arxiv: 2604.18359 · v1 · submitted 2026-04-20 · 🌊 nlin.CG

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Temporal Retention of Information as a Biosignature

Terence P Kee , James mcCrum

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:38 UTC · model grok-4.3

classification 🌊 nlin.CG

keywords biosignatureConway's Game of Lifecellular automatatemporal retentioninformational lifelifelike systemscomplex systems

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The pith

Long-lasting evolutions in Conway's Game of Life indicate temporal retention of information as a biosignature.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends earlier arguments that Conway's Game of Life and similar lifelike cellular automata represent genuine living systems. It examines the ruleset's production of patterns that persist and evolve for unusually extended periods, interpreting this as evidence that information is retained across time. If correct, this positions temporal retention as a detectable informational marker for life that operates independently of physical chemistry.

Core claim

By reversing the prior approach of extracting biosignatures from the Game of Life ruleset, the work starts from the known outlier of very long-lasting evolutions and identifies temporal retention of information as a general informational biosignature concept.

What carries the argument

Temporal retention of information, the capacity of a system to maintain and propagate informational states over extended time scales, observed through the persistent evolutions generated by the Conway's Game of Life ruleset.

If this is right

Biosignature searches could examine other complex systems for patterns that remain active over long durations.
Informational criteria alone could identify life-like behavior in computational or abstract rule-based domains.
Rulesets producing sustained activity would be prioritized when screening for lifelike properties in cellular automata.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar persistence measures might distinguish living from non-living states in neural or ecological models.
Quantitative tests could compare average evolution lengths across many different rulesets to isolate the effect.
Links to biology could involve checking for temporal stability in genetic regulatory networks or population dynamics.

Load-bearing premise

The exceptionally long-lasting evolutions in Game of Life reflect a property tied to livingness rather than a neutral mathematical feature of the chosen rules.

What would settle it

Observing that many non-lifelike cellular automata rulesets generate evolutions of equal or greater duration would undermine the connection between long persistence and an informational biosignature.

Figures

Figures reproduced from arXiv: 2604.18359 by James mcCrum, Terence P Kee.

**Figure 1.** Figure 1: A CGOL glider in motion. (Dorin, 2012) Conway’s Game of Life is the namesake and founding example of a broader class of cellular automata, Lifelike Cellular Automata (LCAs). This is the special class of cellular automata with the following traits: (i) A simple binary state space; each cell can only be off or on, usually referred to as live or dead. (ii) Board consisting of a two-dimensional grid of squares… view at source ↗

**Figure 3.** Figure 3: The short-term (a), long-term (b) and very long-term (c) evolution of random configurations of initial density 15-70% in CGOL. As can be seen, all of the configurations move gradually and continually towards a value of 2.87 – the Flammenkamp Attractor. This data was produced in Fortran 90 (code available upon request). Wolfram has produced a fourfold categorisation of 1D and 2D cellular automata rulesets (… view at source ↗

**Figure 5.** Figure 5: Number of distinct configurations after one evolution of every single LCA on a 3x3 grid. As a 3x3 grid [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

Previous publications by the authors put forward the argument that Lifelike Cellular Automata can be treated as a bona fide example of livingness in and of themselves, not simply a toy analogue to biological life. Traits known to be indicative of biological life, biosignatures, were identified in informational form as particular outlier traits of the ruleset for the lifelike cellular automata known as Conways Game of Life. This publication reverses that logic, looking at a known outlier trait of Conways Game of Life, its very long-lasting evolutions, and using this to point towards temporal retention as an informational biosignature concept.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper reverses the authors' own prior claims to treat long-lived patterns in Conway's Game of Life as evidence for temporal retention of information as a biosignature, but supplies no definitions, metrics, or comparisons.

read the letter

The main move here is a reversal of the authors' earlier work. Instead of using biosignatures to argue that lifelike cellular automata qualify as living systems, the paper now points to the extended persistence of certain GoL configurations and suggests this trait indicates temporal retention of information as a general biosignature idea. That flip is the only clear new element on offer. The observation that GoL supports long-running evolutions is accurate and draws on a well-known feature of the ruleset, but the paper does not develop it further with any fresh analysis. It stays at the level of conceptual suggestion and loops directly back to the authors' previous publications on the same framework. No quantitative measure appears for what counts as retained information, such as a calculation of state compressibility over time or mutual information between successive configurations. There is also no check against other cellular automata rulesets or deterministic systems to show whether the trait is distinctive rather than just a side effect of the specific update rules and initial conditions chosen. The argument therefore rests on assertion plus self-reference rather than independent support. Readers already invested in the authors' series on lifelike CA as livingness might see this as a consistent next step in their line of thinking. Anyone outside that narrow circle, including people working on actual biosignature detection or complexity measures, will find little to use because the claim lacks testable content or external grounding. I would not bring the paper to a reading group or cite it. It does not contain enough substance or rigor to justify sending it out for peer review.

Referee Report

3 major / 0 minor

Summary. The manuscript reverses the authors' prior argument that lifelike cellular automata (specifically Conway's Game of Life) exhibit livingness via outlier traits, instead treating the known longevity of certain GoL evolutions as direct evidence that 'temporal retention of information' constitutes an informational biosignature. The central claim is presented at a high conceptual level without formal definitions, metrics, or cross-system tests.

Significance. If the proposal were developed with a rigorous, falsifiable metric for temporal retention (e.g., mutual information across state trajectories or compressibility measures) and shown to be distinctive rather than rule-specific, it could contribute to discussions of biosignatures in artificial and informational systems. As written, however, the absence of any quantitative grounding or independent validation limits its immediate impact.

major comments (3)

[Abstract] Abstract: The notion of 'temporal retention of information' is introduced solely by reference to 'very long-lasting evolutions' in GoL, yet no operational definition is supplied (e.g., via mutual information I(S_t; S_{t+k}) for lag k, Kolmogorov complexity of the space-time diagram, or any other information-theoretic quantity). Without this, the claim that longevity encodes retained information rather than being a neutral consequence of the deterministic rule cannot be evaluated.
[Abstract] Abstract and introduction: The argument is explicitly constructed as a reversal of the authors' earlier publications on lifelike CA as bona fide livingness. This creates a circular dependency: the biosignature status of temporal retention is asserted to follow from the same outlier trait previously used to support livingness, without providing external grounding or comparison to other deterministic dynamical systems (e.g., other CA rulesets, logistic maps, or Turing machines) that would establish distinctiveness.
[Abstract] The manuscript supplies neither a quantitative metric for retention nor any error analysis, data, or specific examples of how the trait would be measured or falsified. This renders the central claim an assertion rather than a demonstrated result, directly undermining the proposal that longevity qualifies as a biosignature.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive report and for identifying areas where the conceptual proposal requires greater formalization. We address each major comment below and commit to revisions that add operational clarity and comparative discussion without altering the manuscript's core reversal of our prior logic.

read point-by-point responses

Referee: [Abstract] Abstract: The notion of 'temporal retention of information' is introduced solely by reference to 'very long-lasting evolutions' in GoL, yet no operational definition is supplied (e.g., via mutual information I(S_t; S_{t+k}) for lag k, Kolmogorov complexity of the space-time diagram, or any other information-theoretic quantity). Without this, the claim that longevity encodes retained information rather than being a neutral consequence of the deterministic rule cannot be evaluated.

Authors: We agree that an explicit operational definition is needed to move beyond the conceptual framing. In the revised manuscript we will define temporal retention operationally as the sustained persistence of non-trivial, non-periodic structures across multiple time scales in the space-time diagram, and we will relate this to information-theoretic notions such as the decay rate of mutual information between states separated by large lag k. This will allow direct evaluation of whether longevity reflects retained information rather than a generic property of the rule. revision: yes
Referee: [Abstract] Abstract and introduction: The argument is explicitly constructed as a reversal of the authors' earlier publications on lifelike CA as bona fide livingness. This creates a circular dependency: the biosignature status of temporal retention is asserted to follow from the same outlier trait previously used to support livingness, without providing external grounding or comparison to other deterministic dynamical systems (e.g., other CA rulesets, logistic maps, or Turing machines) that would establish distinctiveness.

Authors: The reversal is intentional and does not create circularity: the prior work used the trait to argue for livingness within a specific ruleset, whereas the present work extracts the trait itself as a candidate biosignature that could apply more broadly. We nevertheless accept that external grounding is required. The revision will add a dedicated subsection comparing long-term pattern persistence in GoL to other elementary cellular automata, the logistic map at the edge of chaos, and simple Turing-machine simulations, thereby showing that the informational interpretation is not rule-specific. revision: yes
Referee: [Abstract] The manuscript supplies neither a quantitative metric for retention nor any error analysis, data, or specific examples of how the trait would be measured or falsified. This renders the central claim an assertion rather than a demonstrated result, directly undermining the proposal that longevity qualifies as a biosignature.

Authors: The current version is deliberately conceptual and therefore lacks quantitative metrics and falsification protocols. We will revise by supplying concrete GoL examples (e.g., the persistence statistics of methuselahs), proposing a simple retention metric based on the half-life of pattern complexity in the space-time diagram, and stating explicit falsification criteria (e.g., absence of retention when initial conditions are drawn from a maximum-entropy ensemble). Full error analysis and large-scale statistics will be noted as directions for follow-up work. revision: partial

Circularity Check

1 steps flagged

Biosignature claim constructed as reversal of authors' prior self-referential framework on CA livingness

specific steps

self citation load bearing [Abstract]
"Previous publications by the authors put forward the argument that Lifelike Cellular Automata can be treated as a bona fide example of livingness in and of themselves, not simply a toy analogue to biological life. Traits known to be indicative of biological life, biosignatures, were identified in informational form as particular outlier traits of the ruleset for the lifelike cellular automata known as Conways Game of Life. This publication reverses that logic, looking at a known outlier trait of Conways Game of Life, its very long-lasting evolutions, and using this to point towards temporal re"

The new biosignature proposal is defined as the reversal of the authors' own prior claim that lifelike CA are livingness. The 'prediction' that long evolutions indicate temporal retention of information therefore inherits its status as a biosignature directly from the self-citation rather than from any independent derivation, metric, or external comparison shown in the text.

full rationale

The paper's central derivation explicitly reverses the authors' own previous publications that treat lifelike CA as bona fide livingness and identify biosignatures in their outlier traits. This reversal supplies the justification for elevating GoL longevity into a new 'temporal retention' biosignature concept. No independent formal definition (e.g., mutual information or trajectory compressibility), cross-CA comparison, or external falsifiable benchmark is supplied to ground the claim outside the self-citation chain. The load-bearing premise therefore reduces directly to the authors' prior unverified framework.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the unproven domain assumption from the authors' prior work that lifelike CA exhibit bona fide livingness, plus the ad hoc introduction of temporal retention without independent evidence or quantification.

axioms (1)

domain assumption Lifelike Cellular Automata can be treated as a bona fide example of livingness in and of themselves
Invoked in the abstract as the foundation from previous publications that this work reverses.

invented entities (1)

temporal retention of information no independent evidence
purpose: Informational biosignature derived from long-lasting evolutions
Newly proposed concept with no independent evidence or falsifiable handle outside the paper's framing.

pith-pipeline@v0.9.0 · 5387 in / 1366 out tokens · 41853 ms · 2026-05-10T03:38:24.351370+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

9 extracted references · 8 canonical work pages

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