Manuscript Oai272-A@1 · Oai272-A.tex · section · a40828a0
What this manuscript completes
Scope, provenance, and the three distinct claims › What this manuscript completes · lines 135–163
The supplied plan has stages –. Its mathematical completion must distinguish:
a locally proved implication;
an explicit finite certificate for that implication;
verification that particular external matrices satisfy its hypotheses;
an experimental or computational execution.
None of these categories substitutes for another.
The principal locally proved results are Theorems thm:bit-gap, thm:rational-gap, thm:completion, thm:witness-algorithm, and thm:assembly. The dimension-ten construction is retained as a documentary application target. Consequently, this manuscript is not a purported independent proof of every result in the external Family 272 paper.
The source paper is attributed to OpenAI and dated 27 September 2026 OpenAI272. The companion identification page distinguishes that source from Cheung's programme Companion272. This development uses the requested identifier Oai272-A. It does not assert authorship, registration, approval, or endorsement of this development by N. Cheung.