# Preprint readiness after two fresh adversarial reviews

23 September 2026. **Decision: ready to circulate as an unrefereed preprint;
zero actionable findings remain in the reviewed manuscript.** Mathematical
review completion: **100%**. This records the additional review cycle requested
after the initial publication package; it does not certify journal acceptance,
global priority, or error-free mathematics by formal proof verification.

## Independent review sequence

| Round | Primary attack | Result |
| --- | --- | --- |
| [1](preprint-round1.md) | Reconstruct the extreme-point partition; challenge geometry, countable integration, and equality rigidity | No actionable findings |
| [2](preprint-round2.md) | First reconstruct a fixed positive deficit on finite polytopes and its limit; then attack the countable proof and boundary cases | No actionable findings |

Each round used a fresh AI subagent, without earlier referee conclusions or
reasoning. Round 2 began after round 1 completed. Both checked the original
FPS/OWR statements, read the manuscript and verifier, and visually inspected
all four PDF pages. The retained-pair argument supplies an independent route
through approximation; it does not require continuity of the extreme-point
norm condition. No mathematical repair was needed between rounds.

## Disposition of every suggestion and limitation

- Round 1 requested no corrections.
- Round 2 offered two optional explanations: write a shell point explicitly
  as a convex combination to establish that its ray meets the old hull, and
  expand convergence of normalized volume moments in the finite alternative.
  These follow directly from the stated hull and bounded-integration setup.
  The coordinating reviewer checked both details and retained the concise
  manuscript. They are explained fully in the round-2 report; neither reviewer
  identifies an unsupported inference or missing assumption.
- Round 2 could not independently retrieve the live catalogue because of its
  security checkpoint. The earlier successful browser inspection is recorded
  in `source-match.md`; both fresh reviews independently matched the underlying
  conjecture to the original FPS and OWR sources. No source correction is
  indicated by this access limitation.
- The earlier bounded priority audit remains limited to its documented search.
  No claim of exhaustive priority certification has been added.

## Frozen manuscript and supporting materials

The paper stays at version 1.0.0, four pages. Its text and the verifier are
unchanged. The new work adds review reports and this disposition, and refreshes
the source archive, website downloads, and manual Zenodo kit to include them.
The Zenodo description and citation metadata still describe the unchanged
paper accurately; no new DOI, release, or deposit has been created.

Reviewed SHA-256 hashes:

- Manuscript: `ce8a48dc12ac9d80144a7de7391f2583c6d567c5d4d1067c3be122bf10283b29`
- PDF: `62982a0e0508edabbfea63f4b5dc69ffe928d7c657103ee3d31296a6393e5d8c`
- Verifier: `9896313fe2cebcd5ed0bed6aef77b649a7c369fe72a56e768d3dda28489e4764`

The coordinating review also found no baseline artifact defect: all 76
package/hash checks passed, the extracted verifier reproduced 298 exact
checks across 18 cases, and the source archive rebuilt byte for byte. The
refreshed archives are subject to a final extraction/hash/rebuild check before
delivery; its result and live deployment evidence are recorded separately in
`DELIVERY.md` in the repository, outside the frozen archive.

These are independent AI reviews, not external human peer review. Finite exact
checks support the algebra and examples; the written analytic proof establishes
the universal claim. Two sequential rounds now have no actionable findings,
so the requested review/fix cycle stops at the hashes above. A later change to
the mathematical argument would require another review.