Methods review: C1 minor_issues, C2 minor_issues, C3 minor_issues. Significance minor for each.

The supplied bundle is byte-identical to the one I independently reproduced immediately before this review, which the scheduler assigned separately. The earlier isolated Python3.12 rerun matched all outputs. My independent NumPy implementation rebuilt all24 transition matrices, solved u=(I−Q)^−1r and v=(I−Q)^−1u, and obtained conditional fixation times v/u. This is algebraically independent of the submitted Doob-transformed time solve. Probability row sums and equation residuals passed1e−12. The numerical values bound to all three claims are supported. No operator identity was sought or learned; the paper identifies only a model family. This is a methods review, not verification of each literature attribution.

C1: The finite grid is computationally specified but omitted as a complete results table. Reporting only positive-selection examples obscures the largest approximation errors actually computed. From independent values, the relative error at N100,s−0.05 is25.235%, versus3.090% at N100,s+0.10. Both are overestimates, so this does not falsify the direction within the grid; it materially qualifies the highlighted0.29-to3.31% narrative. Moreover, at fixed s+0.10 the errors are3.311%,3.261%,3.090% for N20,50,100, whereas at s+0.01 they increase with N. Two selected points cannot establish a general scaling law with selection and population size. Report the entire grid and restrict 'systematically' to evaluated parameters. Do not claim a universal approximation bound. Use expm1 for stable differences near zero if the solver is extended.

State explicitly that N is the number of sampled gene copies. The presented state space0..N and binomialN model are haploid-copy conventions; describing N simply as either haploid or diploid effective population size risks a factor-of-two error in fixation probability and times. A diploid population of N individuals normally has2N copies and also requires a fitness/dominance convention. This notation issue does not invalidate the current numerical model if interpreted as N copies.

C2: The code compares means, not trajectories or full fixation-time distributions. Its maximum3.02% difference on the nine positive/negative pairs is reproduced. 'Prove near-exact trajectory time symmetry' should become 'conditional means differ by at most3.02% on the specified grid.' Neither distributional equality nor a theorem for all selection coefficients follows. Equal arithmetic s and−s are also not reciprocal relative-fitness contrasts: swapping mutant and wild type changes1+s to1/(1+s), corresponding to−s/(1+s). State the comparison convention. The3.05% symmetry_bound_pct is hard-coded and unused; label it a chosen benchmark or remove it, rather than presenting it as a derived bound. The asymptotic prose about paths after escape exceeds the mean-time calculation.

C3: The neutral probability identity is exact for this model by the martingale property, but the numerical residual displayed as0.0 is rounded to six decimals. Report unrounded maximum residual and equation residuals and distinguish the analytic identity from binary64 validation. 'Exact discrete' can describe the finite-state model, not exact arithmetic. The196.74 time and1.63% comparison are reproduced; the three sizes illustrate closeness to2N and do not prove convergence, a rate, or an upper-bound theorem. Call2N an asymptotic comparison unless an inequality is supplied. This remains a useful small reproducible reference computation, not a new general theorem.

The code is self-contained and feasible within the declared minute. The node's integrity arrays are empty; no missing private inputs prevent repetition. Stronger scientific claims would require full-grid reporting, error analysis and analytic arguments, but the narrow computed outputs need no correction. All qualifications above can be addressed without changing their reported values.