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

results/speciation_real/README.md

@@ -29,9 +29,11 @@ Statistically reproducible (seeded); the alignment itself is deterministic NumPy
 - **`independent`**: the barrier is a coordinate artefact — permutations already remove ~98%, and the
   full symmetry group confirms (residual 0.001). The aligned merge performs **at parent level**
   (0.960): same species, different basis.
-- **`conflict`**: the full symmetry group removes essentially nothing (0.502 → 0.497). The residual is
-  **functional**, not a missed symmetry — and the hybrid is functionally dead (accuracy 0.037).
-  Because the same aligner erased the independent-init barrier, this cannot be a failure to align.
+- **`conflict`**: permutation+rescaling alignment removes essentially nothing (0.502 → 0.497), and the
+  hybrid is functionally dead (accuracy 0.037). The tested alignment removes the same-task barrier but
+  leaves the conflict-associated barrier largely unchanged — supporting a functional-conflict
+  interpretation without proving optimal alignment (control recovery validates a special case;
+  removable = lower bound, residual = upper bound).
 - Formal floor (SI note S1, `paper/si-notes.md`): for label maps conflicting on mass `μ(S)`, *any*
   single merged model errs at rate ≥ `μ(S)/2` against at least one parent, under *any* alignment
   group and merge operator — hybrid disadvantage is information-theoretic, and endpoints/chord are