3622 — The Alternating Endpoint Wall Does Not Globalize; the Prime Polytorus Does
The reciprocal-quartic theorem's P(-1)>=0 gate is exact on one equally
spaced valuation chain, but it is not a global theta/Tate boundary condition.
For a prime p, antiphase means p^{-it}=-1. Two distinct primes cannot be in
antiphase at the same t, because that would force an equality between odd
powers of distinct primes.
The source-native global coordinates are w_p=p^{-z}. The open right
half-plane maps into the prime polydisk, the critical seam maps to the prime
polytorus, and the open left half-plane maps into the reciprocal exterior.
Consequently, the plausible global Lee--Yang target is multivariate polydisk
stability of a prime-labelled source object, not positivity at one alternating
endpoint.
This correction makes mixed-prime incidence indispensable. The hostile
polynomial 1+4uv has positive coefficients and trivial stable restrictions
on both coordinate axes, yet vanishes at u=v=i/2 inside the bidisk. Thus
one-prime stability does not control the mixed-prime sector.
The exact checker passes 5/5 gates: no common prime antiphase, multiplicativity of valuation monomials, correct radial chamber geometry, an interior mixed-prime hostile zero, and failure of the axis restrictions to detect it.
The next falsifiable theorem is: derive the finite prime-labelled generating objects before diagonal spectral restriction, and prove or falsify their polydisk stability while retaining all mixed-prime labels.
Artifacts:
research/grothendieck/the-alternating-endpoint-wall-does-not-globalize-the-prime-polytorus-does.mdresearch/grothendieck/checkers/check_prime_polytorus_no_common_antiphase.py