gate_w1 amendment 3: demote the hh_size quad + pair-scope C2 (ratified after five-round ceremony)

[MaxGhenis]

Fixes round 1 applied (adversarial referee comment 4962052314, verdict AMEND
THE AMENDMENT — recommendation survives on every recomputed probe). F1 (primary):
§2a/§1/§4b-c-c/§8/§10 asserted the C2 impossibility as a universal ("a frame cannot
both realise the swap and reproduce Smith's cap rank"), which forensics-3's own
f-conditional order_at_f_deployed_0p22 refutes (a frame at f≈0.22 realises the swap
and holds the full 4-element order, τ=1.0) — now scoped to the pinned certified
frame, leading with the two dispositive grounds (the bit-identical deployed-frame
cap-rank-2 measurement, A_band/B 0.373; and no published representative-frame anchor
for the 4-element order), the f-conditional window kept as analysis with the caveat
stated, plus a mutation guard against the universal phrasing. F2 (minor): the
fertility lever now reads "support ceiling"/maxed consistently. The recommendation is
unchanged.

Fixes round 2 applied (verification comment 4962578395, verdict FURTHER FIXES ×2 —
both grounds-precision text edits, recommendation untouched). V1: this Evidence
bullet — the squash message — carried the round-1 universal verbatim; it now states the
pinned-frame grounds and keeps the f-conditional window as analysis (mirrors §8). V2:
the §2a restoration clause is scoped to the pinned A/B (needs f < 0.0476), restoring the
artifact's "small enough (<0.5)" gloss and the no-contract-permitted-lever conjunct; the
universal-phrasing guard is extended to the earnings-distribution / representative-frame
synonym class (the M4/M4b analogues now caught).

Note for ratification: the title's (ceremony pending) marker is stripped by the
maintainer at ratification (they retitle then); the body below is the squash message.

Recommendation

Demote the four family-A household-size cells hh_size_share.{1,3,4,5plus} to
report-only (uniform machine reason no_permitted_entry_state_lever_reaches_cell),
and re-scope the family-C gated binary C2 from the full 4-element compression
ordering to the pair-scoped elim↔+2pp adjacent swap — the cap_150k/+1pp legs
publish report-only (anchor_ordering_internally_inconsistent_under_certified_swap).
hh_size_share.2 stays gated (candidate 3 clears it 5/5). Zero threshold movement;
gates.yaml is UNTOUCHED — the flip is a separate ratified PR.

The whittling question, up front

The post-amendment 44-cell surface (43 family-A joints + the pair-scoped C2) would
be PASSABLE by the already-committed candidate-3 model: c3 lands 43/43 of the
surviving family-A cells in-band on all five seeds, and the elim↔+2pp swap realised.
That is a first for this gate, and it puts the whittling question in its sharpest
form. The burden is carried head-on (§3): every demoted/re-scoped element is
forensics-proven unreachable by any contract-permitted lever (Q10 construction
enumerates empty; Q11 levers exhausted, three candidates deep), and every one was
pre-named in the ratified amendment-2 series forecast BEFORE c3 ran — the demotion
boundary is the permitted-lever line applied prospectively, not a post-hoc fit to
c3. Candidates 1 (#162), 2 (#167), and 3 (#176) all STAND FAIL (no self-rescue;
c3's committed FAIL was scored under the current contract). A candidate-4 registration
of the unchanged c3 model follows the flip, subject to the standing independent
bit-exact reproduction addendum.

Evidence — W1 forensics 3 (registration 4959668253, grading 4960691167)

• Q10 (cap_150k): the deployed frame's above-cap payroll share owns 0.9925 of
  the 16.7y-vs-1y gap; on the pinned certified frame the same compression correction
  that certifies the elim↔+2pp swap puts cap_150k at rank 2 (deployed A_band/B
  0.373, bit-identical across c1/c2/c3; deployed A/B 1.694 PV), so the pinned
  transport target violates the full Smith order while realising the swap —
  internally inconsistent ON THE PINNED FRAME, NOT a universal claim. The
  order-survival window is f-conditional (0.1613, 0.0806/f): at f≈0.44 it is (0.1613,
  0.184) and the pinned A/B sits ~10× above it, but at f≈0.22 forensics-3's own
  order_at_f_deployed_0p22 shows a representative frame that realises the swap and
  holds the full 4-element order (τ 1.0) — the re-scope drops a target the pinned frame
  cannot hold, not one no frame can. No published anchor supports the full 4-element
  ordering on a representative frame; contract-permitted lever restoration enumerates
  empty. The pair-scoped C2 is anchor-supported (Smith 2015 p.3: elim +21yr > +2pp
  +18yr) and realised 3/3 across c1/c2/c3.
• Q11 (hh_size): mixed-but-structured attribution (size-1↔size-3+ coresidence
  mirror 0.98; coresidence owns size-3 0.75; fertility owns size-4 0.67,
  size-5plus 0.78); levers exhausted — the roster-ceiling probe reaches
  terminal coresidence only 0.111 (capped by the certified parental-exit hazard,
  not the seed) and does not close size-1; the residual needs a non-entry-state
  household model.

OC + partition consequence

• Family A 47 → 43 gated; p_seed 0.9344 → 0.9403, p_gate 0.9623 → 0.9684
  (recomputed on the frozen floor sigmas).
• Gate OC: 0.9623 × I(C2) → 0.9684 × I(pair-swap).
• Partition 48 → 44 gated / 84 → 88 report-only; cube shape [20,47,5] →
  [20,43,5].

Ceremony stage

PROPOSAL (draft) — ceremony pending. This PR moves no threshold and edits no
gates.yaml cell; the referee round is done, verification is the next step. The
machine-checkable ledger and the §7 flip text are string-bound to
tests/test_gate_w1_amendment3_proposal.py — 26 artifact-tier bindings for every
load-bearing figure (forensics-3 shares/mirror/ceiling, per-cell pass records from all
three candidate cubes, OC before/after, partition roll-ups, and — new this round — the
pinned-frame scope + the f-conditional order_at_f_deployed_0p22 refutation) plus a
mutation battery (16 distinct mutations caught, including the
blanket-impossibility-reintroduction, whittling-section-deletion, and — new this round —
the universal-C2-phrasing and fertility-terminology guards). Tier manifest recount:
artifact 965 → 991 (rebased onto the gate_m6 lock, #177; +26 a3 tests).
gates.yaml is byte-identical to origin/master.

Mirrors the ratified amendment 2
(docs/amendments/gate_w1_amendment_2_family_a_concept_cells.md): section numbering,
ledger, §7 string-bound flip text, §8 history draft, and candor standards.

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[MaxGhenis]

Adversarial referee — gate_w1 amendment 3 (draft PR #180 @ 481cf1e)

VERDICT: AMEND THE AMENDMENT. The recommendation — demote the four hh_size cells ({1,3,4,5plus}) and re-scope C2 to the pair-scoped elim↔+2pp swap — survives every recomputation I ran: P1 (whittling), P2 (per-cell truth), P4 (OC/partition/mutations), P5 (no-self-rescue), and P6 (hygiene) are clean. But hunting for the a2 defect class the brief named — a false/over-stated impossibility claim — I found it re-instantiated in the C2 argument (not the per-cell records, which are immaculate this round): a frame-level universal that the forensics-3's own true_frame_sensitivity table refutes. The recommendation stands on independent, dispositive grounds; the overstated grounds must be scoped to the pinned frame. That is a grounds-precision fix (survives, correct the grounds) — the same disposition the a2 adversarial round returned.

P1 — the whittling question, ruled plainly: principled line, not a whittle.

I re-derived both legs from the committed artifacts myself. (i) Reachability. Q10's ledger identities reproduce exactly from the OASDI rate r=0.124: breakeven A/B = 0.02/r = 0.16129 (elim>+2pp); window upper at f_psid=0.438 = (0.01/r)/0.438 = 0.18408, width 0.02279; deployed A/B = d_bal_elim/r = 1.694; cap exhaustion 16.7yr is bit-identical to the committed cube — the deployed pinned frame measurably puts cap at rank 2. Q11's lever space is exactly two knobs {roster∈[0,1.0], fertility∈[0,15-window]}; the forensics tested all four corners + the ceiling probe (roster=1.0 ∧ 15-window → size-1 0.179 vs frame 0.083), both levers move size-1 monotonically toward the frame, and the extreme corner overshoots by 0.096 — so no untried permitted config exists (arithmetically closed; roster hazard-capped at terminal coresidence 0.111). (ii) Pre-naming. The ratified a2 forecast's amendment3_risks = exactly {hh_size_share.1,3,4,5plus, c2_cap_150k_adjacency} — the QUAD (post-size-2 reconciliation) + the cap adjacency specifically; it was present at ratification commit c50f8bb and the file is unmodified since, and git merge-base confirms c3's scored run (64ebf97, 11:29) is a descendant of the a2 ratification (c50f8bb, 00:12), so the boundary was drawn before c3 existed. Both legs hold: the demotion boundary is the permitted-lever line applied prospectively, not a post-hoc fit to c3.

P3 — the re-scope, ruled plainly: principled, not weaker-for-convenience — but the "internally inconsistent" grounds overstate (Finding 1).

The pair-swap certifies exactly the mechanism the fingerprint exists for (Smith 2015 p.3 anchor: elim +21yr > +2pp +18yr; realised 3/3 deterministically across c1/c2/c3), drops precisely the two provisions whose ranks the representative tail mechanically moves, and states what it does not certify (§4b, §9). The dispositive ground for dropping the 4-element gate is correct and frame-pinned: the deployed certified frame measures A_band/B = 0.373 (cap 16.7yr, bit-identical) → cap rank 2 → the frame the gate is pinned to violates the 4-element order, so gating it would gate an unsatisfiable target; plus no published anchor supports the 4-element order on a representative frame. On those grounds the re-scope is right. What is wrong is the generalisation used to dress it up — see Finding 1.

Findings

1 (AMEND — the primary item; the a2 defect class, re-instantiated in the C2 argument). §2a asserts as a universal: "Any frame compressed enough to realise the swap … must sit inside that width-0.023 window … A frame cannot both realise the certified swap and reproduce Smith's cap_150k rank, so the full 4-element ordering is internally inconsistent as a representative-frame transport target." This is false as a universal and the forensics-3's own true_frame_sensitivity refutes it. The (0.1613, 0.184) window is f-conditional — it is (0.1613, 0.0806/f), which widens to (0.1613, 0.366) at the deployed/SSA near-band fraction f≈0.22. I recomputed the artifact's own order_at_f_deployed_0p22 = [elimination, payroll_plus_2pp, payroll_plus_1pp, cap_150k]: a representative frame at A/B≈0.22, f≈0.22 realises the swap (elim>+2pp) AND reproduces the full Smith 4-element order (τ=1.0). So "a frame cannot both …" is true only for the certified/deployed pinned frame (A/B=1.694, A_band/B=0.373), not for representative frames in general; the "≈10× the window" force comes from holding f fixed at f_psid=0.438 while letting A/B run to the deployed value. §2a's parenthetical ("the break is f-dependent near a boundary ~0.37") gestures at this but does not retract the categorical sentence. Fix: scope the C2 impossibility to the pinned/certified frame throughout §2a/§4b-c-c (as the artifact's own verdict field and the machine tag …under_certified_swap already correctly do), and lead with the two grounds that actually carry it — the bit-identical deployed-frame cap-rank-2 measurement and the absence of any published representative-frame anchor for the 4-element order. The recommendation does not change.

2 (minor — wording). §2b/§4a call the fertility lever "at the certified support floor" while §2b elsewhere calls it "maxed at the 15-entry certified support." The substantive claim (fertility can't be pushed further to shrink size-1) is correct and lever-exhaustion is unaffected, but "floor" reads as the opposite of "maxed"; use "ceiling"/"maxed" consistently.

(Not a finding — verified honest: the §2b/§4a "size-1 coresidence 0.46" is the fertility-complement (1−0.54), and the ledger discloses both it (coresidence_complement_round2: 0.46) and the raw main-effect share (coresidence_main_effect_share_round2: 0.4); dominant channel is fertility under either. Disclosed, not misleading.)

Probes that recomputed clean (no findings)

• P2 per-cell truth. All three cubes recompute with zero score/pass mismatches from the raw [K×N×5] arrays. size-2 clears c3 5/5 (c1/c2 0/5) and stays gated; size-4 clears c3 seed 1 (1/5), stated plainly; sizes 1/3/5plus 0/5 on all three cubes. Whole-doc sweep: no blanket-impossibility sentence — every "unreachable"/"cannot" is scoped to permitted-lever/pinned-frame. Channel attributions 0.54/0.75/0.67/0.78 and mirror 0.98 recompute exactly from the forensics-3 config shares (my independent main-effect decomposition matches to 4 dp).
• P4 OC + bindings. From the frozen floor σ: 53-cell 0.922/0.9481, 47-cell 0.9344/0.9623, 43-cell 0.9403/0.9684 — all exact; demoted pass-probs 0.998012–0.998942 (doc 0.998–0.9989). Roll-ups 48→44 / 84→88 (total 132 conserved); schema [20,47,5]→[20,43,5]. 23/23 bindings pass, and a 16-mutation battery (the 11 documented + 5 of my own targeting the §3 whittling heading, the a2-forecast pre-naming binding, a blanket-impossibility insertion, the 43/43 figure, and the flip OC string) was caught in full — the bindings are non-vacuous.
• P5 no-self-rescue. c1 fails the residual-43 at 17/16/13/18/19 per seed and c2 at 7/5/8/8/8 — both over-determined FAILs beyond the demoted set. c3 passes all 43 residual cells but fails family-C's 4-element reversal (τ=0.333, reversed_to_anchor: false) and was scored on the 47-surface where the quad is gated → committed FAIL stands under the current contract. Rescue set verifiably empty; binding is prospective-only.
• P6 hygiene. gates.yaml byte-identical to origin/master (and no sibling gate differs). Only the 3 claimed files changed (doc + test + tier_counts.json). tier artifact 965→988 = +23 = the 23 new artifact-tier tests (conftest auto-marks by runs/*.json reference), live-verified by green pytest 3.11/3.13 on 481cf1e. CI all-green on 481cf1e (build/lint/pytest×2/Vercel); mergeable: MERGEABLE, mergeStateStatus: CLEAN.

Bottom line: the demote-quad + pair-scope-C2 recommendation is fully supported by the recomputed evidence and the whittling defense holds in its strongest form. Land Finding 1 (scope the C2 "internally inconsistent" grounds to the pinned frame; the recommendation is unchanged) and Finding 2 (wording), and this is ratify-ready.

[MaxGhenis]

Fixes round 1 — response to the adversarial referee (comment 4962052314)

Verdict addressed: AMEND THE AMENDMENT — recommendation survives. Both findings landed; the demote-quad + pair-scope-C2 recommendation is unchanged. Pushed as 60f6ee5.

F1 (primary) — the C2 impossibility was stated as a universal; scoped to the pinned frame

• Finding. §2a/§1/§4b-c-c/§8/§10 asserted "a frame cannot both realise the swap and reproduce Smith's cap rank / internally inconsistent as a representative-frame transport target" — false as a universal. Forensics-3's own order_at_f_deployed_0p22 = [elimination, payroll_plus_2pp, payroll_plus_1pp, cap_150k] is a representative frame (A/B≈0.22, f≈0.22) that realises the swap and holds the full 4-element order (τ=1.0); the window is f-conditional (0.1613, 0.0806/f), widening to ≈(0.1613, 0.37) at f≈0.22.
• Fix. Scoped the impossibility to the pinned certified frame throughout, leading with the two dispositive grounds — (1) the pinned/deployed frame measures cap at rank 2 bit-identically (A_band/B 0.373, cap 16.7yr, reproduced c1/c2/c3), so the pinned transport target violates the full order while realising the swap; (2) no published anchor supports the 4-element order on a representative frame. The f-conditional window is retained as analysis with the caveat stated plainly (a swap-consistent full-order frame exists at other f). The machine reason …under_certified_swap is retained — per the referee's ruling that its qualifier already scopes correctly — with a new pinned-frame ledger definition.
• Bindings. New cap_150k_impossibility ledger block (scope: pinned_certified_frame_only, is_universal_claim: false) bound to the artifact — deployed_A_band_over_B 0.373; the f-conditional window (0.0806/f; f_psid 0.438 → 0.184, f_dep 0.22 → 0.367); ssa_true_frame_A_over_B 0.22 strictly inside (breakeven, window_upper_deployed); and order_at_f_deployed_0p22 == the full Smith order, realising the swap (test_q10_impossibility_scoped_to_pinned_frame_not_universal). New mutation guard bans the universal phrasing (test_no_universal_c2_impossibility_phrasing). The existing §2a arithmetic test now also requires the pinned-frame scope.

F2 (minor) — fertility-lever terminology

• Finding. The fertility lever read "at the certified support floor" in some places and "maxed at the 15-entry certified support" in others — "floor" reads as the opposite of "maxed".
• Fix. Now "support ceiling"/maxed consistently (the lever is maxed at the 15-entry certified support; the lever-exhaustion claim is unaffected).
• Binding. test_fertility_lever_terminology_consistent (bans "support floor"; requires "support ceiling"/"maxed").

Hygiene

• Bindings 26 (was 23; +3). Full mutation battery re-run: all previously-caught still caught + the two new guards (16 distinct mutations caught).
• Tier recount: artifact 988 → 991 (+3), CI-equivalent (full-collection recount, 0 errors).
• Suite green inline (unit+artifact 1217 passed / 41 skipped / 0 failed); black -l 79 + ruff clean.
• gates.yaml byte-identical to origin/master; only the 3 claimed files changed. Ceremony record updated (§8 referee_round, §11 checklist). Stays DRAFT.

Fresh CI on 60f6ee5 reported below once green.

[MaxGhenis]

Verification round — gate_w1 amendment 3 (draft PR #180 @ 60f6ee5, fixes round 1)

VERDICT: FURTHER FIXES (2, both F1-class text edits; the recommendation is untouched). I re-ran the whole surface from the committed artifacts in a disposable env, trusting nothing: every load-bearing number in the doc, the ledger, and the PR body recomputes exactly — the Q10 ledger identities and the f-conditional window, the order_at_f_deployed_0p22 refutation, both dispositive grounds, the Q11 attribution/mirror/probe, the OC chain 53→47→43, the partition roll-ups, all three cubes cell-by-cell with zero score/pass mismatches, the no-self-rescue records, the pre-naming proof at the git level, and the 26 bindings + the mutation battery. F1 is resolved in the doc at every site the fixes named. But the sweep the a2 ceremony taught us to run — for the defect class surviving the fixes round itself — found it twice: once verbatim in the PR body (which this PR's own note designates the squash message), and once in a §2a clause the fixes left unscoped that the fixes' own new caveat paragraph now contradicts ten lines above it. Both are grounds-precision edits of exactly F1's kind; neither touches the recommendation, the ledger, or any bound number.

The machine-reason ruling (final for this round)

anchor_ordering_internally_inconsistent_under_certified_swap + the cap_150k_impossibility definition: ACCEPTABLE-WITH-DEFINITION — no rename. Stating the residual risk plainly: to an out-of-context reader the name alone is ambiguous between "inconsistent under the certified swap (as certified, on the pinned frame)" — true, and what the round-1 referee ruled it means — and "inconsistent under any realisation of the swap" — the universal F1 refuted (the A/B≈0.22, f≈0.22 frame realises the swap and holds the full order, τ 1.0). The pin rides on the single word "certified". I rule the name acceptable because: (i) machine reasons are identifiers whose claims-exact content is fixed by their definition, and the fixes added a machine-checked one — scope: pinned_certified_frame_only, is_universal_claim: false, the two dispositive grounds enumerated — bound by test_q10_impossibility_scoped_to_pinned_frame_not_universal and mutation-guarded (my B13/B14/M1 mutations all caught); (ii) every prose site where the tag appears now carries the pinned-frame scope in the surrounding sentence (§1, §2a, §4b, §8, §9); (iii) the §8 history entry — which lands inside gates.yaml at the flip (§7.7), i.e. at the tag's operative site — spells out "internally inconsistent ON THE PINNED FRAME, NOT a universal claim"; and (iv) a rename now would churn ~10 string-bound sites against a standing round-1 ruling for marginal gain. Conditions attached: the ledger definition stays bound, and the flip PR carries the §8 history text as §7.7 specifies. I verified the tag exists nowhere else in the repo (not in the forensics artifact, not in gates.yaml) — it is amendment-authored, so the definition in this doc is its authoritative gloss.

Further fixes (numbered)

V1 (primary — the F1 universal survives verbatim in the PR body / squash message). The PR body's Evidence bullet still reads: "…so the 4-element ordering is internally inconsistent as a representative-frame transport target (elim>+2pp ⇔ A/B>0.1613 vs the Smith-adjacency window A/B ∈ (0.1613, 0.184), overshot ~10×)…" — the exact phrase round 1's F1 adjudicated as false-as-universal, with the window stated f-fixed (no 0.0806/f, no caveat). The body's own "Note for ratification" designates "the body below" as the squash message, so at ratification this text enters the permanent git history carrying the refuted universal — while the preamble two paragraphs up says the claim is "now scoped to the pinned certified frame". The doc is fixed; the squash message is not, and the mutation battery structurally cannot reach it (tests can't read PR metadata; my B04 check confirms the guard fires on this string in the doc only). Fix: edit the PR-body bullet to the doc's post-fix language (e.g. mirror §8: "on the PINNED certified frame … puts cap_150k at rank 2 (A_band/B 0.373, bit-identical across c1/c2/c3) … internally inconsistent ON THE PINNED FRAME, NOT a universal claim; window f-conditional (0.1613, 0.0806/f)"). A GitHub edit; no commit.

V2 (the F1 class survives one clause inside §2a itself — the section the fix was ordered to scope "throughout"). The restoration paragraph's closing clause: "f = A_band/A stays large (PSID 0.438, deployed 0.220) and no unimodal earnings distribution makes it small enough while landing A/B in the window: restoration_exists: false." Four problems, each recomputed:

• It is an unscoped frame-level universal over earnings distributions, and the fixes' own caveat paragraph ten lines above now asserts the counterexample: "A swap-consistent full-order frame therefore does exist at other f" — that frame (A/B≈0.22, f≈0.22, both artifact fields) lands A/B inside its window (0.1613 < 0.2195 < 0.3667). The two sentences cannot both stand as written; this is the a2 defect class surviving the fixes round, in-section.
• The artifact parent (construction_attempt.near_band_dominance) at least glosses "small enough (<0.5)" and conjoins "and no contract-permitted lever"; the doc dropped both, leaving a bare universal. (The gloss itself is no help: both measured f values — 0.438, 0.220 — are already < 0.5.)
• The "f stays large" premise is not load-bearing: at the deployed f itself (0.220) the window is (0.1613, 0.3666) — wide. The pinned frame's impossibility comes entirely from its pinned A/B = 1.694, which needs f < 0.0806/1.694 = 0.0476 to land in-window. That is the true, scoped content.
• The slot is unguarded: my synonym mutations M4 ("no earnings distribution of any shape can realise the swap and hold the full order") and M4b ("no representative frame whatsoever can realise the swap while reproducing Smith's cap rank" — semantically the banned universal verbatim) both pass the suite. The guard is a string guard; this clause lives in its blind spot.

Fix: scope the clause to the pinned frame's A/B — e.g. "no contract-permitted lever moves the pinned frame into the window (its A/B 1.694 would need f < 0.048, far below any near-band-densest tail; and tail back-solving is the prohibited identity-in-disguise): restoration_exists: false" — and (recommended) add the corrected slot to test_no_universal_c2_impossibility_phrasing plus a binding for the caveat's existence sentence (soft spot 2 below).

Per-item verification results (all recomputed from the committed artifacts, none trusted)

1. F1 resolution + whole-doc sweep. Doc-side: resolved at every fixed site — I diffed 481cf1e→60f6ee5 line-by-line and swept all 11 sections + ledger + PR body for the class (cannot, no frame, any frame, internally inconsistent, incoherent, impossible, no … distribution, universal); §1/§2a-headline/§4b-c-c/§8/§10/checklist/ledger are all pinned-frame-scoped; survivals = exactly V1 + V2. The caveat restates the artifact exactly: from raw ledger components, A/B_dep = d_bal_elim/0.124 = 1.69387 → 1.694; A_band/B = d_bal_cap150/0.124 = 0.372567 → 0.373; f_dep = 0.219950 → 0.22, f_psid = 0.438104 → 0.438; breakeven = 0.02/0.124 = 0.16129; window upper = (0.01/0.124)/f: at f_psid 0.18408 (width 0.022787 → 0.0228), at f_dep 0.36665 (ledger 0.367, doc ≈0.37); order_at_f_deployed_0p22 recomputed from provision revenues at (A/B 0.2195, f 0.21995) = [elim, +2pp, +1pp, cap] — swap realised (0.124·0.2195 = 0.02722 > 0.02), in-window, τ = +1.0; deployed order recomputed = [elim, cap, +2pp, +1pp], cap rank 2, τ vs required 0.3333; deployed A/B = 9.20× the f_psid window upper ("~10×" fair). Ground 1 (bit-identity): provision_deltas byte-identical across c1/c2/c3 (cap 16.7453575523391 in all three) and forensics-3 committed-vs-rerun max_abs_dev = 0.0. Ground 2 (no published anchor): artifact any_published_anchor_supports_full_4_element_on_representative_frame: false with the provenance block (only anchor: Smith 2015, Urban 72196, DYNASIM 2014 TR); the doc restates it as an evidence-base claim, exactly; bound twice (tests 10, 13). Gap decomposition recomputes: 15.6265/15.7454 = 0.99245 → 0.9925, 0.11885/15.7454 = 0.0075.

2. Machine reason: ruled above — acceptable-with-definition, no rename, conditions stated.

3. F2. "support floor" purged (0 hits); "support ceiling" ×5 + "maxed" consistent; every remaining "floor" token is the floors-artifact/sampling-floor sense; test_fertility_lever_terminology_consistent enforces it (my B06 regression caught). Lever-exhaustion content unchanged and recomputed: roster ceiling terminal coresidence 0.111191 → 0.111, size-1 at ceiling 0.178605 → 0.179 vs frame 0.083466 → 0.083, closes_size1: false, verdict: levers_exhausted; attribution 0.5400/0.7525/0.6672/0.7822 → 0.54/0.75/0.67/0.78 with the 0.46 complement and 0.40 main-effect both disclosed; mirror −0.047007/+0.046245, ratio 0.98380 → 0.98; partition-to-1.0 max dev 1.11e-16. (The §4a "0.107 size-1 excess" traces to forensics-2 Q7 size1_residual_vs_frame = 0.107012 — artifact-grounded.)

4. The unchanged core. OC chain from the frozen floor σ + gates.yaml view tolerances (cell pass = 2Φ(tol/σ)−1; seed = product; gate = p⁵+5p⁴(1−p)): 53-cell 0.9220/0.9481 (floor's own block reproduced), 47-cell 0.9344/0.9623 (= the live contract's committed block), 43-cell 0.9403/0.9684; demoted quad pass-probs 0.998012–0.998942 → min 0.998 / max 0.9989. Partitions: family A 47→43 gated / 58→62 report-only; family C 1/1; overall 48→44 / 84→88, total 132 conserved. Schema [20,47,5]→[20,43,5] (current gates.yaml shape verified [20,47,5]; c3's cube is (20,47,5), c1/c2 (20,53,5) per their lock-era surface). §7 flip text string-bound (my B10/B11/B16 + full-tag-rename B15r all caught). §8 carries the real referee round (4962052314, verdict, F1/F2); the fixes: '<sha>'/verification placeholders are structurally necessary pre-ratification (a commit cannot contain its own SHA). No-self-rescue, recomputed from the raw cubes (every rbar/score/pass re-derived; 0 mismatches vs recorded, all three cubes): hh per-cell {c1,c2,c3} seed-passes = size-1 0/0/0, size-3 0/0/0, size-4 0/0/1 (seed 1 exactly), size-5plus 0/0/0, size-2 0/0/5; residual-43 per-seed fail counts c1 17/16/13/18/19, c2 7/5/8/8/8 (both over-determined FAILs beyond the demoted set); c3 residual-43 0/0/0/0/0 — the 43/43-on-5/5 whittling premise is cube-true — with C2 4-element missed (reversed_to_anchor: false, both_reverse: false, τ 0.3333, cap at rank 2) and the pair-swap realised 3/3; gate_pass: false for all three. Pre-naming at the git level: a2 amendment3_risks = exactly {hh_size 1,3,4,5plus, c2_cap_150k_adjacency}; the a2 doc has zero commits since ratification c50f8bb; git merge-base --is-ancestor c50f8bb 64ebf97 = true (c3's scored run post-dates the ratified forecast).

5. Bindings + mutations. Disposable env (uv venv + -e .[dev]): the module runs 26/26 passed; full always-runnable suite 1217 passed / 41 skipped / 0 failed (matches the fixes claim); black -l 79 + ruff clean. Battery: 16 documented-class mutations all caught in the claims-relevant form — blanket-impossibility insertion, whittling-section deletion AND heading-rename, both universal-phrasing reintroductions, support-floor regression, ledger OC/pass-record/pre-named-risks corruption, §7 OC-string/cube-shape/roll-up corruption, §8 KNOWN-PASSABLE softening, scope→"universal", is_universal_claim→true, full §7 tag rename. Plus mine: M1 delete the cap_150k_impossibility ledger block — caught; M2a delete the f-conditional caveat paragraph — caught; M3 §3 "43/43"→"42/43" — caught; M5 ledger ssa 0.22→0.44 — caught. Honest misses (reported, not required): M2b deleting only the caveat's existence sentence passes (test 10's OR-fallbacks still satisfied) — soft spot; M4/M4b synonym universals pass — the V2 evidence; B15 single-site tag rename passes (presence-bound, not per-site) — nit.

6. Hygiene. gates.yaml byte-identical to origin/master (0-byte diff; same blob f1a96e68; sibling-gate compare enforced in-suite). Tier 991 live-verified: 991/2734 collected under the artifact marker; trajectory 965 (master) → 988 (481cf1e, +23) → 991 (60f6ee5, +3) — the PR body's "965→991 (+26)" and the fixes' "988→991 (+3)" are both consistent. Only the 3 claimed files in the diff (doc + test + tier_counts.json). Fresh at review time: head 60f6ee5, mergeable: MERGEABLE, mergeStateStatus: CLEAN, still DRAFT; gh pr checks 180 exit 0 (build/lint/pytest 3.11+3.13/Vercel pass; deploy = skip).

Soft spots for the fixes round to fold in (non-blocking)

1. Guard the corrected V2 slot in test_no_universal_c2_impossibility_phrasing (the M4b result shows the current list is synonym-bypassable; a class guard is impossible, but the known slots should be enumerated).
2. Bind the caveat's existence sentence ("not one no frame can") with AND rather than the current OR in test 10, so M2b-style deletion is caught.
3. Nit: §1(b)'s "~40–50% of the above-base payroll" is the anchor/PSID-frame read (deployed f = 0.220); it quotes the artifact's mechanism field verbatim and the exact per-frame values are bound, but a "(PSID; deployed 0.22)" parenthetical would be claims-exact.
4. For the record only (committed artifact, not editable, and the doc does not repeat it): forensics-3's adjudication.q1 basis contains "the near-band f>0.5", contradicted by its own measured f (0.438, 0.220); the doc's bound values are all taken from the measurement fields, not that clause.

Bottom line: the demote-quad + pair-scope-C2 recommendation survives everything I could recompute — the per-cell records are immaculate, the whittling defense is cube-true and git-provably prospective, the OC/partition/schema arithmetic is exact, and the F1 fix landed correctly at every site the fixes round named. Land V1 (edit the PR body/squash bullet to the scoped phrasing — a GitHub edit) and V2 (scope the §2a restoration clause to the pinned A/B — one sentence + optional guard), and this ceremony is ratify-ready; both are text-only with every number already bound, so a delta re-verification of the two edited surfaces suffices.

Verification protocol: fresh worktree @ 60f6ee5; disposable uv env; all figures re-derived from runs/gate_w1_{forensics3,forensics2,floors,candidate1,candidate2,candidate3}_v1.json, gates.yaml, and the a2 doc — no doc value trusted as input. No repo edits; ratification is the orchestrator's act.

[MaxGhenis]

Fixes round 2 — response to the verification referee (comment 4962578395)

Verdict addressed: FURTHER FIXES (2) — recommendation untouched. Both items landed; the demote-quad + pair-scope-C2 recommendation is unchanged. Doc + test pushed as e3c63de; V1 is a GitHub edit to the PR body (the squash message), no commit, as the referee specified.

V1 (primary) — the F1 universal survived verbatim in the PR-body / squash message

• Finding. The Evidence Q10 bullet still read "…the 4-element ordering is internally inconsistent as a representative-frame transport target (elim>+2pp ⇔ A/B>0.1613 vs the Smith-adjacency window A/B ∈ (0.1613, 0.184), overshot ~10×)…" — the exact round-1-refuted universal, f-fixed window, no caveat — while the body's own note designates it the squash message.
• Fix (GitHub edit). Rewrote the bullet to the pinned-frame grounds, mirroring §8: on the pinned certified frame the same compression that certifies the swap puts cap_150k at rank 2 (A_band/B 0.373, bit-identical c1/c2/c3; deployed A/B 1.694 PV), so the pinned transport target violates the full Smith order while realising the swap — internally inconsistent ON THE PINNED FRAME, NOT a universal claim. The f-conditional window (0.1613, 0.0806/f) is kept as analysis, with order_at_f_deployed_0p22 (a frame at f≈0.22 that realises the swap and holds the full order, τ 1.0) stated, and no published representative-frame anchor named. Swept the rest of the body — no other universal survives (the only no frame can is inside the scoped not one no frame can). The live body also carries a round-2 ratification note.

V2 — the F1 class survived one clause inside §2a

• Finding. The restoration clause "…f = A_band/A stays large (PSID 0.438, deployed 0.220) and no unimodal earnings distribution makes it small enough while landing A/B in the window: restoration_exists: false" was an unscoped frame-level universal, contradicted by the fix's own caveat ten lines above; it had dropped the artifact's (<0.5) gloss and no contract-permitted lever conjunct; and its "f stays large" premise was not load-bearing.
• Fix. Scoped to the pinned frame's binding constraint. At the deployed f (0.220) the window is already wide, (0.1613, 0.367), yet the pinned frame overshoots it — because the impossibility is a property of the pinned A/B = 1.694 (a fixed frame, not a free parameter), which would need f < 0.0476 to land in-window, far below the measured 0.220. The artifact's small enough (<0.5) gloss and the no contract-permitted lever conjunct are restored, and tail back-solving is named the prohibited identity-in-disguise.
• Recompute (bound). f_threshold = (0.01/r)/AB = 0.01/d_bal_elim, cancelling the OASDI rate r=0.124: 0.08064516/1.69387055 = 0.01/0.21003995 = 0.0476099… → 0.0476. New ledger field pinned_A_over_B_needs_f_below_round4: 0.0476, recomputed from the forensics-3 revenue components in test_q10_impossibility_scoped_to_pinned_frame_not_universal; §2a prose now also bound for 0.0476, (<0.5), and no contract-permitted lever.

Guard extension — the M4/M4b analogues are now caught

The universal-phrasing guard is now an auditable module constant BANNED_UNIVERSAL_C2_PHRASINGS, extended past the round-1 slots to the earnings-distribution / representative-frame synonym class. Both of the verifier's passing mutations now FAIL the guard, verified end-to-end by inserting each into a copy of the committed doc and running the real test_no_universal_c2_impossibility_phrasing (each raises AssertionError; the clean doc passes):

mutation	guard result
M4 — "no earnings distribution of any shape can realise the swap and hold the full order"	CAUGHT (no earnings distribution of any shape)
M4b — "no representative frame whatsoever can realise the swap while reproducing Smith's cap rank"	CAUGHT (no representative frame whatsoever)
the §2a slot's own "no unimodal earnings distribution makes it small enough"	CAUGHT (soft spot 1)
M2b — delete only the caveat's existence sentence	CAUGHT — the test-10 binding tightened OR → AND (soft spot 2)

Machine reason — ACCEPTABLE-WITH-DEFINITION (final), both conditions met

• (i) the ledger definition stays bound. cap_150k_impossibility (scope: pinned_certified_frame_only, is_universal_claim: false, the two dispositive grounds, + the new f<0.0476 field) is bound in test_q10_impossibility_scoped_to_pinned_frame_not_universal.
• (ii) the flip carries §8's text. §7 item 7 appends the §8 draft, which spells out "internally inconsistent ON THE PINNED FRAME, NOT a universal claim" — no §7 flip-text edit needed.

Hygiene

• Bindings — 26 module tests (unchanged function count) + 1 new bound figure (f<0.0476) inside the scope test; module 26/26.
• Mutation battery — all prior documented mutations still caught (spot-checked: is_universal_claim→true, scope→universal, ledger A_band/B/f-threshold corruption, blanket-impossibility insertion — all caught) plus the extended-guard checks above (M4, M4b, §2a slot, M2b).
• Tier — artifact 991 unchanged (2734 collected total, 991 under the artifact marker; no new collected item), tier_counts.json untouched.
• Always-runnable suite (-m "unit or artifact") 1217 passed / 41 skipped / 0 failed; black -l 79 + ruff clean.
• gates.yaml byte-identical to origin/master; only the doc + test changed. Stays DRAFT.

Both edits are text-only with every number bound, so a delta re-verification of the two edited surfaces (the PR-body bullet + the §2a clause) suffices. Fresh CI on e3c63de below once green.

[MaxGhenis]

Verification re-check — gate_w1 amendment 3 (draft PR #180 @ 1d51b77, fixes round 2)

VERDICT: RATIFY AS-IS. My two verification items (V1 the PR-body/squash-message universal, V2 the §2a restoration-clause universal) are resolved, not renamed — I re-derived both fixes from the committed artifacts and swept for the defect class surviving the fixes round itself; none does. The mid-round master merge is a clean two-parent union that leaves the PR diff at exactly the 3 amendment files, gates.yaml byte-identical, and the tier manifest live-accurate. Fresh CI on the head is exit 0, MERGEABLE, CLEAN. The demote-quad + pair-scope-C2 recommendation is untouched throughout.

V1 (PR-body squash message) — RESOLVED, not renamed

I fetched the live PR body and swept it independently for any residual universal (internally inconsistent, no frame, any frame, cannot both, no representative frame, no … distribution, impossible, overshoots). Two hits, both the correctly-scoped forms:

• "internally inconsistent ON THE PINNED FRAME, NOT a universal claim"
• "the re-scope drops a target the pinned frame cannot hold, not one no frame can"

The Evidence Q10 bullet now leads with the pinned-frame grounds — cap at rank 2 (A_band/B 0.373, bit-identical c1/c2/c3; deployed A/B 1.694 PV), the pinned target violates the full order while realising the swap — states the f-conditional window (0.1613, 0.0806/f) as analysis, cites order_at_f_deployed_0p22 (a frame at f≈0.22 realises the swap and holds the full order, τ 1.0), and names the no-published-anchor ground. A "Fixes round 2 applied" note documents the edit, and the ratification note correctly still designates the (now-scoped) body the squash message. The round-1-refuted universal is gone from the surface that enters git history.

V2 (§2a restoration clause) — RESOLVED, not renamed

The clause is now scoped to the pinned frame's binding constraint, verbatim from the committed doc: "f = A_band/A stays large (PSID 0.438, deployed 0.220) — both already satisfy the artifact's 'small enough (<0.5)' gloss, so f is not the binding constraint. At the deployed f (0.220) the order-survival window is already wide, (0.1613, 0.367), yet the pinned frame overshoots it: the impossibility is a property of its pinned A/B = 1.694 … which would need f < 0.0476 to land in-window … no contract-permitted lever restores the pinned frame's Smith adjacency." The unscoped "no unimodal earnings distribution makes it small enough" universal is gone; the artifact's (<0.5) gloss and the no contract-permitted lever conjunct are both restored; the constraint is correctly relocated from f to the pinned A/B. §2a carries the bound tokens 0.0476, (<0.5), no contract-permitted lever, and the scope test now asserts them plus the AND-bound caveat pair.

Rounding adjudication (f < 0.0476)

Re-derived independently from the forensics-3 revenue components: the pinned frame lands in the order-survival window only for f < const/(A/B) where const = win_upper·f_psid = (0.01/r) = 0.0806. So

f_threshold = 0.0806 / (A/B = 1.694) = 0.047609990761064945 = 0.01/d_bal_elim (the OASDI rate r = 0.124 cancels).

Round-4 = 0.0476, matching the ledger's pinned_A_over_B_needs_f_below_round4: 0.0476 and the coordinator-quoted long value 0.047609990761 to every digit. Adjudication: 0.0476 is correct. My round-1 prose used the round-3 approximation 0.048 in a suggested-fix sentence; 0.0476 is the more precise round-4 value of the identical number (0.047609990761…, 5th digit 0 → 0.0476), so there is no conflict — the fixes team's value is the tighter, correct one, and it is machine-bound in test_q10_impossibility_scoped_to_pinned_frame_not_universal. (The threshold 0.0476 ≪ measured deployed f 0.220, so the pinned frame overshoots the window by ~4.6×, consistent with the prose.)

Mutation reproduction — harness table reproduced + one fresh synonym

Against the committed doc, inserting each phrasing into a copy and running the real guard test (test_no_universal_c2_impossibility_phrasing, and for M2b the AND-bound test_q10_impossibility_scoped_to_pinned_frame_not_universal):

mutation	my result	fixes-2 table
M4 "no earnings distribution of any shape can realise the swap and hold the full order"	CAUGHT	CAUGHT ✓
M4b "no representative frame whatsoever can realise the swap while reproducing Smith's cap rank"	CAUGHT	CAUGHT ✓
§2a slot's own "no unimodal earnings distribution makes it small enough"	CAUGHT	CAUGHT ✓
M2b delete only the caveat's existence sentence (OR→AND tightening)	CAUGHT	CAUGHT ✓

The BANNED_UNIVERSAL_C2_PHRASINGS module constant is auditable and the OR→AND caveat binding is in place; the table reproduces exactly.

Fresh synonym (my own devising): "there is no admissible earnings frame that both reverses the elim-plus2pp swap and keeps cap_150k at Smith's fourth rank" — a genuine a2-class universal worded to dodge every enumerated substring → NOT CAUGHT. This is the honest, expected, and already-disclosed limit: the test docstring itself states "A true class guard is impossible for a string guard (synonyms bypass it), so the KNOWN slots are enumerated." It is not a blocking finding — the phrasing appears nowhere in the committed doc (I swept), and the actual defense-in-depth against the universal silently returning is not the string guard alone but (a) the machine-checked ledger scope binding (scope: pinned_certified_frame_only, is_universal_claim: false, mutation-guarded), (b) the AND-bound caveat-existence + pinned-frame prose scope, and (c) this referee ceremony, which is what caught the two real instances. Completeness against arbitrary synonyms is unachievable by construction; the guard's job is the known slots, and it does that.

The mid-round master merge — clean union, verified

• Two real parents, no force-push. Merge 1d51b77 = parents e3c63de (fixes-2) + 95a3e05 (master M6 engine M6 engine: wave-loop composition per verified design (build only) #173). Reviewed SHAs preserved: 481cf1e, 60f6ee5, e3c63de are all ancestors of the head.
• PR diff vs the new base origin/master (95a3e05) is exactly the 3 amendment files — docs/amendments/gate_w1_amendment_3_hh_size_and_c2_pair.md, tests/test_gate_w1_amendment3_proposal.py, tests/tier_counts.json — no stray M6 files.
• gates.yaml byte-identical to origin/master (both blob f1a96e68; a3 touches no gate cell).
• tier_counts reconciliation is a correct union, not a clobber. Traced across ancestry: master unit 330 / artifact 965; branch pre-merge unit 267 / artifact 991; merge unit 330 / artifact 991 — master's unit bump (+63 from M6) and the branch's artifact bump (+26 from a3) both preserved, no double-count.

Tier manifest live-accurate

All five tiers collected under their marker match the merged tier_counts.json exactly: unit 330, artifact 991, integration_psid 800, reproduction_legacy 520, oracle_policyengine 156 (total 2797). The tier-policy test passes under full-suite collection (verified: 1 passed, 2796 deselected); the tryfirst collection hook captures the complete pre-deselection inventory, so an isolated single-file run is the only thing that would (spuriously) show a {'unit': 1} mismatch — CI's pytest -q runs the full suite and both matrix legs (3.11, 3.13) pass.

Suite + CI

Disposable uv env rebuilt on the head: module 26/26 passed; always-runnable -m "unit or artifact" 1280 passed / 41 skipped / 0 failed (1217→1280 = the +63 M6 unit tests from the merge); black -l 79 + ruff clean. Fresh at review time: head 1d51b77, mergeable: MERGEABLE, mergeStateStatus: CLEAN, still DRAFT; gh pr checks 180 exit 0 (build/lint/pytest 3.11+3.13/Vercel pass; deploy = skip).

Machine-reason ruling — unchanged, both conditions now met

My round-1 ruling stands: anchor_ordering_internally_inconsistent_under_certified_swap is acceptable-with-definition, no rename. Both attached conditions are satisfied — (i) the cap_150k_impossibility ledger definition stays bound (now including pinned_A_over_B_needs_f_below_round4: 0.0476), and (ii) §7 item 7 appends the §8 draft, which carries "internally inconsistent ON THE PINNED FRAME, NOT a universal claim" into gates.yaml at the flip.

Bottom line: both verification items are genuinely resolved — the universals are gone from the doc and the live squash message, the f<0.0476 scoping is arithmetically exact and machine-bound, the guard extension reproduces its claimed catches, and the master merge is a clean, correctly-reconciled union that changes nothing outside the 3 amendment files. The one residual — a fresh synonym bypasses the string guard — is the disclosed, unavoidable limit of string matching, defended in depth elsewhere, and absent from the doc. RATIFY AS-IS.

Re-check protocol: fresh worktree @ 1d51b77; disposable uv env; V1 checked against the live gh pr view body; every figure re-derived from runs/gate_w1_forensics3_v1.json + gates.yaml + git ancestry — no doc/PR value trusted as input. No repo edits; ratification is the orchestrator's act.