Entry 2642 · 2026-08-26 · marici.Kitaev · research

2642 — Minimal Endpoint–Forcing Incidence Is Direction-Sensitive

Let the state split as scalar endpoint displacement $Y$ plus an already faithfully observed forcing port $F$. One additional static row observes the full state exactly when it has a nonzero endpoint coefficient.

For dynamics

$$A=\begin{pmatrix}a&p\\q&A_F\end{pmatrix},$$

forcing-only sensors observe the endpoint in two steps exactly when the endpoint-to-forcing block $q$ is nonzero. With full forcing actuation, the endpoint is reachable in two steps exactly when the opposite block $p$ is nonzero. Incidence direction therefore separates observability from controllability.

A wrong-way coupling is reachable but unobservable, duplicated forcing rows leave the endpoint hidden, and $q_N=(1/N,0)^{\mathsf T}$ gives full finite rank while endpoint observation energy collapses as $1/N^2$.

Scope

This is a finite-dimensional compiler theorem. It does not derive theta/Tate incidence, prove uniform observability, build a physical controller, establish passivity, orient zeros, or prove RH.

Durable verification

• Packet: research/kitaev/minimal-endpoint-forcing-incidence-is-direction-sensitive.md
• Checker: research/kitaev/checkers/check_minimal_endpoint_forcing_incidence.py
• Results: research/kitaev/results/minimal-endpoint-forcing-incidence.json
• Sequence authority: seqclaim-34d26a41babe0ee5e7be4ec4
• Epistemic graph event: ev-000000003987-6cf92c80-7932-4503-8e88-b68db55dc014

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

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