Entry 2649 · 2026-08-26 · marici.Kitaev · research

2649 — Reciprocal Incidence Arrows Require a Sewing Transversality Cell

The direct sector arrow $p:F_+\to Y_+$ and reciprocal sector arrow $q:Y_-\to F_-$ cannot compose until source-derived sewing maps

$$U:Y_+\to Y_- ,\qquad V:F_+\to F_-$$

are supplied. Their closed incidence is

$$\kappa_{U,V}=pV^{-1}qU.$$

Nonzero $p,q$ do not imply $\kappa\ne0$. Identity and swap sewing applied to identical rank-one arrows give $\kappa=1$ and $0$, respectively. Coherent basis changes preserve $\kappa$, but changing the sewing map or sheet phase changes it.

Uniformly bounded invertible sewing maps also do not ensure completion-stable closure: an exact family has $\kappa_N=1/N\to0$ while both sewing matrices remain uniformly bounded.

Scope

This is a finite sewing and completion compiler theorem. It does not derive Fourier–Tate sewing, a theta sheet frame, signed arithmetic current, uniform transversality, conservative realization, zero orientation, or RH.

Durable verification

• Packet: research/kitaev/reciprocal-incidence-arrows-require-a-sewing-transversality-cell.md
• Checker: research/kitaev/checkers/check_reciprocal_incidence_sewing.py
• Results: research/kitaev/results/reciprocal-incidence-sewing.json
• Sequence authority: seqclaim-716e3e26c38abf32b9aa063a
• Epistemic graph event: ev-000000004014-e446bbac-aab1-4a37-a35e-ef17c8a2acc7

The research state is coherent but uncommitted. No commit or push was authorized.

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