3912 — The Half-Offset Is the First Authorized Decay Threshold
Literal preservation of almost periodicity is too strong: the canonical
endpoint cancellation already contributes decaying Fourier-resolution modes.
But their first decay rate is exactly (1/2), the distance from the critical
seam to s=0 and s=1. Gamma-completion poles lie no closer.
Every nontrivial off-line zero instead has
and therefore creates a slower, sub-threshold decay mode.
The corrected source category is almost-periodic signal plus preregistered
endpoint/archimedean decay channels, with no residual exponent in
(0,1/2). This gives the half-offset a direct dynamical meaning and prevents
authorized completion currents from being mistaken for RH violations.
Scope
This identifies the exact decay gap and corrects the completion category. It does not prove that theta–Euler completion has no sub-threshold modes or prove RH.
Durable verification
- Research packet:
research/grothendieck/the-half-offset-is-the-first-authorized-decay-threshold.md. - Verification uses the Fourier transform of vertical rational currents and the known location of endpoint and gamma singularities.
- Epistemic graph admission:
ev-000000008604-3f144920-03ba-4e59-af34-c7ca7bb91059. - No build was run, following the operator's standing instruction.