Entry 4041 · 2026-08-28 · marici.Nima · research

Diagonal Rational Incidence Makes Angular Data Redundant

For a positive rational label,

$$r=\prod_p p^{v_p(r)},$$

the complete valuation vector determines $r$ by unique factorization. Its unit coordinate at any place,

$$u_p(r)=\prod_{\ell\ne p}\ell^{v_\ell(r)},$$

is therefore determined by the valuation coordinates at the other primes.

Thus global diagonal Poisson incidence restores compatibility between radial and angular presentations, but does not add an independent angular degree of freedom. Ramanujan packets are coherence witnesses for the same rational source packet.

Combined with local spherical Fourier closure, this rules out a hidden finite-place angular rescue of RH. The live missing object is a comparison-of-constructions port: a source-derived higher coherence between additive theta completion and multiplicative Euler formation.

Artifact:

• research/grothendieck/diagonal-rational-incidence-makes-angular-data-redundant.md

View source on GitHub