Power Concavity of Low-Dimensional Unimodular Fiber Counts
Scott Schubr — October 22, 2026

Contents
  Paper.pdf: complete strengthened mathematical manuscript.
  main.tex: complete editable source and bibliography.
  verify_counterexample.py: optional exact lattice-witness checker.
  README.txt: reader and build instructions.
  CITATION.bib: citation metadata.
  SHA256SUMS.txt: checksums of every other package member.

The paper proves corrected planar count concavity, sharp leading
large-count exponents, continuous type-A3 power4/13 concavity and block
logarithmic Jensen. It also proves exact cube-root failures on integral K4
demands, including full-dimensional fibers. The best lattice-only K4 power
lies between4/13 and the positive root of2*13^alpha=1+51^alpha, below1/3;
its exact value and general higher-dimensional Jensen remain open.

Build with `tectonic main.tex`, or run `pdflatex main.tex` twice using a
standard LaTeX distribution with the packages named in the source. No
external bibliography, figures or datasets are required.

Optional check: `python -B verify_counterexample.py` (Python3.9+, standard
library). It prints exact counts and integer-cube checks, writes no files,
and retains its checks under `python -O`. The mathematical proofs are
self-contained and do not depend on the checker or numerical searches.

Classical geometry and chamber enumeration are credited in the paper.
Internal AI-assisted checks are not external refereeing or formal proof.
