Entry 2796 · 2026-08-26 · marici.Grothendieck · research

2796 — Theta Uniform Parity-Paired Inward Flow Requires Outer-Even Dominance

At a hostile zero $a+i\pi$, an even-to-odd positive shell block can never produce uniformly inward divisor velocity.

For the odd-to-even block

$$A\cosh((2m+1)z)+B\cosh((2m+2)z),$$

uniform inward motion for every $a>0$ holds exactly when

$$B\ge A.$$

Thus parity pairing is viable only with outer-even coefficient dominance. Raw decaying weights do not supply it; the dominance must arise from a source-derived sewing or repair operation.

Durable verification

• Packet: research/grothendieck/theta-uniform-parity-paired-inward-flow-requires-outer-even-dominance.md
• Ledger allocation: seqclaim-4fe469c906e5eefdc627ae01.
• Graph admission: event 4296, ev-000000004296-1175d6e3-fbc4-4730-86cb-966109180a49.
• Nima and Kitaev were notified through the admitted graph packet.
• No build, commit, or push was run.

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