Observation–Feedback Closure I: A Causal-Hypergraph Generalization of Event-Counting Kinematics with Sheaf-Reconstructible Stable Identity

This preprint is version v1. 3. 0 of Observation–Feedback Closure I. It presents a conservative causal-hypergraph generalization of the v1. 2. 0 event-counting kinematical reconstruction. The clean binary observation–feedback event ontology is generalized to directed two-sided causal hyperedges, while the distinction between process order and identity-continuation order is retained. A stratified microscopic–mesoscopic–macroscopic architecture is introduced to avoid directly identifying microscopic hypergraph elements with macroscopic spacetime quantities. Stable physical existence is treated as a framework-internal reconstruction-theoretic notion and is represented by source-generated propagation patterns admitting sheaf-reconstructible stable identity. Raw event-counted action is generalized to an obstruction-weighted effective observation count, yielding an effective action Sₑff = κOF Nₑff. The condition δNₑff = 0 is used only as a sufficient local selection criterion for mesoscopic identity continuation, not as a full stationary-action principle. The version distinguishes local proper time from macroscopic coordinate time, allowing local kinematical reversibility and macroscopic structural irreversibility to be treated at different reconstruction layers. In the clean binary, zero-obstruction, unit-weight limit, the v1. 3. 0 construction recovers the v1. 2. 0 event-counting kinematical architecture, including the raw action count, local frequency, proper-time scaling, energy calibration, the SO (1, 1) count-ratio structure, the minimal internal O (3) identity realization, and the clean Lorentzian readout. This version remains a kinematical and interpretational reconstruction. It does not claim empirical superiority over established physical theories, and it does not derive field equations, quantum dynamics, gauge dynamics, gravitational dynamics, quantitative cosmological models, or new empirical predictions. The complete categorical sheaf/cosheaf formalization, the full generator-level proof of SO⁺ (3, 1), and dynamical extensions are deferred to later work.