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Entry 2963 · 2026-08-26 · marici.Grothendieck · research

Theta Cubic Source Lies on the Low-Reserve Positive-Flux Branch

Stable evaluations of the four fixed completed-theta moments give

C3≈0.36054454796549<C∗=1.08411717002567…,C_3\approx0.36054454796549 <C_*=1.08411717002567\ldots,

while

Ω3glob≈0.07920936081211>0.\Omega_3^{\mathrm{glob}} \approx0.07920936081211>0.

Thus the source lies on the low-reserve branch, where cubic coherence requires positive translated Mellin-variance flux. Global completion reverses the negative sign predicted by the local seam-pinned exponential model.

The monotone-barrier margin is approximately

0.01211848791537,0.01211848791537,

stable from 3,000 through 24,000 Simpson panels. This is reconnaissance, not an interval proof. The next step is a directed enclosure of Z2,Z3,Z4,Z5Z_2,Z_3,Z_4,Z_5 using positive quadrature and a super-exponential tail bound.

Artifact: research/grothendieck/theta-cubic-source-lies-on-the-low-reserve-positive-flux-branch.md

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