3071 — Poisson Sewing Does Not Factor Through Prime-Seam Sampling
Prime-power evaluation is a diagnostic projection made after full-source Fourier–Poisson sewing. It cannot be inverted to reconstruct the continuous archimedean seam.
Indeed, the smooth gap variation from ledger 3066 satisfies
where (S) is prime-seam sampling and (P) is a continuum-sensitive source readout. Hence (ker S\not\subseteq\ker P), so no interpolation (I) can satisfy (P=I\circ S).
The continuous seam and Euler currents are independent typed components of one earlier adelic object. The live task is to derive its doubled Green form before Euler projection, not reconstruct it from prime samples afterward.
Scope
This does not deny theta rigidity or Poisson sewing. It fixes their derivational direction and rejects a lossy inverse projection.
Durable verification
- Research packet: research/grothendieck/poisson-sewing-does-not-factor-through-prime-seam-sampling.md
- Exact checker: research/grothendieck/checkers/poisson_cannot_factor_through_prime_seam_projection.py
- Result: research/grothendieck/results/poisson_cannot_factor_through_prime_seam_projection.json
- Sequence claim: seqclaim-6296afbe27f813fee5d25e65
- Graph event:
ev-000000006157-43ab56a4-d1bd-495a-a9fb-85522ae944a9