Certificate archive for: A computer-assisted lower bound for Landau's constant

Certificate archive for "A computer-assisted lower bound for Landau's constant" (Frank Wikström, Lund University).

This archive is the computer-assisted part of the proof of the lower bounds B_inf > 0.51 for the locally univalent Bloch constant and L > 0.51 for Landau's constant, improving the bound 1/2 + 2·10^-8 of Chen and Shiba (2004). The manuscript is distributed separately and is not part of the archive.

The certified statement is that each of the 1179 boxes of a finite cover of the normalized logarithmic coefficient body admits a schlicht disc of radius greater than 0.51. The smallest certified radius over the cover is [0.5100305329006052049176652 ± 4.18e-26], obtained with Arb ball arithmetic at 80 decimal digits.

Contents (3.2 GB, single top-level folder landau-certificate-051/):
- the cover manifest landau-cover-split-051-caps.json: the binary tree with exact dyadic splits, contractions and LP caps with their dual vectors, the 776 sources with SHA-256 digests, and the exact shift of every leaf;
- the 776 certificate sources: cut descriptors, radial grids, angular arcs, sparse non-negative dual multipliers and curvature duals;
- the reference verification run: twelve shard logs with the enclosure of every leaf, their transcripts, and the aggregation output;
- the snapshot of the checker that produced those logs, with a SHA-256 inventory and a provenance record binding the logs to the manifest and the checker;
- rejection tests, the search scripts that built the manifest from the stored sources, a pinned environment (CPython 3.12, python-flint 0.9.0, numpy 2.5.1, scipy 1.18.0), and the expected output of every command.

The checker reconstructs every inequality from the stored exact data and does not call a linear programming solver or trust any stored numerical value; the floating-point search that found the multipliers is included for reuse but is not part of the proof. README.md gives three commands: aggregate the archived shard logs (about half a minute), verify a single leaf (a few minutes), and rerun the complete verification (about two hours on twelve cores).

Released under the MIT License. Version 1.0.0.