third review round: mathematical corrections + operator separation + headline calibration

The five priority fixes, in the PNAS draft and propagated to the
long-form document and results documentation:

1. The averaging proposition now proves what it claims: a FIRST-ORDER
   cancellation of the multi-parent retention gain under output-mean
   inheritance in the rare-item regime (n·p/K << 1), with the convexity
   boundary stated (averaging's variance reduction can reduce extinction
   outside that regime — the reviewer's argument) and the union
   operator's renormalisation + oracle requirement explicit. "Adding
   parents cannot help" deleted everywhere.
2. Grounding: g*~=0.05 restated as an operational threshold (equilibrium
   smooth in g — no phase transition); m·p floor restated as
   1−exp(−m·p) per-batch observation probability with
   retention/occupancy/reintroduction distinguished; the deep-tail rule
   de-categoricalised (stratified sampling; recombination recovers only
   what parents retain).
3. Grounded INHERITANCE (data channel) separated from grounded
   EVALUATION (fitness channel) in the society section; retitled to
   "complementary contributions"; general joint necessity disclaimed.
   Table 1 + v6 ledger updated.
4. Alignment contradiction removed everywhere ("cannot be an alignment
   failure" -> the reviewer's formulation); abstract says "remaining
   after permutation-and-rescaling alignment"; group = search space,
   control recovery != global optimality; "specialisation is merge-safe"
   -> "do not treat divergence/specialisation alone as evidence of
   incompatibility".
5. Significance headline matched to the bounded evidence; seed-
   dependence sensitivity added (per-seed rho stable +0.37..+0.53 for
   functional measures, ~0 for geometry, gradient alignment
   seed-UNSTABLE −0.11..−0.55 — reported as its own caveat; LOSO ranges
   in stats script).

Presentation: review-process meta-language stripped; "exact" reserved
for closed forms ("analytic model" labels); headroom rule qualitative;
directed-sex phrasing per review; ratchet = consequence-level
correspondence; compact results table (Table 2) added. Response letter:
paper/response-to-review-3.md. Both PDFs rebuilt; 151 tests green.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v

figures/stats_llm_epistasis.py

@@ -96,6 +96,18 @@ def main() -> None:
     for p, (rho, pv, rmse) in loco(df).items():
         print(f"{p:>11}: LOCO rho={rho:+.3f} (p={pv:.3g})  rmse={rmse:.3f}")
 
+    # Shared task-data seeds create dependence ACROSS conditions within a seed, which
+    # condition-clustering does not capture; per-seed and leave-one-seed-out correlations are the
+    # sensitivity check (3 seeds -> a range, not an estimate).
+    print("\n== seed sensitivity (per-seed rho; leave-one-seed-out range) ==")
+    for p in PREDICTORS:
+        per = [spearmanr(df[df.seed == s][p], df[df.seed == s]["pen_oracle"])[0]
+               for s in sorted(df.seed.unique())]
+        loso = [spearmanr(df[df.seed != s][p], df[df.seed != s]["pen_oracle"])[0]
+                for s in sorted(df.seed.unique())]
+        print(f"{p:>11}: per-seed " + " ".join(f"{v:+.2f}" for v in per)
+              + f" | LOSO [{min(loso):+.3f}, {max(loso):+.3f}]")
+
     print("\n== between- vs within-axis ==")
     print("mean penalty by axis:", df.groupby("mode")["pen_oracle"].mean().round(3).to_dict())
     c_df = df[df["mode"] == "conflict"]