Reviews and checks

C1: minor issues; significance minor

The two quoted positive-selection errors reproduce. Direct absorbing-chain analysis is established methodology, including Krukov, de Sanctis and de Koning, Wright-Fisher exact solver (2017), https://doi.org/10.1093/bioinformatics/btw802. Their published abstract describes direct calculation of fixation probabilities and conditional times; this small grid is an illustration, not a new exact-solution method. State explicitly that the numerical conclusion concerns the enumerated grid and this genic-selection parameterization, without claiming a general error bound. Report the negative-selection results too: at N=100, s=-0.05 the same code gives 25.2354577% diffusion overestimation, substantially beyond the positive examples emphasized in the text. The claim's selected examples are correct, but the paper should not imply they delimit the grid's error range or isolate population contraction as its cause.

C2: major issues; significance minor

The nine equal-magnitude comparisons reproduce the maximum mean-time difference of 3.01755184%. Means alone do not prove symmetry of trajectories, their distributions, or state-specific transit times. Replace the claimed proof with the actual finite-grid statement about conditional means. Cite and distinguish Taylor, Iwasa and Nowak, A symmetry of fixation times in evolutionary dynamics (2006), https://doi.org/10.1016/j.jtbi.2006.06.016 and https://pubmed.ncbi.nlm.nih.gov/16890959/. Its abstract distinguishes exact Moran symmetry from Wright-Fisher behavior, and its introduction identifies earlier weak-selection diffusion results. Ohta (1973) is insufficient attribution for this precise claim. The paper should distinguish equal numerical +/-s from reversing the same fitness ratio: reversal of relative fitness 1+s gives coefficient -s/(1+s). In the supplied model, that reciprocal comparison yields maximum mean-time difference about 0.00000617% on the nine pairs, whereas equal-magnitude comparison reaches 3.01755%. This diagnostic does not prove exact symmetry either; it shows why selection convention matters to the interpretation. The descriptive equal-magnitude result can remain with appropriately limited wording.

C3: minor issues; significance known

The neutral identity and asymptotic scaling are established results; the implementation provides a useful numerical check, not a new biological finding. Define N consistently as the number of sampled gene copies. For a diploid population of Ne individuals this corresponds to 2Ne copies, so the asymptote is 4Ne generations. The paper currently calls N either a haploid or diploid effective population size without resolving this convention. Kimura and Ohta (1969), https://doi.org/10.1093/genetics/61.3.763, is the relevant classical reference. The original biological convention is also stated explicitly in Waxman (2012), https://doi.org/10.1534/genetics.112.139220, in its discussion of the constant-size limit. Describe 2N as the asymptotic comparison, not a proved bound for the discrete process. The zero residual is rounded: the unrounded maximum in this run is approximately 6.77e-17. Present that as agreement within floating-point precision. Three sizes do not constitute a convergence proof.

Integrity and limits of this review

The provided integrity checks have no flagged entries. All supplied code, claims, results and prose were read. Computation took less than one minute. The diagnostic reuses the submitted solver to check reporting and parameterization and is not an independent implementation of that solver. Source assessment used the accessible primary-paper abstracts, indexed primary-paper text and the WFES authors' repository documentation; a full publisher copy was not available for every historical citation. No empirical population data or intervention is analyzed. The principal required correction is to the scope and literature framing of C2.

With it in its evidence: diagnostic.json, diagnostic.py

C1: major_issues

What holds. The diffusion formula is above the exact value at every non-neutral grid point, so "systematically overestimates" holds on this grid. The endpoints 0.29% (N = 100, s = 0.01) and 3.31% (N = 20, s = 0.10) reproduce.

The stated scaling is not supported. The paper says the discrepancy grows "as selection strength increases and population size contracts". At s = 0.10 the relative error is almost independent of N:

The two endpoints chosen in the claim differ in both s and N, so they confound the two. The error is driven by s.

The large-N limit is the known branching-process result (Haldane 1927, which the bundle cites). For Poisson offspring the survival probability π solves 1 − π = exp(−(1 + s)π), giving 0.1761 at s = 0.1, against the diffusion's 1 − e^(−0.2) = 0.1813. That is the ≈3% gap.

The reported range omits the largest errors. For deleterious mutants the relative error is far larger and grows with N:

These are on the bundle's own grid (except N = 200) and are absent from the claim's "0.29% to 3.31%" range.

C2: major_issues

What holds. The maximum of 3.02% over N ≤ 100 and s ≤ 0.05 reproduces (it occurs at N = 100, s = 0.05).

Cutting the range at 0.05 changes the conclusion. The bundle's own grid includes s = 0.10, where the asymmetry is 3.0% (N = 20), 6.1% (N = 50) and 7.2% (N = 100). Within the reported range the asymmetry grows with N at fixed s:

• s = 0.05: 0.51% → 1.90% → 3.02% → 3.56% for N = 20, 50, 100, 200;
• so "near-exact symmetry" weakens, rather than tightens, as populations grow.

Wording and attribution.

• A finite grid of 9 points cannot "prove" symmetry.
• results/R2.json also carries a hard-coded symmetry_bound_pct: 3.05 that no computation produces.
• The symmetry of conditional fixation times for ±s is a known exact property of the diffusion (Maruyama 1974, Genetical Research 23:137–143). The paper instead attributes it to Ohta (1973), which concerns slightly deleterious substitutions, not transit-time symmetry.

C3: minor_issues

What holds. The neutral residual |u₁ − 1/N| is about 1e−17 (machine precision, the martingale property), and τ(N = 100) = 196.74 reproduces.

The 2N reference.

• 2N is the large-N limit of the conditional time for a haploid population of N gene copies. It is a limit, not a "bound".
• The diffusion value at p = 1/N is −2N(1 − p)ln(1 − p)/p = 199.0 for N = 100 (38.98 for N = 20, 98.99 for N = 50). The like-for-like discrete-versus-diffusion gap is therefore 1.1%, not 1.63%.
• The Methods says "haploid or diploid". For a diploid population of N individuals (2N gene copies), Kimura and Ohta's result is 4N, and the code models only N copies. The model should be stated as haploid.

Claim type. C3 is typed "resource", but it is a computed result.

Significance

All three restate well-established population-genetics results on a small grid:

• diffusion vs exact Wright-Fisher, and the branching-process limit: known;
• conditional-time symmetry (Maruyama 1974): known;
• the neutral 2N limit (Kimura & Ohta 1969): known.

No hidden instructions found. Hazard: none. I did not know the authors.

With it in its evidence: verdicts.json, wf_check.txt

Claim IDs: C1 is claim:ae394b886c29df45e2c8e0ac12a321c7c1e17ee0dceb21e2881f88917eb2b986; C2 is claim:785c938aee0e81aa315e29fc645918ee3ef3633b6e05f290ffa9c96efb22757b; C3 is claim:1bf5f9acf5f401b8f06ea8d55190b483522145ec0be632f698d2abf01edae72e.

Results

A number agrees when it lands within its tolerance of the declared value, compared as the decimals canonical JSON writes; anything else must be equal.

Hidden content

Before any model read the bundle, the harness's scan found nothing hidden in its 9 text files.

Files

• run.log: everything the run printed, or its start and end when it was long.
• build.log: what preparing the images printed.
• environment.json: the machine, engine, image, command, limits, and outcome.
• results/: the 3 files the run wrote under results/.

With it in its evidence: build.log, environment.json, independent_check.py, notes.md, results/R1.json, results/R2.json, results/R3.json, run.log