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

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

paper/pnas/body.tex

@@ -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}

paper/pnas/build.py

@@ -28,10 +28,16 @@ FIGURES: dict[str, tuple[list[str], str]] = {
         "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 "
+        "exact-match verifier). Colour separates the two categories: the population-genetic theory "
-        "three tiers. Rows are the framework's mechanisms, each defined at the left margin; filled "
+        "tier in blue, the two AI-model tiers in oranges. The same abstractions are carried across "
-        "cells name the experiments run at each tier; dashed cells were not tested, and the composed "
+        "all three. Rows are the framework's mechanisms, each defined at the left margin; filled "
-        "society at language-model scale is the paper's stated gap."),
+        "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."),
     "fig2": (["paper/pnas/figs/fig2.pdf"],
         "Grounding is immigration. (A) Stationary diversity against the grounding fraction in the "
         "minimal inheritance model: simulation (points, 95\\% CI) matches the exact immigration--drift "

paper/pnas/make_figs.py

@@ -50,16 +50,16 @@ def fig1():
         ("Population genetics (exact)", "Wright\u2013Fisher simulator (NumPy)", "closed forms \u00b7 bitwise-reproducible",
          "#3d7eb8", "#eaf2fa"),
         ("Trained networks", "RNN \u00b7 MLP \u00b7 VAE on a synthetic oracle;\nconvolutional VAE on MNIST",
-         "sign-level tests \u00b7 exact oracles", "#3f8f4f", "#edf8ea"),
+         "sign-level tests \u00b7 exact oracles", "#e97313", "#fdefe1"),
         ("Language models", "LoRA specialists on Qwen 0.5B & 7B;\nexact-match verifier",
-         "seed-replicated signs", "#d9650f", "#fdf0e6"),
+         "seed-replicated signs", "#b04e0c", "#fbe6d4"),
     ]
     ROWS = [
         ("Grounding = immigration",
          "fresh verified samples from a\nfixed external source enter the\ntraining mix every generation",
          ["immigration\u2013drift equilibrium:\n$g \\approx 0.05$ retains $\\geq$95% diversity;\nobservation floor $1-e^{-mp}$",
           "collapse & rescue in every\narchitecture; MNIST: dry 30$\\to$1 modes,\n10% grounding holds 30/30;\nestimator-bias learning kernel",
-          None]),
+          "LIT:established at LLM scale in\nprior work (refs. 21, 30);\nnot re-run here"]),
         ("Recombination = sex",
          "a child inherits from several\nparents, reassembling variants\nthat arose in different lineages",
          ["blending conservation law\n(first-order cancellation);\nunion-operator gain; Fisher\u2013Muller",
@@ -86,12 +86,13 @@ def fig1():
     ax.set_axis_off()
     ax.set_xlim(0, 1)
     ax.set_ylim(0, 1)
-    x0, gap = 0.205, 0.008
+    x0, gap, sep = 0.205, 0.008, 0.02              # sep: extra gutter between theory and the AI pair
-    cw = (1.0 - x0) / 3
+    cw = (1.0 - x0 - sep) / 3
+    xs = [x0, x0 + cw + sep, x0 + 2 * cw + sep]
     row_h, row_top = 0.157, 0.805
 
     for j2, (name, arch, guarantee, edge, face) in enumerate(TIERS):
-        x = x0 + j2 * cw
+        x = xs[j2]
         ax.add_patch(FancyBboxPatch((x + gap, 0.825), cw - 2 * gap, 0.155,
                                     boxstyle="round,pad=0.004", fc=edge, ec=edge, lw=1.4))
         ax.text(x + cw / 2, 0.966, name, ha="center", va="top", fontsize=9.5,
@@ -109,7 +110,7 @@ def fig1():
         ax.text(0.0, y1 - 0.054, definition, ha="left", va="top", fontsize=6.2,
                 style="italic", color="#555", linespacing=1.35)
         for j2, cell in enumerate(cells):
-            x = x0 + j2 * cw
+            x = xs[j2]
             edge, face = TIERS[j2][3], TIERS[j2][4]
             if cell is None:
                 ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0,
@@ -117,6 +118,12 @@ def fig1():
                                             lw=0.8, ls=(0, (3, 2))))
                 ax.text(x + cw / 2, yc, "not tested at this tier", ha="center", va="center",
                         fontsize=6.4, style="italic", color="#999")
+            elif cell.startswith("LIT:"):
+                ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0,
+                                            boxstyle="round,pad=0.004", fc="white", ec="#bbbbbb",
+                                            lw=0.8, ls=(0, (3, 2))))
+                ax.text(x + cw / 2, yc, cell[4:], ha="center", va="center",
+                        fontsize=6.4, style="italic", color="#777", linespacing=1.35)
             elif cell == "OPEN":
                 ax.add_patch(FancyBboxPatch((x + gap, y0), cw - 2 * gap, y1 - y0,
                                             boxstyle="round,pad=0.004", fc="white", ec=edge,