# Verification report

## Result

The source proves that a fixed normal `F_g`-deck cover of a closed genus-`g`
surface has nonconstant critical exponent on its quasiconformal Teichmuller
space. Every finite metric has exponent below one, while simultaneous
pinching of the killed cut curves produces exponents tending to one with an
explicit linear rate.

## Gates checked

1. The epimorphism `pi_1(S_g) -> F_g` respects the surface relation and is
   surjective.
2. Its kernel is normal, non-elementary, infinite index, infinitely generated,
   and has the full circle as limit set.
3. Marked quasiconformal maps of the compact base preserve the fixed kernel
   and lift, so all compared groups lie in one `T_qc`.
4. Brooks's theorem applies exactly: compact base, regular cover,
   nonamenable deck group.
5. The Elstrodt--Patterson--Sullivan spectral formula is used on the correct
   branch after the Rayleigh quotient is below `1/4`.
6. The cut-open cell embeds because its fundamental group is generated by
   boundary classes killed by the quotient.
7. Each of the `2g` transition half-collars contributes exactly
   `ell sinh(1)` to both strip area and Dirichlet energy.
8. The denominator lower bound and the constants in both displayed rates
   were recomputed independently.
9. Amenable quotients, pinching non-kernel curves, and confusion between first
   kind and exponent one were tested as likely failure modes.

No critical proof gap survived the audit. No computation is needed for the
general theorem; the verification is symbolic.

## Novelty and artifact status

The final direct-prior search through 2026-09-02 did not locate the fixed-kernel
pinching argument or linear rate. Novelty confidence remains low because all
ingredients are classical and the synthesis may be folklore. No absolute
priority claim is supported.

- Mathematical dossier: complete
- Literature and direct-prior audits: complete through 2026-09-02
- LaTeX/BibTeX build: PASS, five letter-size pages, zero warning classes
- Symbolic proof audit: PASS; no computation is used by the theorem
- Direct 144-DPI visual inspection: PASS on all five pages
- Upload archive: PASS; English paper sources and reproducibility notes only
- Public Zenodo/EulerSolve release: approved on 2026-09-02 under CC BY 4.0; arXiv status is separate

## 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/