[noahgift]

prop_scale_invariance asserted the ε=0 theorem against the ε=1e-6 implementation, and failed whenever α²·mean(x²) ≈ ε — the regime its own generator reaches. Killed #3621's shard 1/3 (the T-0 PR).

Two commits, RED in history:

git checkout <RED>  && cargo test -p aprender-core --test contract_tests regression_3627   # FAILED
git checkout <HEAD> && cargo test -p aprender-core --test contract_tests regression_3627   # ok

The property

With ε in the denominator, exactly:

RMSNorm(α·x) = sign(α) · RMSNorm(x) · √((m+ε)/(m+ε/α²)), m = mean(x²)

Re-derived in f64 on the killing input: relative error 2e-16. The ε=0 theorem (RMSNorm.rms_scale_zero_eps, "Proved for ε=0") is the k→1 limit and is false when α²·m is comparable to ε. The killing input has α²·m = 1.91e-6 against ε = 1e-6 and a 19% discrepancy: y[1] = -1.414158, y_scaled[1] = -1.146122 — the issue's numbers, reproduced independently to six digits.

The implementation is right. The assertion was wrong. Option 1 from the issue: the proptest and the regression case now assert the ε>0 form with relative tolerance 1e-4, in every regime the generator reaches, and the guessed tol = 0.05 if |α| < 0.1 branch is gone.

Evidence

regression_3627_scale_invariance_in_the_eps_dominated_regime	ok — also pins y_scaled[1] = -1.146122, k = 0.810462
cargo nextest run -p aprender-core --test contract_tests prop_scale_invariance × 20, fresh seed each	20/20 (the criterion's own tool, not cargo test)
mutation: k := 1.0 (ε=0 restored) in the regression case	RED, rel = 0.18953769
the whole rmsnorm suite	12 passed, 0 failed
pv validate contracts/rmsnorm-kernel-v1.yaml	valid
cargo test -p aprender-contracts --lib (sigma armed)	1666 / 1666

RN-INV-005's formal now states the ε>0 property; its Lean notes say which regime the ε=0 theorem covers; FALSIFY-RN-002 names both tests and the mutation. The edit adds no file and no triple — census/graph/README unchanged, checked by regenerating with the pinned pv.

The done_when item that had to be withdrawn, and why

The issue asked for the test to be "regenerated with pv probar --binding, no hand edit" — the file's header says DO NOT EDIT — regenerate. That cannot be done. Measured with the pinned pv 0.68.2, both binding paths:

pv probar contracts/rmsnorm-kernel-v1.yaml --binding …  →  7 tests, all #[ignore = "no binding available"]
tracked rmsnorm_contract.rs                              →  5 real property tests

Obeying the header would have replaced five real tests with seven ignored stubs. The bodies came from the pre-monorepo generator (20dda945b, 2026-02-18); the in-tree pv probar has never been able to produce them. This is a declared hand edit, the header on this file now says so and why, and the item was withdrawn on the issue citing this measurement.

Then the class: every crates/aprender-core/tests/contracts/*_contract.rs with a matching contract — ~30 files — differs from its regeneration, and every regeneration is stubs. Not one DO NOT EDIT header in that directory is true. #3630. Not absorbed here; the guard is the deliverable there.

One line for the receipt row

nextest [profile.ci] retries = 2 replayed the case proptest persisted to proptest-regressions/ on TRY 1, so TRY 2 and 3 failed in 0.005 s each — three tries, one failure. A retry cannot un-persist a counterexample; retries are theater for property tests.

Closes #3627 — every remaining done_when item is met on the table above and item 2 was withdrawn on the issue itself (21:40Z) for the measurement this body records; the closing keyword is added against the issue's own text, not this body's summary of it.

keep-open: #3630 is the header class and its guard; #3621 is the T-0 PR this unblocks and merges on its own. Refs #3621, #3630.
ont-delta: none — an obligation's formal and a hand-maintained test, with no ontology type, shape or known-red list touched.

🤖 Generated with Claude Code

[github-actions]

§13.11 rung 1 — quorum shadow verdict

S13-SHADOW pr=3631 head=30493c1e2cc841ee2e3a1245984062319253a3a3 verdict=REFUSE class=Q1 arm_rc=1

Shadow mode: this records a verdict and merges nothing. A refusal
to arm is not a block (§13 adds zero rows to §7) — the pull request is
exactly as green as it was.

[noahgift]

Quorum routing (AD-04, Phase 1 step 4), stated by the author.

Files: contracts/rmsnorm-kernel-v1.yaml, crates/aprender-core/tests/contracts/rmsnorm_contract.rs → |M| = 2 {contracts, crates/aprender-core}.

• Q1 |M|≥3: no
• Q2 spec/plan artifact: arguable — an obligation's formal changed, which is a specification change; flagged rather than waved through
• Q3 five-whys diverge: no
• Q4 --quorum always: no

No trigger under the ≥3-modules rule in force tonight. No quorum receipt exists for this PR; if Q2 is read as firing, this is disarmed until a lane judges it. This PR was not built through paiml-implement, so this is a post-hoc routing statement, not a Phase-1 plan line.

[noahgift]

quorum-review (AD-04): three PASS — agreed (auto_merge: checked=true was_armed=false disarmed=false)

{
 "ticket": "PMAT-3627",
 "head": "fd068099fd8ad3a31c802c18ee1655944dfad49e",
 "width": 3,
 "executor": "agy",
 "agreed": true,
 "auto_merge": {
  "checked": true,
  "was_armed": false,
  "disarmed": false,
  "note": "auto-merge not armed"
 },
 "lanes": [
  {
   "lane": 1,
   "verdict": "PASS",
   "findings": 3
  },
  {
   "lane": 2,
   "verdict": "PASS",
   "findings": 0
  },
  {
   "lane": 3,
   "verdict": "PASS",
   "findings": 5
  }
 ]
}

[noahgift]

AD-04 quorum: 3/3 PASS, three independent lanes

docs/audits/quorum-PMAT-3627.json, executor agy, width 3, judged at head fd068099f, author model claude-opus-5:

lane	model	verdict
1	gemini-3.1-pro-high	PASS (3 findings)
2	gemini-3.8-flash-high	PASS (0 findings)
3	gemini-3.7-flash-high	PASS (5 findings)

dissent: []. Independence inspected: zero references to a sibling lane, $WORK, or the .lanes/ dir in any lane file. None of the three models is in the author's family. The ticket was registered on this branch (fragment + aggregate) so pmat work status could resolve it; the registration commit precedes the receipt.

[noahgift]

Cross-inspection of docs/audits/quorum-PMAT-3627.json lanes (non-author: aprender-04, 23:09Z)

lane	conversation	status	verdict	findings	refs to sibling lanes/receipts	turns
lane 1	8967174e	SUCCESS	PASS	3 (3 cited)	0	1 turns / 377.661577467 s
lane 2	73a37273	SUCCESS	PASS	0 (0 cited)	0	1 turns / 226.892534496 s
lane 3	9ceecf3d	SUCCESS	PASS (structured_output)	0 (0 cited)	0	1 turns / 163.873795262 s

Distinct agy conversation ids: 3/3. No lane's response references another lane's file or any quorum-PMAT-*.json. Each verdict is grounded in its own findings (file:line). Read from /mnt/nvme-raid0/agent-wt/rmsnorm-3627/docs/audits/quorum-PMAT-3627.json.lanes on this box; the receipt on the branch records agreed: true, three PASS, models gemini-3.1-pro-high / 3.8-flash-high / 3.7-flash-high, author claude-opus-5 (flag).

Verdict line: 3/3 PASS, independent. Arming.

Table corrected 23:12Z: two cells first read "None" because my parser took response instead of structured_output; the receipt's verdict_source is structured_output for all three lanes and all three are PASS there. #3617 lane 2 opens with an interim sentence ("running in the background…") but its structured summary records the guard run (check_tag_step_gated.sh rc=0, --self-test rc=0, 3 mutants killed) — a completed review, not a premature PASS.