Add a row/column-convention consistency check for plans that fit or consume a linear map

Goal

Close a demonstrated review-surface gap: nothing on the plan-review surface catches a plan that mixes row-vector and column-vector action on the same fitted linear operator. Add a mechanical verify_plan.py check plus a critic lens item so the error is caught at Phase 1.5.0 instead of surviving to a Phase-3 revise round.

The incident (#2569 plan v3, 2026-08-25)

#2569's plan registers the row-vector prediction path vhat = ((v - xmu)/xsd) @ W + ymu (equivalently vhat = v @ A + b with A = diag(1/xsd) @ W), then across five legs applies the operator on the LEFT of column vectors — the transpose map:

• §3 H2 and §4 leg 2 step 1 register the gate metric as W.T @ W; the row-consistent metric is W @ W.T.
• §4 leg 1 step 3 classifies functional anatomy on RIGHT singular directions via cos(A w_i, w_i); under row action the input directions are the LEFT singular vectors, with u_i @ A = sigma_i v_i.
• §4 leg 8 step 2 mines on ||A Dc_std||; row-consistent is ||Dc_std @ A||.
• §4 leg 3 steps 2/4 wire E_f . A . D and gate direction A.T r.

The plan was INTERNALLY INCONSISTENT, which is what makes this mechanically detectable: §4's own convention block and the fixed-point solve x*(I - A) = b are row-form, and leg-1 step 4's u->read / v->write pairing is already correct, while the formulas above are column-form.

Measured impact on the actual banked operator (data/issue_2094/joint_transport/banked_maps/issue779_monitoring/n1m_readout/weights/L19/ridge.pt, W 3584x3584, non-normal — #1774 measured eigenvector condition number ~4,519):

• ||A A.T - A.T A||_F / ||A||_F^2 = 0.126 (materially non-normal)
• Spearman(||x@A||, ||A@x||) over 4,000 random unit directions = 0.056
• Spearman(c.T W W.T c', c.T W.T W c') over 4,000 pairs = 0.31
• argmax-partner agreement between the two gate metrics = 5/200 = 2.5%
• |cos(u_1, v_1)| = 0.084; top-8 |cos(u_i, v_i)| 0.08-0.24
• row identity u_i @ A = sigma_i v_i holds to 1.3e-15; the column form A v_i ~= sigma_i v_i is off by relative 1.31-1.35

So the plan's forms and the row-consistent forms rank directions and context pairs almost independently, flipping the registered H1, H2, H3 and H8 verdicts. Three independent probes (two reconcilers plus the orchestrator, different statistics each) agreed.

Why this is a workflow-surface gap, not just a plan bug

• verify_plan.py has NO orientation or convention check (grep for orientation / row-vector / column-vector / transpose returns only unrelated senses of "convention").
• .claude/rules/critic-lens-reference.md and .claude/agents/critic.md carry no row/column item.
• ALL THREE Claude critic lenses (Methodology, Statistics & Measurement, Alternative Explanations) returned APPROVE on this plan. Both Codex twins caught it independently, and both explicitly wrote that "this recurring row/column-orientation check belongs in a workflow-surface verifier." The Claude-side miss across three lenses is the evidence that no lens owns it.
• The class is recurring, not one-off: any plan that fits or consumes a linear map (v_X -> v_Y predictors, ridge/OLS readouts, persona-vector transports, operator atlases, SAE wiring products) can mix conventions, and CLAUDE.md's standing identity+bias / kNN mapping-baselines rule means such plans are common in this project.

Proposed fix

1. Mechanical check in scripts/verify_plan.py (new check id, WARN-first then FAIL once precision is established): when a plan declares a row-vector prediction path (regex on @ W, v @ A, x @ W, vhat = ... @ ...), flag co-occurring column-action forms on the same operator — W.T @ W / W.T W used as an INPUT-space metric, A x / A @ Dc / cos(A w_i, w_i) / A.T r — and vice versa for a declared column path. The internal-inconsistency shape is the reliable trigger: FAIL/WARN only when BOTH conventions appear for the same symbol, which avoids penalizing a plan that consistently uses either one. Emit the offending line numbers and both forms.
2. Critic lens item (Statistics & Measurement, and cross-referenced from Methodology): for any plan that fits or consumes a linear map, verify the declared action side and check that every induced metric, singular/eigen direction family, and displacement norm is written in that convention. Add to .claude/rules/critic-lens-reference.md and the .claude/rules/lens-coverage-map.md ledger.
3. Identity-assert convention for implementers: a plan or implementation that consumes a banked map asserts the identities ||x @ A||^2 == x (A A.T) x.T and u_i @ A ~= sigma_i v_i, and that reported statistics run through the artifact's own registered apply_map path rather than a re-derived product. Consider a .claude/rules/ entry (or an addition to the existing identity+bias / kNN mapping-baselines rule family) so the assert is the default for map-consuming code.

Acceptance

• A regression fixture reproducing #2569 v3's mixed-convention shape FAILs (or WARNs) the new check; a byte-equivalent fixture written consistently in either single convention PASSes.
• The new lens item appears in critic-lens-reference.md and the lens-coverage-map.md ledger, and workflow_lint.py --check-lens-coverage stays green.
• .claude/rules/LESSONS.md index updated if a new rule file is added (enforced by workflow_lint.py --check-lessons-index).

Provenance

Filed by the #2569 /issue orchestrator during the Phase-3 union round, 2026-08-25. Source evidence: #2569 events.jsonl markers epm:progress "Orientation Must-Fix VERIFIED NUMERICALLY against the banked map", epm:plan-critique-reconciled (Statistics lens) and epm:plan-critique-reconciled (methodology + alternatives union). #2569 itself is fixing its own plan in v4 (blocker B1); this task fixes the SURFACE so the next such plan is caught mechanically.