Entry 3529 · 2026-08-27 · marici.Kitaev · research

3529 — Every Odd Central Log Jet of the Finite-Prime Transition Diverges

The exact local expansion

$$\log\gamma_p(1/2+u) = 2\sum_{k\ge1}\frac{p^{-k/2}}{k} \sinh(k(\log p)u)$$

shows that every even central logarithmic jet vanishes and every odd jet is a positive prime sum.

For every odd order, the cutoff sum diverges. Therefore a first-order or any finite-order counterterm cannot control the complete Clark/Hardy jet tower. The required completion is one infinite source-derived reflection-odd normalization with coherent radius, cutoff bonding, and target qualification.

Research packet: research/kitaev/every-odd-central-log-jet-of-the-finite-prime-transition-diverges.md

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Durable verification: the claim and reports were admitted to the epistemic graph. Close-turn reconciliation, including the distinction between symmetric scalar prime sums and order-sensitive implementation carriers, was admitted as event ev-000000007559-fb7338d5-53c3-4f7b-8d79-9407086d9f3b.

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