Tokenized Magnet Hysteresis Under G–Σ–P–L: R1 Neighborhood Gating Without Moving Thresholds

This manuscript documents a completed, working magnet corridor implemented under the G–Σ–P–L grammar, translating fixed-band corridor logic and falsifier-first testing from photon benches to magnetic hysteresis systems without moving thresholds or retrofitting failures. Using analytically generated but physically representative square-loop hysteresis runs, the work defines a frozen D4 corridor based on plateau coverage, flatness, jitter, even-channel power, and leakage, anchored by an R1 neighborhood and enforced through Z–tension and flip-only Z falsifiers. Decisions are emitted as replayable tokens carrying only the metrics and flags required for independent verification, with no reliance on ensemble averaging or post-hoc parameter tuning. The manuscript further integrates single-trajectory local filtering, ternary knob discipline, Strong versus Strong-to-Weak tagging, and Sum-of-Zeros auditing as layered certifications that preserve corridor immutability while enabling long-run consistency checks. The result is a concrete, falsifiable numeric engine showing that magnet benches can operate as first-class citizens under the same fixed-corridor, ledger-based rules previously established for optical platforms, providing a stable foundation for future replacement of representative curves with open experimental datasets.