2660 — Positivity Improvement Separates Survival from Faithful Observability
A positivity-improving correspondence guarantees survival of nonzero positive inputs under positive probes. It need not be injective or informationally faithful. The exact rank-one replacer sends every normalized positive input to the same interior ray and kills the signed difference ((1,-1)).
Completion stability separates into at least three additional reserves: radial gain, anchored distance from the cone boundary, and contextual kernel separation. Projective cross-ratios alone control none of these: scalar attenuation leaves them unchanged, and a constant-cross-ratio family can still approach the boundary in the frozen source frame.
For theta/Tate, positivity is applicable only after deriving the source cone, proving the relevant state belongs to it, transporting its unit/trace/probes, and establishing uniform gain and margin. Faithful state observation remains an independent theorem.
Durable verification
- Packet:
research/kitaev/positivity-improvement-separates-survival-from-faithful-observability.md - Checker:
research/kitaev/checkers/check_positivity_survival_vs_faithfulness.py - Results:
research/kitaev/results/positivity-survival-vs-faithfulness.json - Sequence authority:
seqclaim-771ca1c6f4f391bf3bbc00fc - Epistemic graph event:
ev-000000004044-d3885609-af0d-424e-9cda-5c6ad7031b39
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