# Verification report

## Result and scope

The written proof gives all integral reconstructions from two fixed distinct-center cameras, provided the integral image curves are not epipolar lines, over an algebraically closed characteristic-zero field. For a normalized fiber-product component, the degree is h + deg max(B_X,B_Y). It also proves the camera-center base-divisor corrections, the baseline one-cycle formula, the reduced residual saturation statement and the sharp degree interval max(m,n) through m+n-1 when both moving pencil degrees are one.

The source record AIM-ALGEBRAIC_GEOMETRY-0185 is not marked wholly resolved. Real visibility and depth, arbitrary reducible or nonreduced inputs, a general smoothness classification and the full baseline primary ideal are outside the statement. The familiar twisted-cubic example is not counted as a new counterexample.

## Proof audit

The originating researcher performed the detailed self-audit in `reproducibility/proof_audit.md`: ordered pencil identifications; normalization of a possibly singular fiber product; absence of common zeros in the four triangulation sections; birationality and exhaustiveness; camera-center divisors; ramification indices; generic reducedness and absence of embedded components; and basepoint-free sharpness constructions. No unresolved mathematical gap was identified within the stated hypotheses. This is not an independent referee report or proof-assistant certification.

## Exact regression checks

The included Python/SymPy checker uses exact rational or integer arithmetic and explicit runtime checks. Normal and optimized Python runs agree byte for byte:

- Six named saturated-ideal and Hilbert-degree examples.
- All 81 pairs of monomial cones from positive coprime exponent pairs with each total at most five.
- All 285 degree-spectrum constructions for image degrees between one and nine.
- 9,216 local ramification/base-order identities.

These finite checks support the implementation and examples; the manuscript supplies the general proof. Reproduction commands are in `README_submission.md`.

## Sources and novelty

The original AIM question was verified in the retained, hash-checked source page retrieved on 15 October 2026; a fresh fetch on 23 October timed out. Relevant full texts of Kaminski--Fryers--Teicher (2005), Rydell--Sundelius (2024), and Ballico (2024) were read, and the critical theorem/example pages were visually checked. Classical constructions are credited. A targeted search did not locate these exact combined base-divisor statements, but absence from a bounded search is not a novelty or priority certificate.

## Manuscript verification

The six-page English PDF was compiled successfully with the built-in compiler and Tectonic. Every page was rendered and visually inspected. There are no overfull boxes, undefined references or missing characters. One harmless underfull bibliography box remains. The submission preparation script additionally rebuilds the extracted source ZIP, compares page content streams and extracted text, and replays both checker modes before recording acceptance. Its receipts and SHA-256 bindings are retained with the local publication checkpoint.

Third-party full texts are retained only in the research archive and are not included in the upload. The paper is an unrefereed preprint. No new external publication is implied by this verification report.