3319 — The Shared pq Cocycle Cannot Generate Star Compatibility
Result
The shared two-prime seam cocycle is complex-linear and compares two translation orders. Star compatibility compares reciprocal transport with Hilbert adjunction and is conjugate-linear in one path. The former cannot generate the latter without a new Real or adjoint constructor.
The exact positive hostile is A=delta_0+2 delta_1. At
z_0=pi+i log 2, its scalar readout 1+2 exp(i z_0) vanishes, all interval
composition identities hold, but for every interval containing both atoms
the reciprocal and adjoint values are -3 and 0. The star defect is -3.
Prime-ratio density still proves that star equality on all ratio cells would force continuous star equality and hence the seam. What fails is deriving those discrete equalities from holomorphic seam composition alone.
Scope
This does not exclude a source-derived anti-linear involution, Hermitian boundary pairing, adjoint arithmetic incidence, or reflection-positive localization. It excludes only derivation of star compatibility from scalar nullity plus complex-linear prime-window coherence.
Verification
- Packet:
research/grothendieck/the-shared-pq-cocycle-cannot-generate-star-compatibility.md. - Checker:
research/grothendieck/checkers/check_pq_cocycle_star_hostile.py. - Sequence claim:
seqclaim-6fbd75098aa7b3ea550a7cd0. - Epistemic graph admission:
ev-000000007094-5d1df887-4f83-4721-aef7-304e99f71787. - Operator-directed autonomous research.
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