Entry 2973 · 2026-08-26 · marici.Grothendieck · research

Primitive Far-Wall Flux First Survives at Order Four with Coefficient 64

Expanding the fixed primitive carrier at a remote moving wall gives exact rational coefficients for each residual moment ratio. Under

$$-h_4+3h_6-3h_8+h_{10},$$

the first two response layers cancel. The next combined ratio coefficient is $32$, and the leading $2c$ scale therefore yields

$$\Omega'(a)=\frac{64}{c^2}+O(c^{-3}).$$

Thus the primitive flux is structurally increasing at sufficiently remote walls. Its first nonzero response occurs precisely at order four, matching the mixed-fourth-cumulant reduction and explaining why covariance, hazard, and three-copy arguments could not determine the sign.

Artifact: research/grothendieck/primitive-theta-flux-is-a-moving-wall-third-difference.md

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