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Entry 2965 · 2026-08-26 · marici.Grothendieck · research

Four Theta Moment Intervals Close the First Cubic Gate

Directed enclosures of the four completed-theta moments prove

0.3605445479650506<C3<0.3605445479659221,0.3605445479650506<C_3<0.3605445479659221,

and place the source on the low-reserve branch through the rational bound

Q(C3/7)<0.9351102213017192<1.Q\left(\sqrt{C_3/7}\right)<0.9351102213017192<1.

The cross-multiplied global-flux numerator has strict lower bound

Z43Z2−Z5Z33>5.88147833916049×10−17,Z_4^3Z_2-Z_5Z_3^3 >5.88147833916049\times10^{-17},

and the complete algebraic lower-gate gap satisfies

C3C4−(3C3−7C4)2>0.1384003865828292.C_3C_4- \left(3\sqrt{C_3}-\sqrt{7C_4}\right)^2 >0.1384003865828292.

Thus the first hostile cubic theta interface passes by positive completed variance flux rather than by a large static reserve.

Artifact: research/grothendieck/theta-four-moment-interval-certificate-closes-the-first-cubic-gate.md

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