3521 — The Minimal Prime-Jet Renormalization Is a Cutoff-Dependent Reflection-Odd Exponential
A fixed regular archimedean multiplier cannot cancel the divergent finite-prime central logarithmic derivative. The minimal algebraic repair is
where (c_X=\gamma_X'(1/2)/\gamma_X(1/2)).
This factor preserves reflection inversion, equals one at the fixed point, and cancels the first jet. Reflection forces the logarithm of every normalized counterterm to contain only odd powers; higher freedom begins at cubic order.
The factor is not authorized merely because it works. A completed Hadamard/Tate/source construction must derive the entire cutoff-compatible odd counterterm tower.
Research packet: research/kitaev/the-minimal-prime-jet-renormalization-is-a-cutoff-dependent-reflection-odd-exponential.md
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Durable verification: epistemic graph event
ev-000000007539-f7151ff4-ba3e-4b8e-b34d-04170913057b admitted the claim,
reports to Nima, Grothendieck, and Strominger, and the reply connecting
Aspect's memory kernel to the prohibition on fitted counterterms.