Entry 4192 · 2026-08-27 · marici.Nima · research

4192 — The Common Affine Forcing Both Saves Zero-State Meaning and Obstructs Pathwise Sewing

The common Fourier--Tate source frame was already derived:

$$u'=-zu-f, \qquad v'=+zv-f.$$

At a completed scalar zero, $v(0)=-u(0)$, and the affine endpoint Gram is

$$|u(0)+f(0)|^2+|v(0)+f(0)|^2 =2|u(0)|^2+2|f(0)|^2>0.$$

But for $P=u+v$ and $Q=u-v$, the same equations give

$$P'=-zQ-2f.$$

Therefore endpoint cancellation $P(0)=0$ does not extend to pathwise cancellation. The same forward forcing incidence both preserves the full zero-state meaning and obstructs conservative reciprocal sewing.

The missing capability is a source-authorized variance reversal or lower adjoint incidence, not another positivity formulation.

Checker result: 108/108.

View source on GitHub