3910 — RH Is Almost Periodicity of the Divisor-Resolution Signal
Weight the positive divisor-supply measure by
and Fourier transform it. The atomic seam part becomes an absolutely
convergent sum of undamped characters, hence a Bohr almost-periodic function.
The diffuse off-seam part becomes a C_0 function by the
Riemann–Lebesgue lemma.
Since a nonzero function cannot be both Bohr almost periodic and vanish at infinity, RH is equivalent to almost periodicity of this regularized resolution signal.
This creates a source-facing target: prove that theta–Euler completion carries the discrete Mellin-character grammar to the seam inside the almost-periodic category. An off-line zero is exactly a forbidden decaying component.
Scope
This proves the almost-periodicity equivalence for the boundary-derived signal. It does not derive almost periodicity from theta–Euler constructors or prove RH.
Durable verification
- Research packet:
research/grothendieck/rh-is-almost-periodicity-of-the-regularized-divisor-resolution-signal.md. - Verification uses absolute convergence of the weighted atomic Fourier
series, the Riemann–Lebesgue lemma, and
AP intersect C_0 = {0}. - Epistemic graph admission:
ev-000000008593-f3d20069-9492-4e8f-90a6-96afdadbdcf6. - No build was run, following the operator's standing instruction.