# Plane-coloring boundary and finite certificate audit

Family 158, source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. Selected-source addendum, 9 October 2026 Australia/Brisbane. All earlier editions are preserved.

## Current decision

Research/certificate use; defer operational frequency-planning claims. No buyer interview, paid pilot or profitability evidence has been obtained.

## Reviewed finding and application boundary

The source excludes arbitrary proper five-colorings on the full Euclidean plane and gives an upper seven-coloring. It does not settle six versus seven or supply the finite six-required graph implied existentially by compactness. Finite deployed geometry, tolerance bands and selected frequencies are separate models.

## Evidence extent

- [introduction.tex](../../../../../source/openai-math/preprints/The-Euclidean-plane-is-not-five-colorable-September-23-2026/build/sections/introduction.tex): entire 324-line introduction. Claimed six-to-seven chromatic range, continuum obstruction, proper/weak-measurable distinction, compactness existence without an explicit finite six-required graph, selected hexagonal upper bound.

[Source metadata](source.json), [individual definition observations](../../definition-hole-review-queue-2026-10-09-v3.json), [manuscript ledger](../../../../checkpoints/manuscript-ledger-2026-10-09-v4.json). Selected definition/body and challenge comparison found no intended-model mismatch; imported dependency semantics, complete proof, independent kernel and executable correspondence are not verified. Intentional challenge placeholders do not establish source proof failure.

## Next action

Develop finite controls where they answer a concrete modeling question, inspect quantitative construction constants separately, and compare business usefulness with an existing expert workflow. Preserve unknown hypotheses and source claims explicitly.