Manuscript Oai272-A@1 · Oai272-A.tex · section · a40828a0

The five-stage source audit

The five-stage source audit · lines 2001–2052

The external proof architecture is useful, but its components must be audited at their own quantifiers.

Step	Source interface	Local audit and retained obligation
Step	Source interface	Local audit and retained obligation
1	Represented class and PPT stability.	Definitions, stability, and tensor closure are proved in Lemma lem:stability. No assumption that every PPT state is represented is made.
2	Complete transcripts and a four-effect estimate.	The complete-history model is explicit. Common factors, fidelity normalization, and the rational $1/5$ terminal certificate are proved locally. Private outcomes are not promoted to public messages.
3	Choi transfer and product-range obstruction.	The unnormalized Choi convention, transpose-adjoint identity, and sufficient range test are proved in Section sec:choi.
4	Dimension-ten geometry from a map on $M_{4} (C)$ , twenty singular directions, quadratic evaluations, and exact arithmetic.	The source describes this mechanism, but this manuscript does not recompute its elimination, field/Galois arguments, or all required evaluation determinants. This is the remaining external application-verification gate.
5	Trace-preserving completion with an entangled local corner.	The generic $2 d + 1$ construction is proved. The instance $d = 10$ remains conditional on the qualifying external pair. The full channel Choi range is not asserted product-free.

The twenty-direction and quadratic-evaluation mechanism is attributed to the external paper, not a premise drawn from Cheung's sheets OpenAI272. No supplementary integer output is substituted for the missing geometric audit.