# Verification report

Date: 2026-08-30

## Result

`PASS` - the source compiles and all three PDF pages pass visual review.

## Mathematical audit

- The normalized null bundle is compact because it is closed in the unit
  tangent bundle of an auxiliary Riemannian metric over compact M.
- Null completeness supplies a complete affine null geodesic for every
  normalized null initial condition.
- Differentiating the asserted affine formula makes
  `(nabla_v eta)(v)` nonzero on the whole normalized null bundle.
- Compactness upgrades pointwise nonvanishing to a uniform positive lower
  bound for its absolute value.
- Degree-two homogeneity gives a uniform h-speed bound along a fixed complete
  null geodesic.
- The compact norm bound for eta then contradicts nonzero affine growth on R.
- The affine reparametrization law changes the slope by a nonzero square, so
  nonvanishing is scale-independent.

## Claim boundary

Only the exact Burns--Matveev nonzero-slope question is resolved. The paper
does not claim that every projective vector field is affine in arbitrary
indefinite signature.

## Reproducibility

The proof is symbolic and has no computer-dependent step. See
`reproducibility/README.md`.

## Build and PDF QA

- Engine: Tectonic 0.17.0 with BibTeX
- Pages: 3, US Letter (612 x 792 pt)
- Undefined references/citations: 0
- Overfull/underfull boxes: 0
- LaTeX errors: 0
- Visual inspection: all 3 pages at 144 dpi; formulas, theorem text,
  bibliography, margins, and page numbers are legible and unclipped

## Public release and license

The author approved public release on 2026-09-02. This paper, its source files, and this verification report are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0): https://creativecommons.org/licenses/by/4.0/