Optimal concavity powers for lattice counts on smooth toric Fano threefolds
Scott Schubr, Luminary Oddities. October 24, 2026.

Paper.pdf contains the complete mathematical argument. Its individual optimal powers concern ordinary real Riemann-Roch count polynomials, while the split-bundle section separately treats exact logarithmic lattice-row extensions. The preceding public edition is available at https://research.luminaryoddities.com/concavity-of-lattice-counts-on-toric-threefolds/v/2 .

Build with a compatible LaTeX installation, or Python 3.10+ and Tectonic:

    python build.py --tectonic tectonic --output-dir ../build-output

The helper creates a new directory and fixes the PDF timestamp. With the same compiler and dependencies, build-output/main.pdf reproduces Paper.pdf.

Supplementary exact certificates (Python standard library only):

    python verify_fano.py > ../fano-results.json
    python verify_bundle.py > ../bundle-results.json

The same commands support Python's -O flag; all explicit acceptance checks remain active. The Fano checker reads fan_data.json, validates all eighteen smooth Fano fans and their inequivalence, reconstructs complete nef cones and Brion count polynomials, and checks the full coefficientwise Hessian-determinant power certificates and sharp-ray identities. The bundle checker verifies the displayed exact prefix identities. Fanography/GRDB supply input arrays; the article explains how the validated fans and the classical eighteen-type classification establish coverage. Finite direct count replays are consistency checks; full symbolic certificates and the analytic arguments support the universal conclusions.

Keep generated outputs outside this source folder. SHA256SUMS.txt lists every other public package member and excludes itself.
