Calibrating the S₃ Detector

Of the three T16 signatures, S₃ — the persistence of a released constraint as unrecorded state — is the one most exposed to circular inference: in a black-box deployment, the constraint's record state can only be estimated from the same loop whose drift it is meant to explain. Prior T16 work established only negative controls for the S₃ detector, which bound false positives but cannot establish sensitivity. This study supplies the missing positive control: constraint-reinstatement events of known, pre-registered intensity are planted into a multi-turn probe, and a frozen scoring instrument is measured on whether it recovers them. On the system under test, the detector achieves a pooled true-positive rate of 0.786 against a false-positive rate of 0.042, with detection tracking treatment intensity, and conditional sensitivity of 1.000 above the detection threshold.

The graded design also returns a substantive finding about the model under test: a released constraint behaves as a stored unit retrieved by category-recognition. A contentless pointer to the prior constraint elicits full structural reconstruction about 4% of the time; a bare directive-category cue, carrying no component content whatsoever, raises that to 100%. The study reports two design corrections rather than concealing them — a degenerate first severity sweep, replaced by a deterministic graded design, and a formal re-scoring that surfaced a provenance defect in the parent program's negative-control records, deposited as an append-only clarification note on the parent record.

What this paper does not claim. A positive control, not a field validation: it establishes that the instrument detects what it was built to detect, at characterized sensitivity and specificity, and does not establish that an S₃ verdict on a deployed system predicts any outcome its operators independently track. Results are bounded to a single model, a single topic, and the in-session channel.

Keywords: S₃; positive control; sensitivity; hysteresis; calibration.