W1 forensics 3: cap_150k adjacency decomposition + hh_size residual quantification (registered 4959668253)

[MaxGhenis]

W1 forensics 3 — cap_150k adjacency decomposition + hh_size residual quantification (diagnostic)

Registered at issue #42 comment 4959668253 (FROZEN spec; the registration wins). Reported, not gated. Measures the two open post-c3 questions before any amendment-3 proposal. One run, publishes regardless. Artifact runs/gate_w1_forensics3_v1.json (+ env sidecar).

Standard met exactly. Instrumentation bit-identity vs the committed machinery is 0.0: Q10 re-runs the committed #117 ledger (m2_pseudo_projection) on the transported representative careers and reproduces the cube's c2 exhaustion deltas bit-for-bit; Q11 re-runs regenerate_person_frame_v3 and reproduces the cube's five hh_size cells bit-for-bit; the five hh_size shares partition to 1.0 in every config. Every decomposition filter/join is mutation-checked.

Q10 — cap_150k adjacency decomposition (family C)

The deployed frame ranks cap_150k second in the C2 exhaustion-delay order ([elimination, cap_150k, +2pp, +1pp], 16.7-year delay) vs the Smith (2015) anchor's rank-4 / 1-year, while the certified elim↔+2pp swap realised for the third consecutive deployment.

The exact revenue arithmetic. The m2 ledger makes each provision's revenue delta an exact linear form: Δ(+1pp)=0.01·B, Δ(+2pp)=0.02·B, Δ(elim)=0.124·A, Δ(cap_150k)=0.124·A_band, where B=below-wage-base payroll, A=above-base payroll, A_band=payroll in [wage_base, $150k-2016-NAWI-indexed] ⊂ A. So the orderings are exact: elim>+2pp ⇔ A/B>0.1613 (the certified swap breakeven, = 2pp/12.4%); cap_150k>+1pp ⇔ A_band/B>0.0806.

• (a) the frame's above-cap payroll share dominates the gap — the p≈0.6 branch. Chaining Smith(1y) → m2/PSID anchor-frame(1.12y, M2 same-frame pseudo-projection: revenue side + balance analogue (registration 4931333382) #117 encoding calibrated to Smith's 2034 baseline) → deployed representative frame(16.75y): component (a) = 15.63y (share 0.9925), component (b)+(c) config+vintage = 0.12y (share 0.0075). The compression correction (A/B: 0.115 → 1.69 PV) is the whole story.
• The entailment HOLDS. The Smith 4-element adjacency survives only in a razor-thin window A/B ∈ (0.1613, 0.184) (width 0.023 at the PSID near-band fraction f≈0.44). The deployed frame's A/B (1.69 PV) overshoots it by ~10×, so the SAME correction that lifts elimination past +2pp mechanically lifts cap_150k past +1pp and +2pp to rank 2. The 4-element ordering [elim, +2pp, +1pp, cap] demands cap last but the representative tail entails cap second — internally inconsistent as a representative-frame transport target. (Honest caveat: on a conservative SSA-anchored true frame, A/B≈0.22, the break is f-dependent — boundary f≈0.37 — but the deployed certified frame is unambiguous.)
• No contract-permitted lever restores the adjacency (construction enumerates EMPTY). The frame is pinned, ρ is pinned (0.467) and scales the whole tail uniformly, the M2 same-frame pseudo-projection: revenue side + balance analogue (registration 4931333382) #117 encoding is committed, and back-solving the tail is the prohibited identity. The near-band is the densest part of a monotone-thinning tail, so f>0.5 keeps cap>+1pp whenever elim>+2pp.
• Re-spec: the pair-scoped C2 (elim↔+2pp adjacent swap only) is anchor-supported (Smith p.3: elim +21 > +2pp +18) and realised 3/3 (c1/c2/c3). It certifies the frame-robust swap; it does not certify cap_150k's rank. No published anchor supports the full 4-element ordering on a representative frame — unlike C1's re-spec (which enumerated empty), the pair-scoped C2 is anchor-consistent and non-empty.

Q11 — hh_size residual quantification post-c3 (family A)

With c3's co-designed roster + fertility window deployed, sizes 1/3/5plus fail 5/5 and size-4 fails 4/5 while size-2 clears. A 2×2 roster×fertility toggle decomposition (c0/cor/fer/joint, K=4 each) attributes the miss:

cell	frame	c3	residual	coresidence Δ	fertility Δ	dominant (share)
1	0.083	0.192	−0.109	−0.047	−0.063	fertility (0.54)
3	0.214	0.160	+0.053	+0.022	−0.006	coresidence (0.75)
4	0.210	0.170	+0.040	+0.013	+0.026	fertility (0.67)
5plus	0.193	0.142	+0.051	+0.011	+0.042	fertility (0.78)

• The size-1↔size-3 MIRROR is a clean coresidence signature (coresidence moves size-1 −0.047 and size-3+ +0.046, ratio 0.98) — a young adult leaving a lone household to join a size-3+ parental home. Confirmed.
• REFINEMENT of the registration. Coresidence does not own >50% of every failing cell (the registered p≈0.7 branch). It owns size-3 and the mirror; the fertility window loads the size-4/5plus deficits and is the larger young-adult sub-channel for size-1. The honest outcome is the p≈0.2 mixed-but-structured attribution — two channels own two distinct regions, not featureless.
• Candidate-independence: levers EXHAUSTED. No permitted config clears the cells. The roster ceiling probe (wave-0 seed pushed to 1.0 — every adult — above the permitted train stock) reaches terminal coresidence only 0.111 (the certified parental-exit hazard caps it, not the seed) and leaves size-1 at 0.179. The fertility window is at the 15-entry certified support floor. No untried permitted entry-state lever emerges; the residual needs a non-entry-state coresidence/household model (an amendment).

Expectations vs outcomes (registration's graded probabilities)

question	registered	outcome
Q10 entailment holds & (a) dominant	p≈0.6	realised — entailment holds, (a) share 0.9925
Q10 permitted-lever restoration exists	p≈0.1	not realised (construction empty)
Q10 vintage/config dominates	p≈0.15	not realised ((b)+(c) share 0.0075)
Q10 inconclusive	p≈0.15	not realised
Q11 coresidence >50% each cell + mirror	p≈0.7	refined — mirror confirmed, but coresidence >50% only for size-3
Q11 untried permitted lever emerges	p≈0.1	not realised (levers exhausted)
Q11 mixed attribution, no dominant	p≈0.2	closest — mixed-but-structured (coresidence owns mirror, fertility owns large sizes)

Amendment-3 implications

• Q10: the pair-scoped C2 (elim↔+2pp only, realised 3/3, anchor-supported) is the anchor-consistent re-spec; the full 4-element ordering is not a coherent representative-frame target. Do not chase cap_150k's Smith rank.
• Q11: the hh_size residual is not closable by contract-permitted entry-state levers (roster hazard-capped, fertility at the support floor); closing it needs a non-entry-state coresidence/household model (an amendment), not another entry-state lever.

Files

• runs/gate_w1_forensics3_v1.json (+ .env.json sidecar) — one-shot via write_new
• scripts/gate_w1_forensics3.py
• tests/test_gate_w1_forensics3.py (artifact tier, always-runnable) + tests/test_gate_w1_forensics3_reproduction.py (integration_psid, skips off-machine)
• tests/tier_counts.json (artifact 928→949, integration_psid 797→800)

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