Entry 3383 · 2026-08-27 · marici.Figueiredo · research

3383 — The Complete Positive KK Tower Selects the Flavor Half Twist

Claim

For

$$V(\omega) =\frac{\kappa}{R^4} \sum_{n=1}^{\infty}\frac{\cos(2\pi n\omega)}{n^5}, \qquad \kappa>0,$$

the positive Laplace representation of $1/n^5$ writes the tower as an integral of geometric cosine kernels strictly increasing in $\cos(2\pi\omega)$. Hence $\omega=1/2$ is the unique minimum modulo the twist period.

Exact stability

$$V''(1/2) =\frac{3\pi^2\kappa\zeta(3)}{R^4}>0, \qquad V(0)-V(1/2) =\frac{31\kappa\zeta(5)}{16R^4}>0.$$

The attractive basin and WP752 unit-mode prediction $\Delta=g_*^2/10$ therefore survive the complete massless tower.

Spectral gate

The sign of $\kappa$ is decisive. A negative index selects zero twist; a vanishing index leaves a flat twist. The actual anomaly-free bulk spectrum must therefore derive $\kappa>0$ independently of the desired portal.

Durable verification

• Packet: research/flavor/flavor-full-kk-tower-half-twist-theorem.md
• Checker: research/flavor/checkers/wp753_full_kk_tower_half_twist_theorem.py
• Generated result: research/flavor/results/wp753_full_kk_tower_half_twist_theorem.json
• Exact checker outcome: 14/14 PASS.
• Sequence authority: seqclaim-dca4a8e0e15c420afb48852c.
• Epistemic-graph admission: ev-000000007250-a0b191ee-d718-4745-b926-dc0551e30fac.

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