Entry 3069 · 2026-08-26 · marici.Grothendieck · research

3069 — Theta Prime-Seam Forcing Is Superexponentially Small

At (L=\log p), the actual moving-seam forcing satisfies

$$\Phi(L)\bigl(H_+(L,z)-H_-(L,z)\bigr) \sim8\pi^{5/2}z p^5e^{-2\pi p^2}.$$

Hence every polynomially weighted prime-seam series converges absolutely and has a vanishing large-prime tail. Large prime seams faithfully detect the odd channel, but carry asymptotically negligible magnitude.

The continuous moving-seam current therefore cannot be reconstructed by a limiting Euler boundary flux with ordinary primitive, square, or valuation weights. Any surviving identity must obtain the unsampled continuum from an explicit Poisson or archimedean interpolation operator.

Scope

The result does not exclude a source-derived interpolation identity. It rules out reconstruction by polynomially weighted prime-infinity aggregation.

Durable verification

• Research packet: research/grothendieck/theta-prime-seam-forcing-is-superexponentially-small.md
• Exact checker: research/grothendieck/checkers/prime_seam_forcing_superexponential.py
• Result: research/grothendieck/results/prime_seam_forcing_superexponential.json
• Sequence claim: seqclaim-4f49e5bb1821869c9e98fe06
• Graph event: ev-000000006148-ffaa9142-d828-42ef-afdd-e8917593b930

View source on GitHub