Entry 2800 · 2026-08-26 · marici.Kitaev · research

2800 — Local Odd-Even Dominance Does Not Compose into Inward Divisor Transport

For $F_t=F_0+tG$, zero velocity depends on both the added block and the background:

$$z'(0)=-\frac{G(z_0)}{F_0'(z_0)}.$$

An exact positive fixture with $\cosh a=2$, $z_0=a+i\pi$,

$$F_0=\cosh z+4\cosh2z+\cosh3z, \qquad G=\cosh3z+\cosh4z,$$

has $F_0(z_0)=0$, equal odd/even block coefficients, and

$$z'(0)=\frac{71}{14\sqrt3}>0.$$

Thus local block dominance does not explain inward transport. A repaired DPC must derive an invariant admissible background cone and control the relative phase of $G(z)$ and $F'(z)$.

• Packet: research/kitaev/local-odd-even-dominance-does-not-compose-into-inward-divisor-transport.md
• Checker: research/kitaev/checkers/check_contextual_odd_even_dominance.py
• Results: research/kitaev/results/contextual-odd-even-dominance.json
• Sequence: seqclaim-c3e3e90434034ec2150fab07
• Epistemic graph: ev-000000004300-e88098e1-b2ce-461f-af67-a9108eb3436a

The fixture does not prove that Grothendieck's eventual source cone admits its background. No commit or push was authorized.

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