2e5a387" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">So can you make an argument for eating plankton and algae over higher animals using assembly index?<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 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37.3223 31.4556 35.5506 32.1119 33.5179C33.5027 33.2332 34.8167 32.6547 35.9659 31.821C37.115 30.9874 38.0728 29.9178 38.7752 28.684C39.8458 26.8371 40.3023 24.6979 40.0789 22.5748C39.8556 20.4517 38.9639 18.4544 37.5324 16.8707ZM22.4978 37.8849C20.7443 37.8874 19.0459 37.2733 17.6994 36.1501C17.7601 36.117 17.8666 36.0586 17.936 36.0161L25.9004 31.4156C26.1003 31.3019 26.2663 31.137 26.3813 30.9378C26.4964 30.7386 26.5563 30.5124 26.5549 30.2825V19.0542L29.9213 20.998C29.9389 21.0068 29.9541 21.0198 29.9656 21.0359C29.977 21.052 29.9842 21.0707 29.9867 21.0902V30.3889C29.9842 32.375 29.1946 34.2791 27.7909 35.6841C26.3872 37.0892 24.4838 37.8806 22.4978 37.8849ZM6.39227 31.0064C5.51397 29.4888 5.19742 27.7107 5.49804 25.9832C5.55718 26.0187 5.66048 26.0818 5.73461 26.1244L13.699 30.7248C13.8975 30.8408 14.1233 30.902 14.3532 30.902C14.583 30.902 14.8088 30.8408 15.0073 30.7248L24.731 25.1103V28.9979C24.7321 29.0177 24.7283 29.0376 24.7199 29.0556C24.7115 29.0736 24.6988 29.0893 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20.9586 32.5474 20.7328 32.4332 20.5338C32.319 20.3348 32.154 20.1698 31.955 20.0556ZM35.3055 15.0128C35.2464 14.9765 35.1431 14.9142 35.069 14.8717L27.1045 10.2712C26.906 10.1554 26.6803 10.0943 26.4504 10.0943C26.2206 10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="82e544e1-0059-4608-9328-3ba78237649f" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Absolutely, let’s explore the argument for consuming plankton and algae over higher animals using the concept of the Pathway Assembly (PA) index:</p><h3>Simplicity in the Assembly Index</h3><p><strong>1. Lower PA of Plankton and Algae:</strong></p><ul><li><strong>Simplicity</strong>: Plankton and algae have simpler biological structures compared to higher animals. This simplicity could be reflected in a lower PA, as these organisms require fewer biological processes for their growth and reproduction. For example, many types of algae and phytoplankton perform photosynthesis, which is a direct and efficient way to convert sunlight into energy, involving relatively straightforward chemical pathways.</li></ul><p><strong>2. Higher PA of Higher Animals:</strong></p><ul><li><strong>Complexity</strong>: Higher animals, such as mammals, birds, and fish, exhibit complex physiological structures and systems, including circulatory systems, complex organs, and intricate reproductive methods. The assembly of these organisms from a biological standpoint involves numerous developmental stages, each adding complexity and increasing the PA.</li></ul><h3>Energy and Resource Efficiency</h3><p><strong>3. Efficient Resource Use:</strong></p><ul><li><strong>Lower Trophic Level</strong>: Algae and plankton are at the base of the food chain. Consuming food sources lower on the trophic scale is generally more energy-efficient, as less energy is lost in biological processes that occur at each successive trophic level. Higher animals require more resources and energy inputs, which are consumed in maintaining their complex bodies and ecological interactions.</li></ul><p><strong>4. Biomass Conversion Efficiency:</strong></p><ul><li><strong>Direct Consumption</strong>: Directly consuming plankton and algae skips energy levels that would otherwise be used up by higher trophic levels. This is akin to a shorter PA, where fewer steps mean less energy and fewer resources are required to produce a consumable output. Higher animals convert only a small percentage of their plant-based or lower-trophic-level food into body mass, the rest being expended.</li></ul><h3>Environmental Impact</h3><p><strong>5. Sustainability:</strong></p><ul><li><strong>Lower Environmental Footprint</strong>: Cultivating or harvesting algae and plankton typically requires less space, water, and does not involve rearing with complex feed or extensive farming infrastructure. This contrasts sharply with the higher environmental costs associated with livestock farming, such as methane emissions, use of antibiotics, and habitat destruction.</li></ul><p><strong>6. Scalability and Potential for Innovation:</strong></p><ul><li><strong>Cultivation Technology</strong>: Technological innovations in the cultivation of algae and plankton (like controlled bioreactors for algae that capture carbon dioxide) can further reduce the PA by streamlining the process. In contrast, innovations in animal farming often aim to manage inherent complexities, rarely reducing the fundamental biological PA.</li></ul><h3>Nutritional Arguments</h3><p><strong>7. Nutrient Density:</strong></p><ul><li><strong>Rich in Essential Nutrients</strong>: Algae, like spirulina and chlorella, are high in proteins, vitamins, and essential fatty acids, yet require significantly less input in terms of energy and resources to grow compared to producing equivalent nutrients from animal sources.</li></ul><p>Using the concept of the PA index as a metaphor for resource and energy use, ecological impact, and nutritional output offers a compelling argument for favoring the consumption of simpler, lower-trophic organisms like plankton and algae over more complex higher animals. This approach promotes a sustainable, efficient, and potentially more adaptable dietary practice that aligns with principles of conservation and environmental responsibility.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11 4.9099C11 4.47485 10.4828 4.24734 10.1621 4.54132L6.67572 7.7372C6.49129 7.90626 6.25019 8.00005 6 8.00005H4C3.44772 8.00005 3 8.44776 3 9.00005V15C3 15.5523 3.44772 16 4 16H6C6.25019 16 6.49129 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6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-16" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21414-516e-42a5-8062-3581fe72e9c9" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">It's kind of curious that whales have discovered this technique<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-17" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 25.8215 3.85078C24.8796 2.7893 23.7219 1.94125 22.4257 1.36341C21.1295 0.785575 19.7249 0.491269 18.3058 0.500197C16.1708 0.495044 14.0893 1.16803 12.3614 2.42214C10.6335 3.67624 9.34853 5.44666 8.6917 7.47815C7.30085 7.76286 5.98686 8.3414 4.8377 9.17505C3.68854 10.0087 2.73073 11.0782 2.02839 12.312C0.956464 14.1591 0.498905 16.2988 0.721698 18.4228C0.944492 20.5467 1.83612 22.5449 3.268 24.1293C2.81966 25.4759 2.66413 26.9026 2.81182 28.3141C2.95951 29.7256 3.40701 31.0892 4.12437 32.3138C5.18791 34.1659 6.8123 35.6322 8.76321 36.5013C10.7141 37.3704 12.8907 37.5973 14.9789 37.1492C15.9208 38.2107 17.0786 39.0587 18.3747 39.6366C19.6709 40.2144 21.0755 40.5087 22.4946 40.4998C24.6307 40.5054 26.7133 39.8321 28.4418 38.5772C30.1704 37.3223 31.4556 35.5506 32.1119 33.5179C33.5027 33.2332 34.8167 32.6547 35.9659 31.821C37.115 30.9874 38.0728 29.9178 38.7752 28.684C39.8458 26.8371 40.3023 24.6979 40.0789 22.5748C39.8556 20.4517 38.9639 18.4544 37.5324 16.8707ZM22.4978 37.8849C20.7443 37.8874 19.0459 37.2733 17.6994 36.1501C17.7601 36.117 17.8666 36.0586 17.936 36.0161L25.9004 31.4156C26.1003 31.3019 26.2663 31.137 26.3813 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28.5155 15.1505 28.5173C15.1307 28.5191 15.1107 28.516 15.0924 28.5082L7.04046 23.8557C5.32135 22.8601 4.06716 21.2235 3.55289 19.3046C3.03862 17.3858 3.30624 15.3413 4.29707 13.6194ZM31.955 20.0556L22.2312 14.4411L25.5976 12.4981C25.6142 12.4872 25.6333 12.4805 25.6531 12.4787C25.6729 12.4769 25.6928 12.4801 25.7111 12.4879L33.7631 17.1364C34.9967 17.849 36.0017 18.8982 36.6606 20.1613C37.3194 21.4244 37.6047 22.849 37.4832 24.2684C37.3617 25.6878 36.8382 27.0432 35.9743 28.1759C35.1103 29.3086 33.9415 30.1717 32.6047 30.6641C32.6047 30.5947 32.6047 30.4733 32.6047 30.3889V21.188C32.6066 20.9586 32.5474 20.7328 32.4332 20.5338C32.319 20.3348 32.154 20.1698 31.955 20.0556ZM35.3055 15.0128C35.2464 14.9765 35.1431 14.9142 35.069 14.8717L27.1045 10.2712C26.906 10.1554 26.6803 10.0943 26.4504 10.0943C26.2206 10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="3002c26b-2e55-4155-9dbb-f00ed25c639e" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Indeed, it's fascinating that some of the largest creatures on Earth, such as baleen whales, utilize a feeding strategy that involves consuming plankton and small aquatic organisms. This method is not only effective but also showcases an evolutionary adaptation that aligns with principles of energy efficiency and sustainability, much like the arguments for human consumption of lower trophic level organisms like algae and plankton.</p><h3>Evolutionary Efficiency</h3><p><strong>1. <strong>Energy Conservation</strong>:</strong> Baleen whales, including species like the blue whale and humpback whale, have evolved a feeding mechanism that allows them to intake vast quantities of water rich in plankton, krill, and small fish. They then filter this intake through their baleen plates, which act like a sieve. This method is highly energy-efficient, as it allows them to consume millions of tiny organisms in one gulp, maximizing their caloric intake per effort expended.</p><p><strong>2. <strong>Low Trophic Level Feeding</strong>:</strong> By feeding at a low trophic level, whales can access a vast, renewable source of nutrition. Plankton blooms are abundant and can regenerate quickly, making them a reliable food source. This is more sustainable compared to predators that rely on larger, longer-lived species that are lower in abundance and reproduce more slowly.</p><h3>Ecological Impact</h3><p><strong>3. <strong>Ecosystem Services</strong>:</strong> The feeding habits of baleen whales have significant ecological impacts beyond just their survival. Their consumption of plankton and subsequent movements through the water columns help to mix ocean layers, bringing nutrients from the deep to the surface. This nutrient cycling supports marine productivity and can even impact global carbon cycling, as their fecal plumes help sequester carbon to the ocean floor.</p><p><strong>4. <strong>Biomass Control</strong>:</strong> By consuming large amounts of plankton, whales help regulate the populations of these organisms. This has a cascading effect on marine ecosystems, helping to maintain balance within the food web.</p><h3>Adaptation and Survival</h3><p><strong>5. <strong>Specialized Adaptations</strong>:</strong> The anatomical and physiological adaptations of baleen whales for filter-feeding are remarkable. Their baleen plates, which are made of keratin (the same material as human fingernails), have evolved to filter small organisms efficiently while allowing water to flow back out of their mouths. This adaptation highlights a sophisticated evolutionary response to the availability of plankton as a primary food source.</p><p><strong>6. <strong>Survival Strategy</strong>:</strong> The sheer size of baleen whales is supported by their feeding strategy. Consuming lower trophic level organisms in large quantities allows them to meet the energy demands of their massive bodies, which would be much more challenging if they were reliant on scarcer, larger prey.</p><p>Whales have essentially capitalized on a high-volume, low-effort feeding strategy that is remarkably efficient and sustainable over evolutionary timescales. This strategy not only ensures their survival and reproductive success but also demonstrates an intrinsic understanding of ecological efficiency that humans are only beginning to appreciate and emulate in sustainable practices.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11 4.9099C11 4.47485 10.4828 4.24734 10.1621 4.54132L6.67572 7.7372C6.49129 7.90626 6.25019 8.00005 6 8.00005H4C3.44772 8.00005 3 8.44776 3 9.00005V15C3 15.5523 3.44772 16 4 16H6C6.25019 16 6.49129 16.0938 6.67572 16.2629L10.1621 19.4588C10.4828 19.7527 11 19.5252 11 19.0902V4.9099ZM8.81069 3.06701C10.4142 1.59714 13 2.73463 13 4.9099V19.0902C13 21.2655 10.4142 22.403 8.81069 20.9331L5.61102 18H4C2.34315 18 1 16.6569 1 15V9.00005C1 7.34319 2.34315 6.00005 4 6.00005H5.61102L8.81069 3.06701ZM20.3166 6.35665C20.8019 6.09313 21.409 6.27296 21.6725 6.75833C22.5191 8.3176 22.9996 10.1042 22.9996 12.0001C22.9996 13.8507 22.5418 15.5974 21.7323 17.1302C21.4744 17.6185 20.8695 17.8054 20.3811 17.5475C19.8927 17.2896 19.7059 16.6846 19.9638 16.1962C20.6249 14.9444 20.9996 13.5175 20.9996 12.0001C20.9996 10.4458 20.6064 8.98627 19.9149 7.71262C19.6514 7.22726 19.8312 6.62017 20.3166 6.35665ZM15.7994 7.90049C16.241 7.5688 16.8679 7.65789 17.1995 8.09947C18.0156 9.18593 18.4996 10.5379 18.4996 12.0001C18.4996 13.3127 18.1094 14.5372 17.4385 15.5604C17.1357 16.0222 16.5158 16.1511 16.0539 15.8483C15.5921 15.5455 15.4632 14.9255 15.766 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13.1902V5C15.0045 4.44772 14.5568 4 14.0045 4ZM17.0045 13V5C17.0045 4.64937 16.9444 4.31278 16.8338 4H18.0045C18.5568 4 19.0045 4.44772 19.0045 5V12C19.0045 12.5523 18.5568 13 18.0045 13H17.0045Z" fill="currentColor"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r6g:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-18" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21168-c8f5-4766-81a0-a9cc3e788c22" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">So humans can make protein directly from air, but I think that there is an argument to also include all plants, since and deconstructing them using giant centrifuges (centrifugal <div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" 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20.0556ZM35.3055 15.0128C35.2464 14.9765 35.1431 14.9142 35.069 14.8717L27.1045 10.2712C26.906 10.1554 26.6803 10.0943 26.4504 10.0943C26.2206 10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="7026a2e6-5c39-4ec9-8c11-3935f45afb49" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Your idea touches on some fascinating concepts at the intersection of innovative technology and sustainability. The concept of creating protein directly from air, known as air protein or microbial protein synthesis, involves using carbon capture to feed microorganisms that can produce protein. This process is highly efficient in terms of space and resources and represents a leap towards sustainable food production.</p><p>Including plants in this innovative cycle and using mechanical processes like centrifugal force for their deconstruction could further enhance the efficiency of resource use and potentially increase the yield and accessibility of plant-based nutrients. Here’s how this might work and the benefits it could bring:</p><h3><strong>Integration of Plant Biomass with Innovative Technologies</strong></h3><p><strong>1. <strong>Efficient Resource Utilization</strong>:</strong> By integrating plants into these cycles, we can harness the entire plant biomass more effectively. Traditional agriculture and food production often involve significant waste, whether during harvesting, transport, or processing. Using centrifugal technology to deconstruct plant materials could help in breaking down cellulose and other complex compounds more efficiently, leading to better extraction and utilization of nutritional components such as proteins, vitamins, and essential minerals.</p><p><strong>2. <strong>Enhanced Processing Techniques</strong>:</strong> The use of centrifugal forces can aid in the separation of different plant components at high speeds, allowing for the isolation of high-value ingredients like fibers, oils, and proteins. This can be particularly useful in creating more refined and nutrient-dense food products, minimizing waste and maximizing output from the same amount of raw plant material.</p><h3><strong>Sustainability and Environmental Impact</strong></h3><p><strong>3. <strong>Reduction in Chemical Use</strong>:</strong> Conventional processing of plants often requires chemicals for extraction and refinement. Mechanical processes like using centrifuges might reduce the need for such chemicals, thus lowering the environmental impact of plant processing.</p><p><strong>4. <strong>Lower Energy Consumption</strong>:</strong> If the energy used in the centrifugal process can be sourced from renewable energy, the overall carbon footprint of plant processing could be significantly reduced compared to more energy-intensive methods like thermal treatments or extensive chemical processing.</p><h3><strong>Broader Implications for Food Security</strong></h3><p><strong>5. <strong>Diversifying Protein Sources</strong>:</strong> Combining air protein technologies with enhanced plant processing methods can help diversify the protein sources available for human consumption. This diversification can make our food supply more resilient to shocks like climate change, pandemics, and economic disruptions.</p><p><strong>6. <strong>Addressing Nutritional Deficiencies</strong>:</strong> Improved processing techniques can increase the availability of plant-based nutrients that are essential for human health but are often less accessible in diets that rely heavily on staple grains and meats. This could help combat global nutritional deficiencies in vitamins and minerals.</p><h3><strong>Scalability and Practical Challenges</strong></h3><p><strong>7. <strong>Technological and Economic Challenges</strong>:</strong> While the concept is promising, scaling up such technologies to a global level will require substantial investment in research and development, as well as infrastructure overhaul. There will also be challenges related to the economic viability, acceptance, and regulatory compliance of such technologies.</p><p><strong>8. <strong>Integration with Existing Agricultural Practices</strong>:</strong> To implement these technologies effectively, they would need to be integrated into existing agricultural and food production systems in a way that complements traditional practices and enhances overall productivity without displacing the workforce.</p><p>By advancing these technologies and integrating them thoughtfully into our food systems, there is potential to significantly enhance the efficiency of food production and make a positive impact on food security and sustainability. The argument for including plants in these innovative cycles is strong, especially when considering the urgent need to address the environmental impact of our current food production and consumption patterns.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md-heavy"><path fill-rule="evenodd" clip-rule="evenodd" d="M11 4.9099C11 4.47485 10.4828 4.24734 10.1621 4.54132L6.67572 7.7372C6.49129 7.90626 6.25019 8.00005 6 8.00005H4C3.44772 8.00005 3 8.44776 3 9.00005V15C3 15.5523 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lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-20" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb219ca-75be-4ab4-a197-a55954c8f6ce" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">Sorry I was trying to say Centrifugal Kelp Baleen filtration (to separate material for starch, protein, oil, building materials, with excess being used for hydrothermal liquefaction (hydrous pyrolysis) or further processes with yogurt vat arrays.<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 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10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="4ac70c0b-c758-469c-9cfb-be58c4574fc3" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Ah, got it! The idea of using centrifugal force to mimic baleen whale filtration for processing kelp and similar biomaterials is quite innovative and aligns well with principles of biomimicry—where human engineering is inspired by natural processes. The method you're suggesting, which we could call "Centrifugal Kelp Baleen Filtration," can efficiently separate kelp into useful components such as starch, protein, and oil, while the excess could be utilized in other processes like hydrothermal liquefaction or integrated into yogurt vat arrays for additional bioprocessing. Here’s how this system might work and the potential benefits:</p><h3><strong>System Overview</strong></h3><ol><li><p><strong>Centrifugal Baleen Filtration</strong>: Kelp, harvested from marine environments, would be processed using a system that emulates the filter feeding mechanism of baleen whales. A centrifugal force would be applied to the kelp slurry, rapidly separating components based on their size and density. Solids like cellulose could be filtered out for use in building materials, while more soluble components like starch, proteins, and oils are collected separately.</p></li><li><p><strong>Component Utilization</strong>:</p><ul><li><strong>Starch and Protein</strong>: These could be used directly in food production or as feed in aquaculture systems.</li><li><strong>Oil Extraction</strong>: Oils extracted from kelp can be used in the production of biofuels or as a base for biochemical products.</li><li><strong>Building Materials</strong>: The structural components of kelp, like cellulose, could be processed into biodegradable plastics, composites, or even used directly in construction.</li></ul></li><li><p><strong>Excess Biomass Handling</strong>:</p><ul><li><strong>Hydrothermal Liquefaction</strong>: Excess materials not suitable for direct use could be subjected to hydrous pyrolysis, transforming this biomass into bio-crude oil, further enhancing the sustainability of this process.</li><li><strong>Yogurt Vat Arrays</strong>: Fermentation processes could be applied to further break down the biomass, potentially creating products like biogas, specialty chemicals, or even probiotic-rich foods.</li></ul></li></ol><h3><strong>Potential Benefits</strong></h3><ul><li><p><strong>Sustainability</strong>: This method leverages renewable marine biomass, which does not require freshwater or arable land, presenting a significant environmental advantage over traditional crop-based resources.</p></li><li><p><strong>Efficiency</strong>: Mimicking natural systems such as the baleen filters of whales can offer a highly efficient method of biomass processing, potentially reducing energy use and increasing yield.</p></li><li><p><strong>Versatility</strong>: The variety of output products makes this approach extremely versatile, with potential applications in food, energy, and materials industries.</p></li><li><p><strong>Circular Economy</strong>: By utilizing nearly every part of the kelp, this system promotes a circular economy where waste is minimized, and the value of raw materials is maximized.</p></li></ul><h3><strong>Challenges and Considerations</strong></h3><ul><li><p><strong>Technological Complexity</strong>: The design and scaling of such a sophisticated system pose significant challenges. The centrifugal baleen filtration system would need to be meticulously designed to handle the specific properties of kelp and other similar biomasses.</p></li><li><p><strong>Economic Viability</strong>: Initial costs for research, development, and deployment could be high, and establishing a market for the diverse range of products might take time.</p></li><li><p><strong>Regulatory and Environmental Concerns</strong>: Sustainable and responsible harvesting of kelp must be ensured to prevent ecological imbalance. Additionally, regulatory approval would be necessary for new food and material products.</p></li><li><p><strong>Integration into Existing Systems</strong>: For maximum impact, this system would need to be integrated into existing agricultural and industrial systems, potentially requiring significant changes to current processes.</p></li></ul><p>By developing and implementing such innovative technologies, we can take inspiration from nature to create more sustainable and efficient production systems, reflecting a significant step forward in how we think about and utilize biological resources.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span 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10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="b601ecfc-01c0-4f86-83d8-9d65bbf528ff" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The concept of using Centrifugal Kelp Baleen Filtration for efficient biomass processing connects well with the previous discussions about the Pathway Assembly (PA) index, sustainable food sources like plankton and algae, and the evolutionary adaptations of baleen whales. Here’s how these topics interlink:</p><h3><strong>Pathway Assembly (PA) Index and Efficient Biomass Processing</strong></h3><p>The design of a centrifugal system to mimic baleen filtration aligns with the concept of reducing the Pathway Assembly (PA) index for biomass processing:</p><ul><li><strong>Efficiency and Complexity</strong>: Just as lower PA indices suggest simpler, more direct pathways for constructing objects, the proposed centrifugal system aims to streamline the process of separating kelp into usable components, effectively reducing the complexity and steps involved compared to traditional methods.</li><li><strong>Sustainability</strong>: The system's design to utilize almost all parts of the kelp mirrors the principles of reducing waste and increasing efficiency, core tenets of lowering the PA in production systems.</li></ul><h3><strong>Sustainable Food Sources and Marine Biomass</strong></h3><p>The discussion about the advantages of consuming lower trophic level organisms like plankton and algae parallels the use of kelp in sustainable production systems:</p><ul><li><strong>Low Trophic Level Utilization</strong>: Kelp, like plankton and algae, is a lower trophic level organism. Its use in biomass processing systems not only emphasizes energy efficiency but also underscores the sustainability of sourcing food and materials from lower on the food chain.</li><li><strong>Resource Efficiency</strong>: Utilizing kelp efficiently showcases how biomimicry (inspired by whale feeding mechanisms) can enhance our ability to sustainably harness biological resources, providing a broad range of products from a single input source.</li></ul><h3><strong>Whale Feeding Mechanisms and Technological Innovation</strong></h3><p>The adaptation of baleen whale feeding mechanisms into a technological solution offers a direct link to evolutionary biology and the innovative use of natural systems:</p><ul><li><strong>Biomimicry</strong>: The centrifugal filtration system directly mimics the natural filtering process of baleen whales, an evolutionary adaptation that allows these massive creatures to efficiently consume vast quantities of small organisms. This biological inspiration is applied to create a similarly efficient process for kelp.</li><li><strong>Ecological Impact</strong>: Just as whales play a crucial role in their ecosystems, the proposed system could significantly impact how we manage biomass, potentially leading to more sustainable industrial ecosystems that mimic natural processes.</li></ul><h3><strong>Overall System Integration</strong></h3><p>Integrating this biomimetic approach into broader systems of production and waste management reflects the growing trend towards sustainability and the circular economy, where waste is minimized, and the lifecycle of materials is extended:</p><ul><li><strong>Circular Economy</strong>: The use of all extracted components of kelp and the transformation of excess into energy or other products illustrates principles of the circular economy, much like the efficient energy use seen in lower trophic level consumption by whales.</li><li><strong>Innovation and Sustainability</strong>: The innovative application of natural principles to industrial processes shows how understanding and applying biological and ecological insights can lead to more sustainable technological solutions, reducing our environmental footprint while enhancing resource use efficiency.</li></ul><p>By weaving together these concepts—PA index, sustainable food sources, biomimicry, and ecological responsibility—we can create a cohesive narrative that promotes a sustainable future, inspired by and aligned with natural processes.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg width="24" 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gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary">A list of all of the topics we've discussed.<div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 group-hover/conversation-turn:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" 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10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="de4f14f7-423a-464e-8abe-a506012b35f2" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Here's a summary of the topics we've discussed so far:</p><ol><li><p><strong>Pathway Assembly (PA) Index</strong>:</p><ul><li>A theoretical framework for quantifying the complexity and assembly pathway of objects by analyzing the minimal steps required for their reassembly.</li></ul></li><li><p><strong>Biological and Technological Processes</strong>:</p><ul><li>The interconnectedness of biological origins in technological processes and the implications for identifying biosignatures and technosignatures.</li></ul></li><li><p><strong>Centrifugal Kelp Baleen Filtration</strong>:</p><ul><li>A proposed system that uses centrifugal force to mimic baleen whale filtration, designed for processing kelp into various usable components like starch, protein, and oils.</li></ul></li><li><p><strong>Sustainability and Efficiency</strong>:</p><ul><li>Discussing the sustainability of lower trophic level consumption (plankton, algae) and how these concepts can be applied to food production and environmental management.</li></ul></li><li><p><strong>Biomimicry and Whale Feeding Mechanisms</strong>:</p><ul><li>How the feeding mechanisms of baleen whales can inspire technological innovations for efficient resource use and environmental sustainability.</li></ul></li><li><p><strong>Hydrothermal Liquefaction</strong>:</p><ul><li>The process of converting excess biomass into bio-crude oil, highlighting an approach to manage waste and enhance the circular economy.</li></ul></li><li><p><strong>Yogurt Vat Arrays</strong>:</p><ul><li>The potential use of fermentation processes in bioreactors for further processing of biomass, enhancing nutrient extraction and bioconversion.</li></ul></li><li><p><strong>Circular Economy</strong>:</p><ul><li>Principles of minimizing waste and extending the lifecycle of resources through innovative production and waste management techniques.</li></ul></li></ol><p>These discussions have woven together themes from biology, technology, sustainability, and innovation, illustrating how natural processes can inform and improve human industrial and environmental practices.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center 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id="radix-:r4j:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="text-token-text-primary border border-transparent inline-flex items-center justify-center gap-1 rounded-lg text-sm dark:transparent dark:bg-transparent leading-none outline-none cursor-pointer hover:bg-token-main-surface-secondary dark:hover:bg-token-main-surface-secondary focus-visible:bg-token-main-surface-secondary radix-state-active:text-token-text-secondary radix-disabled:cursor-auto radix-disabled:bg-transparent radix-disabled:text-token-text-tertiary dark:radix-disabled:bg-transparent m-0 h-0 w-0 border-none bg-transparent p-0"></button><button class="flex items-center justify-center text-token-text-primary juice:h-8 juice:w-8 dark:text-white juice:rounded-full focus-visible:outline-black dark:focus-visible:outline-white juice:mb-1 juice:ml-1.5" aria-disabled="false"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" fill-rule="evenodd" d="M9 7a5 5 0 0 1 10 0v8a7 7 0 1 1-14 0V9a1 1 0 0 1 2 0v6a5 5 0 0 0 10 0V7a3 3 0 1 0-6 0v8a1 1 0 1 0 2 0V9a1 1 0 1 1 2 0v6a3 3 0 1 1-6 0z" clip-rule="evenodd"></path></svg></button><div type="button" aria-haspopup="dialog" aria-expanded="false" aria-controls="radix-:r4l:" data-state="closed"></div></div></div><div class="flex min-w-0 flex-1 flex-col"><textarea id="prompt-textarea" tabindex="0" data-id="request-52dba091-fce2-430e-a57a-3ddb2f9c8b72-0" dir="auto" rows="1" placeholder="Envía un mensaje a ChatGPT" class="m-0 resize-none border-0 bg-transparent px-0 text-token-text-primary focus:ring-0 focus-visible:ring-0 max-h-[25dvh] max-h-52" style="height: 40px; overflow-y: hidden;"></textarea></div><button data-testid="fruitjuice-send-button" class="mb-1 me-1 flex h-8 w-8 items-center justify-center rounded-full bg-black text-white transition-colors hover:opacity-70 focus-visible:outline-none focus-visible:outline-black disabled:bg-[#D7D7D7] disabled:text-[#f4f4f4] disabled:hover:opacity-100 dark:bg-white dark:text-black dark:focus-visible:outline-white disabled:dark:bg-token-text-quaternary dark:disabled:text-token-main-surface-secondary" disabled=""><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" fill="none" viewBox="0 0 32 32" class="icon-2xl"><path fill="currentColor" fill-rule="evenodd" d="M15.192 8.906a1.143 1.143 0 0 1 1.616 0l5.143 5.143a1.143 1.143 0 0 1-1.616 1.616l-3.192-3.192v9.813a1.143 1.143 0 0 1-2.286 0v-9.813l-3.192 3.192a1.143 1.143 0 1 1-1.616-1.616z" clip-rule="evenodd"></path></svg></button></div></div></div></div></form></div></div><div class="relative px-2 py-2 text-center text-xs text-token-text-secondary md:px-[60px]"><span>ChatGPT puede cometer errores. Comprueba la información importante.</span></div></div></div><div class="group fixed bottom-3 end-3 z-10 hidden gap-1 juice:bottom-2 juice:end-2 md:flex juice:lg:bottom-3 juice:lg:end-3"><button class="flex h-6 w-6 items-center justify-center rounded-full border border-token-border-light text-xs text-token-text-secondary" type="button" id="radix-:r4m:" aria-haspopup="menu" aria-expanded="false" data-state="closed">?</button></div></main></div></div><div class="absolute left-0 right-0 top-0 z-[2]"></div><audio class="fixed bottom-0 left-0 hidden h-0 w-0" autoplay="" crossorigin="anonymous"></audio></div><next-route-announcer><p aria-live="assertive" id="__next-route-announcer__" role="alert" style="border: 0px; clip: rect(0px, 0px, 0px, 0px); height: 1px; margin: -1px; overflow: hidden; padding: 0px; position: absolute; top: 0px; width: 1px; white-space: nowrap; overflow-wrap: normal;">ChatGPT</p></next-route-announcer><div portal-container=""><span class="pointer-events-none fixed inset-0 z-[60] mx-auto my-2 flex max-w-[560px] flex-col items-stretch justify-start md:pb-5"></span></div><div id="enforcement-containerchatgpt-paid" tabindex="0" style="position: fixed; top: 0px; left: 0px; width: 100vw; height: 100vh; z-index: 1000; background-color: rgba(255, 255, 255, 0.85); align-items: center; box-sizing: border-box; flex-direction: column; justify-content: center; text-align: center; opacity: 0; transition: opacity 0.5s ease 0s; pointer-events: auto; display: none;"><div style="position: fixed; top: 20px; right: 20px; height: 20px; width: 20px; background-repeat: no-repeat; background-position: center center; z-index: 1500; cursor: pointer; transform: scale(1); background-image: url("data:image/svg+xml;base64,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");"></div><div aria-hidden="false" class="arkose-35536E1E-65B4-4D96-9D97-6ADB7EFF8147-wrapper" aria-modal="true" role="dialog"><iframe src="cid:[email protected]" class="r34K7X1zGgAi6DllVF3T active inline" title="Verification challenge" aria-label="Verification challenge" data-e2e="enforcement-frame" style="width: 0px; height: 0px;"></iframe></div></div></body></html>
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html.ZnJ1aXRqdWljZQ { --text-secondary: #7d7d7d; --text-error: #f93a37; --surface-error: 249 58 55; }
.dark { --text-primary: var(--gray-100); --text-secondary: var(--gray-300); --text-tertiary: var(--gray-400); --text-quaternary: var(--gray-500); --text-error: var(--red-500); --border-light: hsla(0,0%,100%,.1); --border-medium: hsla(0,0%,100%,.15); --border-heavy: hsla(0,0%,100%,.2); --border-xheavy: hsla(0,0%,100%,.25); --main-surface-primary: var(--gray-800); --main-surface-secondary: var(--gray-750); --main-surface-tertiary: var(--gray-700); --sidebar-surface-primary: var(--gray-900); --sidebar-surface-secondary: var(--gray-800); --sidebar-surface-tertiary: var(--gray-750); --link: #7ab7ff; --link-hover: #5e83b3; }
html.ZnJ1aXRqdWljZQ.dark { --text-secondary: var(--gray-400); --text-tertiary: var(--gray-500); --text-quaternary: var(--gray-600); --text-error: #f93a37; --surface-error: 249 58 55; }
.popover { --main-surface-primary: var(--white) !important; --main-surface-secondary: var(--gray-100) !important; --main-surface-tertiary: var(--gray-200) !important; --sidebar-surface-primary: var(--white) !important; }
.dark .popover, .dark.popover, .popover .dark { --main-surface-primary: var(--gray-750) !important; --main-surface-secondary: var(--gray-700) !important; --main-surface-tertiary: var(--gray-600) !important; --text-primary: var(--gray-50) !important; --text-secondary: var(--gray-200) !important; --text-tertiary: var(--gray-400) !important; --text-quaternary: var(--gray-500) !important; --sidebar-surface-primary: var(--gray-750) !important; }
textarea:focus { border-color: inherit; box-shadow: none; outline: none; }
.container { width: 100%; }
@media (min-width: 640px) {
.container { max-width: 640px; }
}
@media (min-width: 768px) {
.container { max-width: 768px; }
}
@media (min-width: 1024px) {
.container { max-width: 1024px; }
}
@media (min-width: 1280px) {
.container { max-width: 1280px; }
}
@media (min-width: 1536px) {
.container { max-width: 1536px; }
}
@media (min-width: 2006px) {
.container { max-width: 2006px; }
}
.prose { color: var(--tw-prose-body); max-width: 65ch; }
.prose :where([class~="lead"]):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-lead); font-size: 1.25em; line-height: 1.6; margin-bottom: 1.2em; margin-top: 1.2em; }
.prose :where(a):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-links); font-weight: 500; text-decoration: underline; }
.prose :where(strong):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-bold); font-weight: 600; }
.prose :where(a strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(blockquote strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(thead th strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(ol):not(:where([class~="not-prose"] *)) { list-style-type: decimal; margin-bottom: 1.25em; margin-top: 1.25em; padding-left: 1.625em; }
.prose :where(ol[type="A"]):not(:where([class~="not-prose"] *)) { list-style-type: upper-alpha; }
.prose :where(ol[type="a"]):not(:where([class~="not-prose"] *)) { list-style-type: lower-alpha; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: upper-alpha; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: lower-alpha; }
.prose :where(ol[type="I"]):not(:where([class~="not-prose"] *)) { list-style-type: upper-roman; }
.prose :where(ol[type="i"]):not(:where([class~="not-prose"] *)) { list-style-type: lower-roman; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: upper-roman; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: lower-roman; }
.prose :where(ol[type="1"]):not(:where([class~="not-prose"] *)) { list-style-type: decimal; }
.prose :where(ul):not(:where([class~="not-prose"] *)) { list-style-type: disc; margin-bottom: 1.25em; margin-top: 1.25em; padding-left: 1.625em; }
.prose :where(ol > li):not(:where([class~="not-prose"] *))::marker { color: var(--tw-prose-counters); font-weight: 400; }
.prose :where(ul > li):not(:where([class~="not-prose"] *))::marker { color: var(--tw-prose-bullets); }
.prose :where(hr):not(:where([class~="not-prose"] *)) { border-color: var(--tw-prose-hr); border-top-width: 1px; margin-bottom: 3em; margin-top: 3em; }
.prose :where(blockquote):not(:where([class~="not-prose"] *)) { border-left-color: var(--tw-prose-quote-borders); border-left-width: 0.25rem; color: var(--tw-prose-quotes); font-style: normal; font-weight: 500; margin-bottom: 1.6em; margin-top: 1.6em; padding-left: 1em; quotes: "“" "”" "‘" "’"; }
.prose :where(blockquote p:first-of-type):not(:where([class~="not-prose"] *))::before { content: open-quote; }
.prose :where(blockquote p:last-of-type):not(:where([class~="not-prose"] *))::after { content: close-quote; }
.prose :where(h1):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-size: 2.25em; font-weight: 800; line-height: 1.11111; margin-bottom: 0.888889em; margin-top: 0px; }
.prose :where(h1 strong):not(:where([class~="not-prose"] *)) { color: inherit; font-weight: 900; }
.prose :where(h2):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-size: 1.5em; font-weight: 700; line-height: 1.33333; margin-bottom: 1em; margin-top: 2em; }
.prose :where(h2 strong):not(:where([class~="not-prose"] *)) { color: inherit; font-weight: 800; }
.prose :where(h3):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-size: 1.25em; font-weight: 600; line-height: 1.6; margin-bottom: 0.6em; margin-top: 1.6em; }
.prose :where(h3 strong):not(:where([class~="not-prose"] *)) { color: inherit; font-weight: 700; }
.prose :where(h4):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-weight: 600; line-height: 1.5; margin-bottom: 0.5em; margin-top: 1.5em; }
.prose :where(h4 strong):not(:where([class~="not-prose"] *)) { color: inherit; font-weight: 700; }
.prose :where(img):not(:where([class~="not-prose"] *)) { margin-bottom: 2em; margin-top: 2em; }
.prose :where(figure > *):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; margin-top: 0px; }
.prose :where(figcaption):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-captions); font-size: 0.875em; line-height: 1.42857; margin-top: 0.857143em; }
.prose :where(code):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-code); font-size: 0.875em; font-weight: 600; }
.prose :where(code):not(:where([class~="not-prose"] *))::before { content: "`"; }
.prose :where(code):not(:where([class~="not-prose"] *))::after { content: "`"; }
.prose :where(a code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(h1 code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(h2 code):not(:where([class~="not-prose"] *)) { color: inherit; font-size: 0.875em; }
.prose :where(h3 code):not(:where([class~="not-prose"] *)) { color: inherit; font-size: 0.9em; }
.prose :where(h4 code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(blockquote code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(thead th code):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(pre):not(:where([class~="not-prose"] *)) { background-color: transparent; border-radius: 0.375rem; color: currentcolor; font-size: 0.875em; font-weight: 400; line-height: 1.71429; margin: 0px; overflow-x: auto; padding: 0px; }
.prose :where(pre code):not(:where([class~="not-prose"] *)) { background-color: transparent; border-radius: 0px; border-width: 0px; color: inherit; font-family: inherit; font-size: inherit; font-weight: inherit; line-height: inherit; padding: 0px; }
.prose :where(pre code):not(:where([class~="not-prose"] *))::before { content: none; }
.prose :where(pre code):not(:where([class~="not-prose"] *))::after { content: none; }
.prose :where(table):not(:where([class~="not-prose"] *)) { font-size: 0.875em; line-height: 1.71429; margin-bottom: 2em; margin-top: 2em; table-layout: auto; text-align: left; width: 100%; }
.prose :where(thead):not(:where([class~="not-prose"] *)) { border-bottom-color: var(--tw-prose-th-borders); border-bottom-width: 1px; }
.prose :where(thead th):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-headings); font-weight: 600; padding-bottom: 0.571429em; padding-left: 0.571429em; padding-right: 0.571429em; vertical-align: bottom; }
.prose :where(tbody tr):not(:where([class~="not-prose"] *)) { border-bottom-color: var(--tw-prose-td-borders); border-bottom-width: 1px; }
.prose :where(tbody tr:last-child):not(:where([class~="not-prose"] *)) { border-bottom-width: 0px; }
.prose :where(tbody td):not(:where([class~="not-prose"] *)) { vertical-align: baseline; }
.prose :where(tfoot):not(:where([class~="not-prose"] *)) { border-top-color: var(--tw-prose-th-borders); border-top-width: 1px; }
.prose :where(tfoot td):not(:where([class~="not-prose"] *)) { vertical-align: top; }
.prose { --tw-prose-body: var(--text-primary); --tw-prose-headings: var(--text-primary); --tw-prose-lead: var(--text-primary); --tw-prose-links: var(--text-primary); --tw-prose-bold: var(--text-primary); --tw-prose-counters: var(--text-primary); --tw-prose-bullets: var(--text-primary); --tw-prose-hr: var(--border-xheavy); --tw-prose-quotes: var(--text-primary); --tw-prose-quote-borders: #e5e7eb; --tw-prose-captions: var(--text-secondary); --tw-prose-code: var(--text-primary); --tw-prose-pre-code: #e5e7eb; --tw-prose-pre-bg: #1f2937; --tw-prose-th-borders: #d1d5db; --tw-prose-td-borders: #e5e7eb; --tw-prose-invert-body: var(--text-primary); --tw-prose-invert-headings: var(--text-primary); --tw-prose-invert-lead: var(--text-primary); --tw-prose-invert-links: var(--text-primary); --tw-prose-invert-bold: var(--text-primary); --tw-prose-invert-counters: var(--text-primary); --tw-prose-invert-bullets: var(--text-primary); --tw-prose-invert-hr: var(--border-xheavy); --tw-prose-invert-quotes: var(--text-primary); --tw-prose-invert-quote-borders: #374151; --tw-prose-invert-captions: var(--text-secondary); --tw-prose-invert-code: var(--text-primary); --tw-prose-invert-pre-code: #d1d5db; --tw-prose-invert-pre-bg: rgba(0,0,0,.5); --tw-prose-invert-th-borders: #4b5563; --tw-prose-invert-td-borders: #374151; font-size: 1rem; line-height: 1.75; }
.prose :where(p):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; margin-top: 1.25em; }
.prose :where(video):not(:where([class~="not-prose"] *)) { margin-bottom: 2em; margin-top: 2em; }
.prose :where(figure):not(:where([class~="not-prose"] *)) { margin-bottom: 2em; margin-top: 2em; }
.prose :where(li):not(:where([class~="not-prose"] *)) { margin-bottom: 0.5em; margin-top: 0.5em; }
.prose :where(ol > li):not(:where([class~="not-prose"] *)) { padding-left: 0.375em; }
.prose :where(ul > li):not(:where([class~="not-prose"] *)) { padding-left: 0.375em; }
.prose :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.75em; margin-top: 0.75em; }
.prose :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.25em; }
.prose :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; }
.prose :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.25em; }
.prose :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; }
.prose :where(ul ul, ul ol, ol ul, ol ol):not(:where([class~="not-prose"] *)) { margin-bottom: 0.75em; margin-top: 0.75em; }
.prose :where(hr + *):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(h2 + *):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(h3 + *):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(h4 + *):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(thead th:first-child):not(:where([class~="not-prose"] *)) { padding-left: 0px; }
.prose :where(thead th:last-child):not(:where([class~="not-prose"] *)) { padding-right: 0px; }
.prose :where(tbody td, tfoot td):not(:where([class~="not-prose"] *)) { padding: 0.571429em; }
.prose :where(tbody td:first-child, tfoot td:first-child):not(:where([class~="not-prose"] *)) { padding-left: 0px; }
.prose :where(tbody td:last-child, tfoot td:last-child):not(:where([class~="not-prose"] *)) { padding-right: 0px; }
.prose :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-sm :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.571429em; margin-top: 0.571429em; }
.prose-sm :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.14286em; }
.prose-sm :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.14286em; }
.prose-sm :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.14286em; }
.prose-sm :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.14286em; }
.prose-sm :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-sm :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-base :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.75em; margin-top: 0.75em; }
.prose-base :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.25em; }
.prose-base :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; }
.prose-base :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.25em; }
.prose-base :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.25em; }
.prose-base :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-base :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-lg :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.888889em; margin-top: 0.888889em; }
.prose-lg :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.33333em; }
.prose-lg :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.33333em; }
.prose-lg :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.33333em; }
.prose-lg :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.33333em; }
.prose-lg :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-lg :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-xl :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.8em; margin-top: 0.8em; }
.prose-xl :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.2em; }
.prose-xl :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.2em; }
.prose-xl :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.2em; }
.prose-xl :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.2em; }
.prose-xl :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-xl :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.prose-2xl :where(.prose > ul > li p):not(:where([class~="not-prose"] *)) { margin-bottom: 0.833333em; margin-top: 0.833333em; }
.prose-2xl :where(.prose > ul > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.33333em; }
.prose-2xl :where(.prose > ul > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.33333em; }
.prose-2xl :where(.prose > ol > li > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 1.33333em; }
.prose-2xl :where(.prose > ol > li > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 1.33333em; }
.prose-2xl :where(.prose > :first-child):not(:where([class~="not-prose"] *)) { margin-top: 0px; }
.prose-2xl :where(.prose > :last-child):not(:where([class~="not-prose"] *)) { margin-bottom: 0px; }
.form-input, .form-multiselect, .form-select, .form-textarea { --tw-shadow: 0 0 transparent; appearance: none; background-color: rgb(255, 255, 255); border-color: rgb(155, 155, 155); border-radius: 0px; border-width: 1px; font-size: 1rem; line-height: 1.5rem; padding: 0.5rem 0.75rem; }
.form-input:focus, .form-multiselect:focus, .form-select:focus, .form-textarea:focus { --tw-ring-inset: var(--tw-empty,/*!*/ /*!*/); --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: #2563eb; --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(1px + var(--tw-ring-offset-width)) var(--tw-ring-color); border-color: rgb(37, 99, 235); box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow); outline: transparent solid 2px; outline-offset: 2px; }
.form-input::placeholder, .form-textarea::placeholder { color: rgb(155, 155, 155); opacity: 1; }
.form-input::-webkit-datetime-edit-fields-wrapper { padding: 0px; }
.form-input::-webkit-date-and-time-value { min-height: 1.5em; }
.form-input::-webkit-datetime-edit, .form-input::-webkit-datetime-edit-day-field, .form-input::-webkit-datetime-edit-hour-field, .form-input::-webkit-datetime-edit-meridiem-field, .form-input::-webkit-datetime-edit-millisecond-field, .form-input::-webkit-datetime-edit-minute-field, .form-input::-webkit-datetime-edit-month-field, .form-input::-webkit-datetime-edit-second-field, .form-input::-webkit-datetime-edit-year-field { padding-bottom: 0px; padding-top: 0px; }
.btn { align-items: center; border-color: transparent; border-radius: 0.5rem; border-width: 1px; display: inline-flex; flex-shrink: 0; font-size: 0.875rem; font-weight: 500; justify-content: center; line-height: 1.25rem; min-height: 38px; padding: 0.5rem 0.75rem; pointer-events: auto; }
.btn.focus-visible, .btn:focus { outline: transparent solid 2px; outline-offset: 2px; }
.btn:focus-visible { outline: transparent solid 2px; outline-offset: 2px; }
.btn:disabled { cursor: not-allowed; opacity: 0.5; }
.ZnJ1aXRqdWljZQ .btn { border-radius: 9999px; padding-left: 0.875rem; padding-right: 0.875rem; }
.btn:active { opacity: 0.8; }
.btn-green, .btn-primary { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(16,163,127,var(--tw-bg-opacity)); color: rgba(255,255,255,var(--tw-text-opacity)); }
.btn-green:hover, .btn-primary:hover { --tw-bg-opacity: 1; background-color: rgba(26,127,100,var(--tw-bg-opacity)); }
.btn-green.focus-visible, .btn-primary.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(25,195,125,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-green:focus-visible, .btn-primary:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(25,195,125,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-blue { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(0,102,222,var(--tw-bg-opacity)); color: rgba(255,255,255,var(--tw-text-opacity)); }
.btn-blue:hover { --tw-bg-opacity: 1; background-color: rgba(29,78,216,var(--tw-bg-opacity)); }
.btn-blue.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(29,78,216,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-blue:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(29,78,216,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.ZnJ1aXRqdWljZQ .btn-primary { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(13,13,13,var(--tw-bg-opacity)); color: rgba(255,255,255,var(--tw-text-opacity)); }
.ZnJ1aXRqdWljZQ .btn-primary:hover { --tw-bg-opacity: 1; background-color: rgba(33,33,33,var(--tw-bg-opacity)); }
.ZnJ1aXRqdWljZQ .btn-primary.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(155,155,155,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.ZnJ1aXRqdWljZQ .btn-primary:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(155,155,155,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.ZnJ1aXRqdWljZQ .btn-primary:is(.dark *) { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(249,249,249,var(--tw-bg-opacity)); color: rgba(13,13,13,var(--tw-text-opacity)); }
.ZnJ1aXRqdWljZQ .btn-primary:hover:is(.dark *) { --tw-bg-opacity: 1; background-color: rgba(236,236,236,var(--tw-bg-opacity)); }
.btn-danger { --tw-bg-opacity: 1; --tw-text-opacity: 1; background-color: rgba(239,68,68,var(--tw-bg-opacity)); color: rgba(255,255,255,var(--tw-text-opacity)); }
.btn-danger:hover { --tw-bg-opacity: 1; background-color: rgba(185,28,28,var(--tw-bg-opacity)); }
.btn-danger.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(248,113,113,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-danger:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(248,113,113,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-danger:disabled:hover { --tw-bg-opacity: 1; background-color: rgba(185,28,28,var(--tw-bg-opacity)); }
.btn-danger-outline { --tw-border-opacity: 1; --tw-text-opacity: 1; background-color: var(--main-surface-primary); border-color: rgba(220,38,38,var(--tw-border-opacity)); border-width: 1px; color: rgba(220,38,38,var(--tw-text-opacity)); }
.btn-danger-outline:hover { background-color: var(--main-surface-secondary); }
.btn-danger-outline.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(220,38,38,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-danger-outline:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(220,38,38,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-secondary { background-color: var(--main-surface-primary); border-color: var(--border-medium); border-width: 1px; color: var(--text-primary); font-size: 0.875rem; line-height: 1.25rem; }
.btn-secondary:hover { background-color: var(--main-surface-secondary); }
.btn-secondary.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(103,103,103,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-secondary:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-opacity: 1; --tw-ring-color: rgba(103,103,103,var(--tw-ring-opacity)); --tw-ring-offset-width: 2px; box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); }
.btn-ghost:hover { background-color: rgba(0, 0, 0, 0.05); }
.btn-ghost.focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-color: rgba(0,0,0,.05); box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); outline: transparent solid 2px; outline-offset: 2px; }
.btn-ghost:focus-visible { --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); --tw-ring-color: rgba(0,0,0,.05); box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow,0 0 transparent); outline: transparent solid 2px; outline-offset: 2px; }
.btn-ghost:hover:is(.dark *) { background-color: rgba(255, 255, 255, 0.1); }
.btn-small { min-height: 30px; padding: 0.25rem 0.5rem; }
.ZnJ1aXRqdWljZQ .btn-small { padding-left: 0.75rem; padding-right: 0.75rem; }
.btn-giant, .btn-large { min-height: 46px; }
.btn-large { padding-bottom: 0.75rem; padding-top: 0.75rem; }
.ZnJ1aXRqdWljZQ .btn-large { padding-left: 1rem; padding-right: 1rem; }
.btn-giant { font-size: 1rem; font-weight: 600; line-height: 1.5rem; padding: 0.625rem 1.25rem; }
.ZnJ1aXRqdWljZQ .btn-giant { padding-left: 1.5rem; padding-right: 1.5rem; }
.divide-token-border-light > :not([hidden]) ~ :not([hidden]) { border-color: rgba(0, 0, 0, 0.1); }
.border-token-border-heavy { border-color: rgba(0, 0, 0, 0.2); }
.border-token-border-light { border-color: rgba(0, 0, 0, 0.1); }
.border-token-border-medium { border-color: rgba(0, 0, 0, 0.15); }
.border-token-border-xheavy { border-color: rgba(0, 0, 0, 0.25); }
.border-token-main-surface-secondary { }
.border-token-main-surface-tertiary { }
.border-token-surface-error\/15 { }
.border-token-text-primary { }
.border-token-text-secondary { }
.border-token-text-tertiary { }
.border-y-token-border-medium { border-bottom-color: rgba(0, 0, 0, 0.15); border-top-color: rgba(0, 0, 0, 0.15); }
.border-l-token-sidebar-surface-secondary { }
.\!bg-token-main-surface-primary { }
.\!bg-token-text-primary { }
.bg-token-border-light { background-color: rgba(0, 0, 0, 0.1); }
.bg-token-border-medium { background-color: rgba(0, 0, 0, 0.15); }
.bg-token-main-surface-primary { }
.bg-token-main-surface-secondary { }
.bg-token-main-surface-tertiary { }
.bg-token-sidebar-surface-primary { }
.bg-token-sidebar-surface-secondary { }
.bg-token-sidebar-surface-tertiary { }
.bg-token-surface-error { background-color: rgb(theme(colors.red.700)/var(--tw-bg-opacity)); }
.bg-token-text-primary { }
.bg-token-text-quaternary { }
.bg-token-text-secondary { }
.bg-token-text-tertiary { }
.fill-token-main-surface-primary { }
.stroke-token-main-surface-tertiary { }
.\!text-token-main-surface-primary { }
.\!text-token-text-primary { }
.text-token-link { color: rgb(41, 100, 170); }
.text-token-main-surface-primary { }
.text-token-main-surface-tertiary { }
.text-token-text-error { }
.text-token-text-primary { }
.text-token-text-quaternary { }
.text-token-text-secondary { }
.text-token-text-tertiary { }
.decoration-token-link { text-decoration-color: rgb(41, 100, 170); }
.decoration-token-text-primary { }
.caret-token-text-primary { }
body, html { background-color: var(--main-surface-primary); }
#__next, #root, body, html { height: 100%; }
.markdown { max-width: none; }
.markdown h1 { font-weight: 600; }
.markdown h1:first-child { margin-top: 0px; }
.markdown h2 { font-weight: 600; margin-bottom: 1rem; margin-top: 2rem; }
.markdown h2:first-child { margin-top: 0px; }
.markdown h3 { font-weight: 600; margin-bottom: 0.5rem; margin-top: 1rem; }
.markdown h3:first-child { margin-top: 0px; }
.markdown h4 { font-weight: 600; margin-bottom: 0.5rem; margin-top: 1rem; }
.markdown h4:first-child { margin-top: 0px; }
.markdown h5 { font-weight: 600; }
.markdown h5:first-child { margin-top: 0px; }
.markdown blockquote { --tw-border-opacity: 1; border-color: rgba(155,155,155,var(--tw-border-opacity)); border-left-width: 2px; line-height: 1.5rem; margin: 0px; padding-bottom: 0.5rem; padding-left: 1rem; padding-top: 0.5rem; }
.markdown blockquote > p { margin: 0px; }
.markdown blockquote > p::after, .markdown blockquote > p::before { display: none; }
.markdown table { --tw-border-spacing-x: 0px; --tw-border-spacing-y: 0px; border-collapse: separate; border-spacing: var(--tw-border-spacing-x) var(--tw-border-spacing-y); margin-bottom: 0.25rem; margin-top: 0.25rem; width: 100%; }
.markdown th { background-color: var(--border-light); border-bottom-width: 1px; border-color: var(--border-medium); border-left-width: 1px; border-top-width: 1px; padding: 0.25rem 0.75rem; }
.markdown th:first-child { border-top-left-radius: 0.375rem; }
.markdown th:last-child { border-right-width: 1px; border-top-right-radius: 0.375rem; }
.markdown td { border-bottom-width: 1px; border-color: var(--border-medium); border-left-width: 1px; padding: 0.25rem 0.75rem; }
.markdown td:last-child { border-right-width: 1px; }
.markdown tbody tr:last-child td:first-child { border-bottom-left-radius: 0.375rem; }
.markdown tbody tr:last-child td:last-child { border-bottom-right-radius: 0.375rem; }
.markdown a { color: var(--link); font-weight: 400; text-decoration-line: none; }
.markdown a:hover { color: var(--link-hover); }
.gizmo .markdown > :not(pre), .gizmo .markdown > :not(pre) > :not(a) { color: var(--text-primary); }
button.scroll-convo { display: none; }
@keyframes blink {
100% { visibility: hidden; }
}
.result-streaming > :not(ol):not(ul):not(pre):last-child::after, .result-streaming > pre:last-child code::after { content: "●"; font-family: Circle, system-ui, -apple-system, "Segoe UI", Roboto, Ubuntu, Cantarell, "Noto Sans", sans-serif; line-height: normal; margin-left: 0.25rem; vertical-align: baseline; }
.result-thinking:empty:last-child::after { -webkit-font-smoothing: subpixel-antialiased; animation: 1.25s ease-in-out 0s infinite normal none running pulseSize; backface-visibility: hidden; background-color: var(--text-primary); border-radius: 50%; box-sizing: border-box; content: " "; display: block; height: 12px; position: absolute; top: 7px; transform: translateZ(0px); transform-origin: center center; width: 12px; will-change: transform; }
@supports (selector(:has(*))) {
.result-streaming > ol:last-child > li:last-child > ol:last-child > li:last-child::after, .result-streaming > ol:last-child > li:last-child > ol:last-child > li:last-child > ol:last-child > li:last-child::after, .result-streaming > ol:last-child > li:last-child > ol:last-child > li:last-child > ul:last-child > li:last-child::after, .result-streaming > ol:last-child > li:last-child > ul:last-child > li:last-child::after, .result-streaming > ol:last-child > li:last-child > ul:last-child > li:last-child > ol:last-child > li:last-child::after, .result-streaming > ol:last-child > li:last-child > ul:last-child > li:last-child > ul:last-child > li:last-child::after, .result-streaming > ul:last-child > li:last-child > ol:last-child > li:last-child::after, .result-streaming > ul:last-child > li:last-child > ol:last-child > li:last-child > ol:last-child > li:last-child::after, .result-streaming > ul:last-child > li:last-child > ol:last-child > li:last-child > ul:last-child > li:last-child::after, .result-streaming > ul:last-child > li:last-child > ul:last-child > li:last-child::after, .result-streaming > ul:last-child > li:last-child > ul:last-child > li:last-child > ol:last-child > li:last-child::after, .result-streaming > ul:last-child > li:last-child > ul:last-child > li:last-child > ul:last-child > li:last-child::after, .result-streaming > ul:last-child > li:last-child[*|\:not-has\(]::after { content: "●"; font-family: Circle, system-ui, -apple-system, "Segoe UI", Roboto, Ubuntu, Cantarell, "Noto Sans", sans-serif; line-height: normal; margin-left: 0.25rem; vertical-align: baseline; }
.result-streaming > ul:last-child > li:last-child:not(:has(* > li))::after { content: "●"; font-family: Circle, system-ui, -apple-system, "Segoe UI", Roboto, Ubuntu, Cantarell, "Noto Sans", sans-serif; line-height: normal; margin-left: 0.25rem; vertical-align: baseline; }
.result-streaming > ol:last-child > li:last-child[*|\:not-has\(]::after { content: "●"; font-family: Circle, system-ui, -apple-system, "Segoe UI", Roboto, Ubuntu, Cantarell, "Noto Sans", sans-serif; line-height: normal; margin-left: 0.25rem; vertical-align: baseline; }
.result-streaming > ol:last-child > li:last-child:not(:has(* > li))::after { content: "●"; font-family: Circle, system-ui, -apple-system, "Segoe UI", Roboto, Ubuntu, Cantarell, "Noto Sans", sans-serif; line-height: normal; margin-left: 0.25rem; vertical-align: baseline; }
}
@supports not (selector(:has(*))) {
.result-streaming > ol:last-child > li:last-child::after, .result-streaming > ul:last-child > li:last-child::after { content: "●"; font-family: Circle, system-ui, -apple-system, "Segoe UI", Roboto, Ubuntu, Cantarell, "Noto Sans", sans-serif; line-height: normal; margin-left: 0.25rem; vertical-align: baseline; }
}
@keyframes pulseSize {
0%, 100% { transform: scaleX(1); }
50% { transform: scale3d(1.25, 1.25, 1); }
}
@keyframes toast-open {
0% { opacity: 0; transform: translateY(-100%); }
100% { transform: translateY(0px); }
}
@keyframes toast-close {
0% { opacity: 1; }
100% { opacity: 0; }
}
button[data-state="closed"] .toggle-item-button-closed, button[data-state="open"] .toggle-item-button-open { display: none; }
.toast-root { align-items: center; display: flex; flex-direction: column; height: 0px; transition: all 0.24s cubic-bezier(0, 0, 0.2, 1) 0s; }
.toast-root[data-state="entered"], .toast-root[data-state="entering"] { animation: 0.24s cubic-bezier(0.175, 0.885, 0.32, 1) 0s 1 normal both running toast-open; }
.toast-root[data-state="exiting"] { animation: 0.12s cubic-bezier(0.4, 0, 1, 1) 0s 1 normal both running toast-close; }
.toast-root .alert-root { box-shadow: rgba(67, 90, 111, 0.3) 0px 0px 1px, rgba(67, 90, 111, 0.3) 0px 5px 8px -4px; flex-shrink: 0; pointer-events: all; }
.interact-bounce { transition-duration: 0.15s; transition-property: transform; transition-timing-function: cubic-bezier(0.4, 0, 0.2, 1); }
.interact-bounce:hover { --tw-scale-x: 1.05; --tw-scale-y: 1.05; }
.interact-bounce:active, .interact-bounce:hover { transform: translate(var(--tw-translate-x),var(--tw-translate-y)) rotate(var(--tw-rotate)) skewX(var(--tw-skew-x)) skewY(var(--tw-skew-y)) scaleX(var(--tw-scale-x)) scaleY(var(--tw-scale-y)); }
.interact-bounce:active { --tw-scale-x: .9; --tw-scale-y: .9; }
.title { font-feature-settings: normal; font-family: ui-sans-serif, system-ui, -apple-system, "Segoe UI", Roboto, Ubuntu, Cantarell, "Noto Sans", sans-serif, "Helvetica Neue", Arial, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; font-variation-settings: normal; }
.icon-xs { stroke-width: 1.5; flex-shrink: 0; height: 0.75rem; width: 0.75rem; }
.icon-sm { stroke-width: 2; }
.icon-sm, .icon-sm-heavy { flex-shrink: 0; height: 1rem; width: 1rem; }
.icon-sm-heavy { stroke-width: 2.5; }
.icon-md { stroke-width: 1.5; }
.icon-md, .icon-md-heavy { flex-shrink: 0; height: 18px; width: 18px; }
.icon-md-heavy { stroke-width: 2.5; }
.icon-lg { stroke-width: 1.5; flex-shrink: 0; height: 1.5rem; width: 1.5rem; }
.icon-lg-heavy { stroke-width: 2; flex-shrink: 0; height: 22px; width: 22px; }
.icon-xl { stroke-width: 1.5; flex-shrink: 0; height: 1.75rem; width: 1.75rem; }
.icon-xl-heavy { stroke-width: 2; flex-shrink: 0; height: 24px; width: 24px; }
.icon-2xl { stroke-width: 1.5; flex-shrink: 0; height: 2rem; width: 2rem; }
.icon-workspace-avatar-preview { stroke-width: 1.5; height: 96px; width: 96px; }
.icon-cover { stroke-width: 1.5; height: 234px; width: 234px; }
.icon-shimmer { animation: 5s cubic-bezier(0.2, 0.44, 0.38, 1.02) 0s infinite normal none running icon-shimmer; background-repeat: no-repeat; mask: linear-gradient(80deg, currentcolor 30%, rgba(0, 0, 0, 0.333), currentcolor 70%) right center / 300% 100%; }
@keyframes icon-shimmer {
0% { mask-position: right center; }
20% { mask-position: left center; }
100% { mask-position: left center; }
}
.loading-shimmer { -webkit-text-fill-color: transparent; animation-delay: 0.5s; animation-duration: 3s; animation-iteration-count: infinite; animation-name: loading-shimmer; background-image: ; background-attachment: ; background-origin: ; background-color: ; background-clip: text; background-position: -100% top; background-repeat: no-repeat; background-size: 50% 200%; display: inline-block; }
.loading-shimmer:hover { -webkit-text-fill-color: var(--text-primary); animation: auto ease 0s 1 normal none running none; background: transparent; }
@keyframes loading-shimmer {
0% { background-position: -100% top; }
100% { background-position: 250% top; }
}
.gizmo-shadow-stroke { position: relative; }
.gizmo-shadow-stroke::after { --tw-shadow: inset 0 0 0 1px rgba(0,0,0,.1); --tw-shadow-colored: inset 0 0 0 1px var(--tw-shadow-color); border-radius: 9999px; inset: 0px; content: ""; position: absolute; }
.dark .gizmo-shadow-stroke::after, .gizmo-shadow-stroke::after { box-shadow: var(--tw-ring-offset-shadow,0 0 transparent),var(--tw-ring-shadow,0 0 transparent),var(--tw-shadow); }
.dark .gizmo-shadow-stroke::after { --tw-shadow: inset 0 0 0 1px hsla(0,0%,100%,.2); --tw-shadow-colored: inset 0 0 0 1px var(--tw-shadow-color); }
.no-scrollbar::-webkit-scrollbar { display: none; }
.no-scrollbar { scrollbar-width: none; }
.gizmo-bot-avatar { outline: solid 1px var(--main-surface-tertiary); }
.dark .dark\:prose-invert { --tw-prose-body: var(--tw-prose-invert-body); --tw-prose-headings: var(--tw-prose-invert-headings); --tw-prose-lead: var(--tw-prose-invert-lead); --tw-prose-links: var(--tw-prose-invert-links); --tw-prose-bold: var(--tw-prose-invert-bold); --tw-prose-counters: var(--tw-prose-invert-counters); --tw-prose-bullets: var(--tw-prose-invert-bullets); --tw-prose-hr: var(--tw-prose-invert-hr); --tw-prose-quotes: var(--tw-prose-invert-quotes); --tw-prose-quote-borders: var(--tw-prose-invert-quote-borders); --tw-prose-captions: var(--tw-prose-invert-captions); --tw-prose-code: var(--tw-prose-invert-code); --tw-prose-pre-code: var(--tw-prose-invert-pre-code); --tw-prose-pre-bg: var(--tw-prose-invert-pre-bg); --tw-prose-th-borders: var(--tw-prose-invert-th-borders); --tw-prose-td-borders: var(--tw-prose-invert-td-borders); }