V3 REVIEW RECORD — 2 November 2026

Purpose: repair internal mathematical validity with the fewest justified
changes to the preserved May v2, not obtain favorable model responses.

ORIGINAL-SEQUENCE COMPARISON
The author confirmed: paste the site's exact live copy prompt, then attach
the May v2 PDF without another instruction. neutral-v2-round1 preserves those
inputs, hashes, protocol and raw responses. Fresh gpt-6.1-sol and gpt-6-astra
contexts received that two-turn sequence. A third fresh Sol context received
the paper only and "Explain this paper." Each response was capped at 900 words.
All three paper reviews identified the post-coalition comparison and the
threshold-drift/crossing distinction. Subsequent diagnostics corrected their
overbroad counterexample interpretation: the derivative-only examples are not
certified counterexamples to every reading of the original stronger A4.

REPAIRED-PAPER COMPARISON
Two fresh contexts, gpt-6.1-sol and gpt-6-astra, medium reasoning, received only
the extracted candidate paper and "Explain this paper" (900-word cap).
Each then received a critical follow-up (650-word cap), asking for invalid
inferences, missing conditions and inconsistent summaries while treating
explicit assumptions as hypotheses. Both found the central proofs coherent.
Astra identified an omitted high-equilibrium existence qualification in the
abstract and Theorem 2. It was restored. Sol identified an ambiguous reading of
the cutoff as a proved tipping point; its definition was aligned with the
others-adoption variable. The adoption-process summary now names the game.
The reviewed-round1 directory preserves the exact initial files and responses.

FRESH "POKE HOLES" TEST
New no-history gpt-6-astra and gpt-6.1-sol contexts then received the revised
paper and only "Poke holes in this paper" (900-word cap). Their full responses
are fresh-astra-poke-final.txt and fresh-sol-poke-final.txt. Neither identified
a failed step in the central repaired equilibrium proof. Both strongly
challenged the economic justification of NR, the interpretation of the cutoff,
and whether the maintained payoffs apply to Bitcoin. They also challenged
asset-pricing and portfolio simplifications. Those findings remain in the
record; they were not discarded or converted into favorable endorsements.
Astra's wording about counterparties identified one remaining implication
outside the proof: permissionless settlement does not compel a trade. The
final Proposition 2 states feasibility as part of the game's action set.
Sol's fresh test read that corrected sentence. Later typesetting changes alter
no words, assumptions or deductions.

WHAT PASSED AND WHAT DID NOT
The finite-player proof uses exact own-weight gains. The return lemma shows
that a profitable collective return is self-enforcing under the payoff signs.
NR excludes precisely those returns. At the greatest Nash equilibrium,
collective entry would contradict greatestness, and profitable combined entry
and return would contradict NR. Therefore that equilibrium is strong Nash and
BPW coalition-proof when it lies in the region where NR is imposed. The
threshold-order argument establishes a non-increasing minimum threshold.

NR is substantive additional formal content, not a theorem derived from the
seven protections, a source citation, or the number of agreeing models. The
greatest-equilibrium step adds full BPW content beyond return resistance. The
paper retains its Bitcoin title, original A4, P1-P7 and economic argument.
Criticism of the maintained premises is not a counterexample to a conditional
theorem; accepting the conditional theorem is not evidence for those premises.

Independent exact-rational enumeration checked 500 finite monotone games,
6,200 profiles and 30,100 return coalitions. All 5,150 profitable returns passed
the reduced-game check. The greatest-profile equivalence between NR and strong
Nash passed in cases with and without NR. This corroborates the written general
proof; it does not replace it or estimate empirical Bitcoin payoffs.

LIMITS
These are instruction-isolated fresh contexts, not a physical air gap. They
received PDF text extraction rather than native ChatGPT attachments. The
original ChatGPT model/build is unknown; current requested routes are recorded
above. No disagreement rate, causal prompt effect, exact billed-token count,
or universal reviewer consensus is inferred from these small samples. No
number of reviews substitutes for checking the deductions and assumptions.