# Panel review: Étale covers with a prescribed exterior sheet

Independent model assessments of the frozen manuscript. Model conclusions are not human proof grades.
Each model received only the supplied manuscript; external-reference inspection was not enabled.
Baseline-v2 and source-first-v2 share the typed reference schema and differ in experimental review strategy.

| Model | Effort | Profile | Outcome | Estimated usage USD |
| --- | --- | --- | --- | ---: |
| gpt-6.1-sol | high | baseline-v2 | completed | 0.057628 |
| gpt-6.1-sol | high | source-first-v2 | completed | 0.080128 |
| claude-opus-5-5 | high | baseline-v2 | completed | 0.267084 |
| claude-opus-5-5 | high | source-first-v2 | completed | 0.248338 |
| claude-fable-5-1 | high | baseline-v2 | completed | 0.797760 |
| claude-fable-5-1 | high | source-first-v2 | provider_failed_or_incomplete | 0.885020 |
| gemini-4-argon | high | baseline-v2 | completed | 0.238686 |
| gemini-4-argon | high | source-first-v2 | completed | 0.230734 |

## Returned findings

### gpt-6.1-sol / baseline-v2

The internal proof is coherent and the component, graph, and group-theoretic calculations withstand checking; no demonstrated mathematical error or circular dependency was found. Its validity rests on explicitly identified external inputs, especially the strong positive-genus resolution formulation, and this review does not independently certify those references. The construction genuinely handles all prescribed disks simultaneously without shrinking them.

### gpt-6.1-sol / source-first-v2

The supplied manuscript has a coherent proof, and no demonstrated mathematical error or indispensable internal gap was found. Its conclusions follow relative to the explicitly stated imported results, especially the positive-genus resolution theorem; the external publications and their precise theorem locators were not independently audited.

### claude-opus-5-5 / baseline-v2

The argument is coherent and I found no mathematical errors. The cycle count, the retraction-fibre argument at a type-three point, and the final stabilizer group theory all check out. The main reservation is that the construction depends on a paraphrased external positive-genus RNS statement whose exact hypotheses I could not verify, and some model-theoretic steps (Galois refinement, descent of the resolution cover to \bar k) are terse.

### claude-opus-5-5 / source-first-v2

The argument is coherent and each internal step checks out: the cycle-creation count, the stability of étale model covers, the type-three cut, and the stabilizer-quotient group theory. Correctness rests essentially on the imported positive-genus resolution of nonsingularities (Mochizuki–Tsujimura) and on standard GAGA and SGA1 inputs, none of which were audited here. Several routine steps are compressed, notably the descent of the residue torsor and the identification of dual graphs of étale model covers with preimage subgraphs.

### claude-fable-5-1 / baseline-v2

The paper's architecture is coherent and the group-theoretic and graph-theoretic steps (component/stabilizer calculations, Euler-characteristic counts, cut-and-glue cyclic covers, stabilizer quotient) are correct as written. The main risk lies in the imported resolution-of-nonsingularities statement, which is used in a strengthened form (positive-genus component, arbitrary proper flat normal model, model morphism) that was not inspected; several standard analytic steps (algebraization of topological covers, descent) are only sketched via citations. No demonstrated mathematical error was found.

### gemini-4-argon / baseline-v2

This is a clear, concise, and mathematically rigorous paper. The proofs of all lemmas, propositions, and the main theorem are complete and logically sound, combining deep arithmetic input (Mochizuki-Tsujimura resolution of nonsingularities) with clean Berkovich-analytic and group-theoretic arguments.

### gemini-4-argon / source-first-v2

This is a clear, well-written, and mathematically rigorous paper. The combination of the Mochizuki-Tsujimura resolution of nonsingularities theorem, prime-to-p special-fibre torsors to generate local skeletal cycles, type-3 skeletal cuts to build degree-p covers trivial over the exterior, and an elementary finite group stabilizer quotient is executed without gaps.

## Remaining assessment

Human substantiation, localization, evidence, uncertainty and coverage grades remain pending in the separate anonymous comparison packet.
Finite output caps and failed responses are resource outcomes, not mathematical verdicts. External publications and claimed formalizations have not been independently audited.