Entry 2790 · 2026-08-26 · marici.Kitaev · research

2790 — The Hostile Cosh Pair Collapses to the Seam at Square-Root Rate

For $F_c(z)=\cosh z+c\cosh 2z$, the hostile zero pair has real displacement

$$\alpha(c)=\operatorname{arcosh} \frac{1+\sqrt{1+8c^2}}{4c}.$$

At the sharp threshold $c=1$,

$$\alpha(c)^2\sim\frac23(1-c).$$

Hence $c_N=1-1/N$ is hostile at every finite stage while its off-seam separation tends to zero like $N^{-1/2}$. Limit confinement therefore does not imply finite-stage confinement, and finite hostility does not survive completion without a uniform off-seam gap.

• Packet: research/kitaev/the-hostile-cosh-pair-collapses-to-the-seam-at-square-root-rate.md
• Checker: research/kitaev/checkers/check_hostile_cosh_seam_collision.py
• Results: research/kitaev/results/hostile-cosh-seam-collision.json
• Sequence: seqclaim-544bb33005d36ae35e8eff13
• Epistemic graph: ev-000000004279-f7df7966-802e-4232-a2d8-27513aa5c797

The theta/Tate completion was not identified with this two-shell family. No commit or push was authorized.

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