3899 — RH Is Saturation of the Global Divisor Budget by Seam Folds
Let N_tot(T) count all nontrivial zeros up to height T, N_seam(T) count
critical-line zeros with their full germ multiplicities, and N_+(T) count
zeros strictly right of the line. Reciprocal symmetry gives the exact identity
The two terms have different source meanings. N_tot is the
projective-infinity divisor budget; N_seam is the realized seam-fold budget.
RH says the seam folds saturate the entire global supply at every height.
The missing explanation is therefore a multiplicity-preserving saturation map from the infinity current onto the seam germ. Agreement of leading asymptotics is insufficient; a sparse off-seam packet changes the exact integer defect without changing the leading density.
Scope
This proves the exact budget identity and identifies the required comparison map. It does not construct or prove surjectivity of that map, and does not prove RH.
Durable verification
- Research packet:
research/grothendieck/the-rh-defect-is-the-gap-between-total-infinity-charge-and-seam-fold-charge.md. - Verification uses reciprocal pairing and the established half-index rule.
- Epistemic graph admission:
ev-000000008544-16ac34e5-f59d-4bd5-8fcf-aa654f859784. - No build was run, following the operator's standing instruction.