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Fig. 1: colour-separate theory from AI tiers; explain every empty cell

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Category separation per GG: population genetics stays blue, both AI tiers move
to shades of orange, with a wider gutter between the theory column and the AI
pair. The grounding x LLM cell is upgraded from "not tested" to "established
at LLM scale in prior work (21, 30); not re-run here" (Shumailov's Nature
collapse result; Gerstgrasser's real-data rescue) - it was never a gap, it was
already settled. The caption now states the fill principle: each claim is
tested at the cheapest tier that can falsify it; a costlier tier is entered
only where it adds a discriminating test, and the LLM society is the one
genuinely open cell.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v
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Giorgio Gilestro 2026-09-07 11:35:59 +01:00
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@ -20,7 +20,7 @@ An operator of a model population faces recurring decisions for which there is n
\begin{figure*}[p]\centering % fig1
\includegraphics[width=\textwidth]{figs/fig1.pdf}
\caption{The experimental programme. Each population-genetic abstraction (Table 1) is tested at up to three tiers, ordered left to right by increasing realism: an exact Wright--Fisher simulator over knowledge distributions (closed forms; bitwise-reproducible), trained neural networks measured against exact oracles (recurrent, feedforward, and variational-autoencoder generators on a synthetic mode universe, and a convolutional VAE on MNIST), and language models (LoRA specialists on Qwen bases at 0.5B and 7B, scored by an exact-match verifier). The same population-genetic abstractions are carried across the three tiers. Rows are the framework's mechanisms, each defined at the left margin; filled cells name the experiments run at each tier; dashed cells were not tested, and the composed society at language-model scale is the paper's stated gap.}\label{fig1}
\caption{The experimental programme. Each population-genetic abstraction (Table 1) is tested at up to three tiers, ordered left to right by increasing realism: an exact Wright--Fisher simulator over knowledge distributions (closed forms; bitwise-reproducible), trained neural networks measured against exact oracles (recurrent, feedforward, and variational-autoencoder generators on a synthetic mode universe, and a convolutional VAE on MNIST), and language models (LoRA specialists on Qwen bases at 0.5B and 7B, scored by an exact-match verifier). Colour separates the two categories: the population-genetic theory tier in blue, the two AI-model tiers in oranges. The same abstractions are carried across all three. Rows are the framework's mechanisms, each defined at the left margin; filled cells name the experiments run at each tier. Each claim is tested at the cheapest tier that can falsify it, and a costlier tier is entered only where it adds a discriminating test rather than a replication: grounding at language-model scale is established in prior work (21, 30) and is not re-run; epistasis and the society skip the middle tier, whose distinctive value (exact oracles) does not bear on those operator-level questions; and the society at language-model scale is the integrative experiment this paper specifies but does not run --- its stated gap.}\label{fig1}
\end{figure*}
\section*{The minimal model, and where its exactness ends}