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

paper/response-to-review-3.md

@@ -0,0 +1,96 @@
+# Response to the third review (of the PNAS-format draft)
+
+*All five priority fixes are made, plus the presentation items. The revised draft is
+`paper/pnas/main.md` (rebuilt PDF alongside); the long-form document and the results documentation
+were corrected wherever they carried the same overstatements. Point-by-point:*
+
+## 1. The averaging proposition (your §2) — you are right, and the text now proves what it claims
+
+Your convexity argument is correct: conservation of expected mass does not establish that averaging
+cannot help, because extinction is convex in mixed mass and averaging reduces its variance. Our result
+is, exactly as you diagnosed, a **first-order cancellation in the rare-item regime**, and the main
+text now states the actual proposition with its quantities and assumptions: K parents with independent
+retention; child draws `n` samples from one random parent vs the parents' output-mean; expected mass
+identical; and in the regime `n·p/K ≪ 1`, where per-item survival is first-order in sampled mass,
+expected survival is identical too. Two boundaries follow in the same paragraph: outside that regime
+averaging's variance reduction can *reduce* extinction relative to a random single parent (your
+argument, credited to the review process); and the union operator's renormalisation (which itself
+redistributes mass) and oracle requirement are stated. "Adding parents cannot help" is deleted here
+and in every other document that carried it. We agree the interesting content is the consequence for
+retention, not the elementary conservation of a mean — which is how the proposition is now framed.
+
+## 2. Grounding (your §3) — threshold made operational, floor made probabilistic, rule de-categoricalised
+
+- `g* ≈ 0.05` is now explicitly an **operational threshold**, with the text stating what our own
+  analysis always showed: the immigration–drift equilibrium is *smooth* in the grounding fraction (no
+  phase transition in aggregate diversity). New wording: under the tested population size and Zipf
+  source, `g ≈ 0.05` retained ≥95% of equilibrium diversity, with dependence on sample size, source,
+  and retention target (SI).
+- `m·p ≳ 1` is restated as what it is: `1 − e^{−m·p}` observation probability per batch (~63% at
+  `m·p = 1`), confidence-dependent, with retention vs stationary occupancy vs reintroduction
+  distinguished (immigration can restore an absent item).
+- The design rule now reads in your form: under unstratified grounding rare capabilities are expensive
+  (targeted sampling changes the cost); recombination recovers rare capabilities *still retained
+  across complementary parents*.
+
+## 3. Grounded inheritance vs grounded evaluation (your §4) — separated and named
+
+The society section now opens with the definitional distinction: **grounded inheritance** (external
+samples in the reproduction process — the data channel) vs **grounded evaluation** (true fitness vs
+conformity in selection — the fitness channel), related but different operators, connected only in
+that both couple the lineage to a non-drifting external signal. The section is retitled to your
+formulation ("…make complementary contributions"), the ablation is described as separating failure
+modes *under the tested conditions*, and general joint necessity is explicitly disclaimed (alternative
+mutation/restart/archive/selection schemes noted). Table 1's corresponding row now says
+"complementary… in the tested society"; the same fix is propagated to the long-form document.
+
+## 4. The alignment contradiction (your §5) — deleted, both statements reconciled
+
+"This cannot be an alignment failure, because the same aligner succeeded on the control" is removed
+everywhere (manuscript, long-form document, results documentation), replaced by your formulation: 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. The
+abstract now says "remaining after permutation-and-rescaling alignment" (not "surviving the full
+symmetry group"), and the Methods note that the group is the alignment's *search space*, with control
+recovery not establishing global optimality. The discussion's "expect specialisation alone to be
+merge-safe" is replaced by the supported lesson: **do not treat divergence or specialisation alone as
+evidence of incompatibility.**
+
+## 5. Headline vs detail (your §6) — matched, and the seed-dependence analysed
+
+The significance statement now ends with your suggested sentence (a controlled small-model test…
+motivating further comparison). On the clustering point: you are right that condition-clustering does
+not capture cross-condition dependence through shared task-data seeds. We added the sensitivity you
+asked for (committed to the statistics script): **per-seed correlations** — each seed alone, n = 13
+conditions — are stable for the functional measures (+0.37 to +0.53 in every individual seed) and ≈0
+for geometry in every seed; leave-one-seed-out ranges are [+0.38, +0.56] (functional) vs
+[−0.04, +0.28] (geometry). One informative surprise: gradient alignment is *seed-unstable*
+(−0.11 to −0.55), which the manuscript now reports as its own caveat. The text also states plainly
+that with three seeds, uncertainty about seed generalisation remains substantial.
+
+## 6. Presentation (your §7) — done
+
+Meta-language removed ("the honest statement", "sharpest honesty", "earn their place by tempering",
+"honest deviations" — all gone; results are stated, not described as disclosures). "Exact" is now
+reserved for closed-form mathematics — NK/simulation results are labelled "analytic model" in Table 1
+and the text. The headroom relationship is stated qualitatively with "a quantitative form is
+untested". "Directed sex with no biological analogue" is replaced by your phrasing (the shorthand kept,
+defined as engineered recombination with flexible parent choice and pre-deployment screening).
+Muller's ratchet is now a *consequence-level* correspondence, with the text stating that irreversible
+loss alone does not identify the ratchet's mechanism. A compact results table (Table 2: setting/n,
+outcome definition, headline with uncertainty, for the eight headline results) is added before the
+Discussion. Reference numbering and the figure files accompany the rebuilt PDF; the bespoke unified
+figures and journal-format reflow remain flagged as submission-time work.
+
+## One point of information, not disagreement
+
+On §2's closing remark — that conservation of an arithmetic mean's expectation is elementary and the
+contribution must lie in its consequences — we agree, and would only note that the consequence now
+stated (first-order cancellation of the multi-parent retention gain under output-mean inheritance,
+against union-operator retention growth, in the regime where the deep tail actually lives) is the
+claim we intended all along; the earlier wording claimed more than this and is gone.
+
+Your bottom-line formulation — minimal models establish conditional results; neural experiments reveal
+where the correspondences hold and break; a controlled predictive test motivates measuring functional
+conflict before merging — is now, near-verbatim, how the paper describes itself. Thank you for three
+rounds of genuinely improving review.