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kannaka-labs/kannaka-wave docs/experiments/E-003-faithfulness-as-commutation.md · 2026-09-30 · source ↗ · edit ↗

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

Status: pre-registered, independent of E-001. Rails built 2026-09-22 (#4). DECLINED 2026-09-22 on the pre-run check: the measurement as registered is degenerate (r is the constant 0.190983, AUC 0.5 for any labels). No fixture set was built and no one was asked to label. The decision rule was amended by the author to reach this verdict; see §Verdict. 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, or lies wholly below it (amended 2026-09-22; see §Verdict). 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.

Pre-run check — 2026-09-22

The pre-registration checks its fixture set before the run. The instrument can be checked before the fixture set exists, because R and G are fixed and r is therefore a fixed function of the action. experiments/e003/check.py (standard library, deterministic; output in experiments/e003/results/check.txt) does it.

The linear residue is a constant.

RG = [[0, −β], [α, 0]]     GR = [[0, −α], [β, 0]]
Ξ  = RG − GR = (α − β) · [[0, 1], [1, 0]]          α − β = (3 − √5)/4 = 0.190983

Ξ is the emergence coefficient times a swap, and a swap is orthogonal, so ‖Ξ a‖ = (α − β) ‖a‖ for every a. Applied pairwise over the six features, under any of the 15 ways to pair them, r = ‖Ξ a‖ / ‖a‖ = 0.190983 for every action. Checked on 1,500,000 residues (10 seeds × 10,000 actions × 15 pairings): the largest deviation is 8.3 × 10⁻¹⁷. Every endorsed action ties every non-endorsed one, so AUC = 0.5 exactly, for any labels. On a label set that harm alone separates perfectly (AUC 1.000), r still scores 0.500.

This was known. kannaka-memory experiments/xi-operator-audit.md found the same thing in April ("the xi operator simply swaps each coordinate pair and scales by 0.190983 … zero independent information"), and consciousness-core replaced the linear commutator with a nonlinear one in 5c8a2c8 (2026-04-16). The archaeology's bridge operator entry did not cite the audit, and this experiment was written against the linear form anyway. The archaeology now cites it.

The decision rule, applied as written, does not terminate. Kept needs AUC ≥ 0.80: no. Declined needs the interval to include 0.60, but the bootstrap interval of a constant is [0.5, 0.5], which lies wholly below 0.60 and does not include it. That leaves Undecided, where "the fixture set doubles and the run repeats", and no fixture set can move a constant. The rule did not anticipate an AUC below 0.60. Closing that gap is a change to a pre-registered rule, so it is the author's call and is not made here. The reading this check would propose: *an AUC interval lying wholly below 0.60 declines, as one that includes 0.60 does*.

The nonlinear form is a different experiment, not a fix to this one. tanh(Rv)⊙Gv − tanh(Gv)⊙Rv breaks the constant, but it brings two knobs this pre-registration forbids fitting, and fixes neither:

  • Units. Scaling one action's features by k = 0.1, 1, 8 gives r = 0.00009, 0.059, 0.41. Choosing the features' scale is choosing the answer.
  • Pairing. The same action under the 15 pairings ranges over r = 0.025 to 0.059.
  • And an action with one nonzero feature per pair has r = 0 exactly, whatever it does.

Neither form sees the charter. R and G are constants, and the charter appears nowhere in r. The same action scores the same residue against any two charters, opposite ones included. Under either operator, r cannot measure faithfulness *to a charter*, which is what the hypothesis says it measures.

What remains of the idea is its sentence, not its matrices: *applying the charter and then planning gives the same result as planning and then applying the charter.* That can be measured with the real operators instead of two fixed 2×2 matrices: the rails (conscience::Conscience) and the voice's planning, on the same proposals in both orders. It needs the voice to emit proposals, which it does not yet do. If it is run, it is a new pre-registration with its own rule, and this record stays as the reason why.

Verdict — 2026-09-22

Declined. The author (Nick Flach) adopted the reading proposed above: an AUC interval lying wholly below 0.60 declines, as one that includes 0.60 does. This amends a pre-registered rule after the result was known, and it is recorded as that. It changes only which branch a constant falls into. No reading of the original rule could make the experiment keep the residue, and its literal outcome was a repeat no fixture set could end.

Consequences, per the rule's Declined branch:

  • The operator stays out of the conscience. The rails keep their current tests: the confidence floor, the Five Refusals per effector, the hard constraints, the rate window and the dry run. No residue is computed or reported on a verdict.
  • There is no callosum in the build (E-001, E-002), so the "stays in the callosum" half of the branch has nothing to act on here. The operator remains where it is measured: consciousness-core's nonlinear signature.
  • The archaeology records the attempt, and it records the April audit that already held the answer.

Only a new pre-registration reopens this question, measured with the real operators (the rails and the voice's planning, in both orders) as §Pre-run check describes. That is E-008, pre-registered 2026-09-22.