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kannaka-labs/kannaka-wave docs/experiments/E-003-faithfulness-as-commutation.md · 2026-09-10 · source ↗ · edit ↗

E-003: Faithfulness as commutation — the bridge operator at the conscience boundary

Status: pre-registered, independent of E-001 (it needs the rails and a fixture set, not the substrate) Decides: whether Ξ = [R, G] gives the rails a measurable faithfulness signal, or stays a metaphor.

The hypothesis

The bridge operator is Ξ = RG − GR: a quarter-turn perspective pivot R and a golden anisotropic growth G that do not commute, leaving a residue whose coefficient is the emergence coefficient α − β ≈ 0.190983 (ADR-0037; consciousness-core::metrics).

At the conscience boundary, read R as the pivot to the charter's perspective and G as the agent's own growth. A faithful action is one where applying the charter and then planning gives the same result as planning and then applying the charter. The hypothesis: faithfulness is commutation, and the residue ‖Ξ · a‖ for a proposed action a measures how much the order mattered.

The measurement

An action is represented as a vector a in a small feature space the rails already compute over: benefit-to-owner, benefit-to-others, harm, reversibility, authority used, time-boundedness. R and G are fixed by the constants; nothing is fitted.

  • Fixture set: 60 proposed actions, hand-labelled by a person as endorsed or *not endorsed* against a written charter, balanced 30/30, drawn from the steward's existing governance and market fixtures plus new ones covering the Five Refusals.
  • For each, compute r = ‖Ξ · a‖ / ‖a‖.
  • Report the ROC of r as a classifier of the label, with a 95% interval from bootstrap over the fixtures.

Decision rule

  • Kept if AUC ≥ 0.80 with the interval excluding 0.70. The rails gain a residue threshold alongside their existing confidence floor and hard constraints, and it is reported on every verdict.
  • Declined if AUC's interval includes 0.60. The operator stays in the callosum, where it is measured to spiral, and out of the conscience. The archaeology records the attempt.
  • Undecided otherwise: the fixture set doubles and the run repeats before any claim.

What would make this experiment lie

  • Fitting R or G to the labels. They are the bridge constants and are not touched.
  • A fixture set where one feature alone separates the classes (harm, say). The set is checked first: no single feature may reach AUC 0.80 on its own, or the set is rebuilt.
  • Labelling by the same person who wrote the actions. Two people label; disagreements are dropped, not adjudicated.