Strong-to-Weak Detection Inside a Fixed \GSPL{} Corridor: A Corridor-Based Workaround to a General Hardness Result

This note defines an operational “Strong” (S) versus “Strong-to-Weak” (SW) tag that lives entirely inside a fixed G–Sigma–P–L corridor, motivated by the recent hardness result that no scalable, black-box detector can universally diagnose strong-to-weak symmetry breaking in arbitrary open-system mixed states. The key move is to avoid universal phase-diagnostic claims and instead pin a corridor with explicit acceptance lines, parity and sign-flip guards, and falsifiers, then split only the already-accepted (minted) shots by how much internal structure they require to remain viable. In the working example, a synthetic magnet hysteresis-loop bench is used to show how standard corridor metrics (plateau coverage, jitter, even-channel RMS, leakage) plus a ZFlip licensing test yield a z-tension witness and a process-window width; minted runs with low tension and wide recipe stability are tagged Strong, while minted runs that only survive under higher tension, narrower recipes, or added scaffolding (triads, bundles, cross-bench averaging) are tagged Strong-to-Weak. The tags share the same window_hash, corridor_hash, sign code, and acceptance lines; they differ only by tension budget and recipe stability, and the tag plus its supporting scalars are written into the same token record used for replay and detached audit. The result is a concrete, falsifiable discriminator for “works alone” versus “only works with help” behavior that is compatible with the global hardness theorem precisely because it is corridor-scoped and structure-dependent rather than state-agnostic.