# Verification report

Work: Exact Small-Softness Stabilization of Euclidean Lattice Packings.
Author: Alper Ferudun, Mercury Software GmbH. Date: 9 October 2026.

The general proof was checked step by step in the originating researcher's
self-audit. Its key ingredients are the exact pair-overlap formula,
vanishing lens slope, positive linear covolume margin on the feasible
Gram cone, uniform local optimality, Mahler compactness, and the final
minimum-kissing-number selection. The full audit is included in the
source archive. No unresolved gap was found in the stated theorem.

The standard-library Fraction checker passed 18,218 checks in normal and
optimized Python, with identical output bytes. It checks 1,701 rational
FCC-cone matrices, 2,112 lens-distance cases, polynomial coefficients,
shell completeness and local constants. Negative controls cover the
excluded one-dimensional and cubical-norm settings, an infeasible
trace-zero strain and an incorrect pair-counting factor. Finite tests
are regression evidence, not a proof of the general result.

The six-page English PDF compiled successfully with the desktop LaTeX
compiler and Tectonic. All six rendered pages were inspected, including
equations, references, author footnote and the prose AI disclosure.
No unresolved references, overfull boxes or visual defects were found.
Package hashes and portable rerun results are recorded in the manifests.

Scope: every fixed Euclidean dimension d >= 2, Bravais lattices only,
sufficiently small positive softness. FCC is uniquely optimal in
dimension three. The global threshold is existential; 1/200 and 1/16
certify only a local FCC comparison. The source's nonlattice conjecture
and the full open-ended AIM Stability record remain unresolved here.

The work is unrefereed. There has been no independent review or
proof-assistant certification. Earlier local FCC optimality and all
classical inputs are credited. A bounded current search did not locate
an identical global theorem, but does not certify absolute priority.