The v3 repair makes the coalition argument substantially more defensible. The main vulnerability is now the distance between the conditional mathematics and the economic claim of Bitcoin dominance.

1. **The strongest persistence result is assumed.** NR says that every returning coalition contains someone who would not strictly benefit from returning. That is precisely the absence of a strictly profitable return coalition. The paper acknowledges this equivalence, so it is not a hidden mathematical error. But the economic burden remains: why should Bitcoin satisfy NR? Neither cryptographic security nor individual switching costs establishes an inequality comparing current payoffs with payoffs after coordinated abandonment. Give primitive, independently defensible conditions that imply NR, and show when they fail. Otherwise the central persistence result amounts to: adoption persists if collective abandonment is unprofitable.

2. **The “critical mass” is not a tipping threshold.** The minimum individual threshold identifies the easiest allocator to attract, measured in *others’* adoption. It does not identify a basin boundary, a cascade threshold, or the adoption level at which NR begins to hold. Calling it critical mass lends it economic significance that the definition does not establish. A small enthusiastic allocator can drive this minimum toward zero while almost all capital remains unwilling to exit. Derive a collective threshold from the weighted best-response map, or call this the minimum individual threshold.

3. **Existence of an attractive equilibrium does not imply adoption reaches it.** Consider two equal-weight players with reduced payoffs

   uE(p) = 2p − 1.5; uS(p) = −0.1p.

   These have the payoff slopes used by the proof. All-Stay is a strict Nash equilibrium: exiting alone pays −0.5 rather than 0. All-Exit is also strict Nash: staying alone pays −0.05 rather than 0.5. At all-Exit, NR holds even for the grand coalition, whose return would pay 0. The minimum threshold is 5/21. Thus the high equilibrium can satisfy the persistence condition while the economy stays indefinitely at zero adoption. Monotonically decreasing thresholds need not fall far enough to change that. The revised theorem admits this, but the introduction’s causal story and the dominance label still suggest more than equilibrium existence and conditional stability establish.

4. **Network usefulness is conflated with investment return.** M1 assumes that expected real returns increase with adoption. Greater liquidity or usefulness need not imply greater *prospective* returns: an acquisition price can already capitalize those advantages. The model contains no price formation, seller behavior, or market clearing to distinguish appreciation during adoption from expected returns after adoption. This omission matters especially for a fixed-supply asset. Derive M1 in an asset-pricing model, or identify it explicitly as a contested economic premise rather than a consequence of network effects.

5. **The comparison suppresses the strongest alternatives.** Stay combines cash, bonds, equities, and other claims under one return, while §3.5 asserts persistently negative real returns. An inflation tax wedge does not by itself establish that productive assets have negative total real returns. Binary, whole-capital choices also exclude diversification, liability matching, and partial Bitcoin exposure. Removing volatility does not make risk a money illusion; rational allocators can care about drawdowns, consumption timing, and collateral constraints. The claimed conclusion needs to survive a portfolio model with distinct assets and state-dependent risks.

6. **Bitcoin’s institutional properties are premises, not demonstrated closures.** Secret-key control does not establish immunity to physical coercion; permissionless protocol participation does not establish practical access under every legal regime. Computational hardness alone establishes neither an honest mining majority nor cheap settlement during congestion. P7 also assumes successful adaptation without modeling the governance needed to achieve it. These distinctions matter because properties presented as closing attack channels support the economic interpretation of NR. The mining discussion likewise cannot dismiss attacks generally by arguing that a large short position would be difficult: an attacker’s objective need not be trading profit.

7. **The ratchet and Bitcoin identification need independent content.** Thresholds fall because threshold ordering and monotonic macro states are maintained. Allowing “short-horizon reversals” while leaving the structural horizon unspecified makes contradictory observations easy to relabel. Specify measurable state variables, horizons, and observations that reject the restrictions. Finally, Theorem 2 bundles generic game results after Definition 1 has already designated Bitcoin as neutral settlement. It does not compare Bitcoin with competing neutral assets or establish the exclusivity conditions deferred to future papers. The defensible contribution is a conditional coordination-game result; Bitcoin’s comparative dominance remains an additional empirical and institutional hypothesis.