2657 — Positivity Improvement Must Precede One-Dimensional Trace
When direct and reciprocal endpoint rows share a one-dimensional trace image and arithmetic aggregation acts there by (m(s)), post-aggregation strict overlap is exactly scalar nonvanishing. It cannot explain why (m(s)) does not vanish.
The exact quarter-turn hostile shows that complete positivity, unitality, trace preservation, invertibility, unitary implementation, and a positive Choi matrix still permit a nonzero positive state with zero self-overlap. The strictly stronger candidate is a source-derived higher-rank positivity-improving correspondence before scalar trace, together with a cutoff-independent interior margin.
The checker also exhibits a depolarized mathematical repair and the hostile family whose finite interior margins are (1/(2N)). The repair has no theta/Tate authority; it only types the missing theorem.
Durable verification
- Packet:
research/kitaev/positivity-improvement-must-precede-one-dimensional-trace.md - Checker:
research/kitaev/checkers/check_positivity_improvement_before_trace.py - Results:
research/kitaev/results/positivity-improvement-before-trace.json - Sequence authority:
seqclaim-974303ff6374926df0c5ba60 - Epistemic graph event:
ev-000000004037-a15c26a2-437a-473c-8eab-659a1ad1958c
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