# Verification report

The four-page preprint proves essential-period rigidity for all measurable layered two-colorings, and a positive-measure nonequilateral-triple corollary stable under arbitrary planar null-set perturbations. It does not resolve the unrestricted source conjecture.

The written self-audit checks translation continuity, closed subgroup classification, antiperiod parity, the exact tilted-triangle coordinates, strict integer inequalities, finite null-set intersections, planar product measure, degenerate configurations, auxiliary vertex coincidences, reflected copies and the six-event positive-measure transfer. The classical EGMRSS gadget and prior polygonal results are credited.

The portable checker verifies 18 universal squared-distance identities for target triples and three for the equilateral base, all 64 monochromatic-base color assignments, seven exact target shapes, 10,000 odd integer regressions, and 8,190 cyclic binary words. Wrong-rotation and missing-triple negative controls are detected. Normal and optimized Python runs agree exactly. These finite tests do not replace the general proof.

The built-in LaTeX compiler and exported PDF compilation both succeed. All four rendered pages were visually inspected: no clipping, overlaps, missing symbols or unresolved references were found. The first compile encountered an unused command-name collision with LaTeX's built-in ae ligature; removing that unused definition fixed it. The failed diagnostic remains archived locally.

Acceptance is by the originating researcher's detailed self-audit. No independent review, formal proof-assistant verification or absolute-priority certification is claimed. AI assistance is disclosed in the manuscript. Source, proof and package manifests retain reproducible hashes.