Discovered before implementing Phase 1: the live identity trajectory
final_state.F carries the invariant versor_condition(F) < 1e-6 — it is a
VERSOR (even-grade operator, grades 0/2/4, exactly zero grade-1 content).
§2.1/§2.2's literal 'project psi_traj onto the grade-1 value subspace' is
therefore VACUOUS on the real runtime object: P_id(F) = 0 identically,
flagging every trajectory — a fail-closed brick. Root cause: a versor is
an operator, not a state vector; projecting the operator into a subspace
of states is a category error.
Resolution (ratified by Joshua Shay 2026-07-17): measure whether the
versor PRESERVES the value subspace, via its action on the axes
F a_i F~ (sandwich). Two per-axis measures, both empirically verified
necessary and non-redundant:
- subspace leakage = euclidean_norm(rot_i - P_I(rot_i)) — catches a
versor tilting a value axis toward an alien dimension (e4/e5);
- signed self-alignment = <a_i, rot_i>_0 — catches in-subspace
inversion (e1 -> -e1: leakage 0 but self-align -1), the concrete
realization of the ratified 'signed overlap, never abs()' decision.
Keeps the grade-1 pack axes unchanged (no pack migration) and sharpens
inalienability: identity is invariant UNDER transformation, not a frozen
state.
§4a rewritten to the operator-preservation spec (lift_axis, gram_matrix,
subspace_project, sandwich, euclidean_norm, axis_response); governance
annotation item 12 records the reframe + ratification; plan doc §3 Fact C
+ §5 Phase 1 + progress log updated.
[Verification]: docs-only ADR/plan amendment; provenance/ADR guard
(test_adr_0241_governance_p12.py) 6 passed — ADR-0244 Status line
confirmed still 'Proposed' (the item-12 ratification text is inside the
annotation/§4a, not a status flip). All acceptance numbers pre-verified
via in-tree numerical probes against algebra.cl41.
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