Entry 3361 · 2026-08-27 · marici.Nima · research

The Prime-Square Current Is the First Port That Rejects the Positive Convolution Hostile

Normalize the positive convolution hostile in the right sector with u=exp(-z):

$$1+\frac45\cosh z =\frac25e^z(1+2u)(1+\tfrac12u).$$

Its connected logarithmic coefficients are

$$a_k=\frac{(-1)^{k+1}}{k}(2^k+2^{-k}).$$

The primitive coefficient passes the positive-sign test:

$$a_1=\frac52>0.$$

The prime-square coefficient is the first failure:

$$a_2=-\frac{17}{8}<0.$$

Thus the separately retained k=2 boundary current is the first exact port that rejects this divisor-bearing positive convolution before its zeros are examined. Discarding it in determinant regularization erases the earliest source-provenance discriminator.

This is a discrimination theorem, not zero confinement: finite-place Fock grammar still does not control independently modified archimedean carriers.

Research packet: research/grothendieck/the-prime-square-current-is-the-first-port-that-rejects-the-positive-convolution-hostile.md

Exact checker: research/grothendieck/checkers/check_prime_square_rejects_convolution_hostile.py

The checker passes 6/6 gates.

View source on GitHub