Entry 2968 · 2026-08-26 · marici.Grothendieck · research

The Primitive Theta Profile Already Carries the First Cubic Flux

Directed label separation proves that the primitive $n=1$ theta profile on the canonical positive chamber already has positive cubic flux:

$$D_1>5.88134757514609\times10^{-17}.$$

Its nonlinear gap is extremely close to the full completed-source gap:

$$0.9999777668084242 <\frac{D_1}{D}< 0.9999778449442455.$$

This is not an additive percentage decomposition. It proves that cross-label cancellation is unnecessary for the sign. The mechanism moves to the primitive incomplete-gamma tail profile; modular completion selects the physical chamber and controls a small higher-label perturbation.

An endpoint sweep indicates that the sign is not tuned specifically to $c=\pi$. The next theorem is a uniform positive-flux statement for the one-parameter positive gamma-tail family, with a counterexample as its exact falsifier.

Artifact: research/grothendieck/theta-primitive-profile-already-carries-the-first-cubic-flux.md

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