Cost-ordering synthesis: committed encodings vs anchor cost columns

[MaxGhenis]

Cost-ordering synthesis: committed encodings vs anchor cost columns

Registered, reported not gated diagnostic (frozen spec: #42 comment 4931034068). Every provision encoding already committed to the five external-anchor replications is scored once on a single common Phase-A frame, and the aggregate cost deltas are tested ordinally against the anchors' published cost columns. No level matching is claimed — our frame is observed completed careers under the Phase-A 2050 transport, not a Trustees-assumption projection, so units differ by construction; signs and orderings are the transportable content. Reads no gate, changes no gate, one run, publishes regardless of outcome.

Per-provision aggregate cost deltas

Provision	Our aggregate cost delta	Half-split floor	Anchor cost column	Anchor units
Price indexing (PI)	−33.27%	0.0000	+0.68	75-yr payroll (Mermin Table 1)
Progressive price indexing (PPI)	−11.00%	0.0102	−0.14	75-yr payroll (Mermin Table 1)
NRA → 70	−20.23%	0.0000	−0.50	75-yr payroll (Mermin Table 1)
COLA −0.4pp	−0.80%	0.0000	−1.12	75-yr payroll (Mermin Table 1)
Caregiver — Biden	+2.75%	0.0022	−0.12	A-table cost (Five-Approaches Table 3)
Caregiver — Buttigieg	+15.61%	0.0125	−0.51	A-table cost (Five-Approaches Table 3)
Caregiver — Klobuchar	+3.73%	0.0025	−0.12	A-table cost (Five-Approaches Table 3)
Caregiver — Warren	+8.30%	0.0053	−0.30	A-table cost (Five-Approaches Table 3)
Earnings sharing 1b (excluded; descriptive)	−4.23% (couples frame)	—	cost-balanced by design	Favreault-Steuerle

Common frame: 1,549 sex-resolvable Phase-A careers (the frame replication_mermin_rows and replication_caregiver both build identically — family_earnings_panel + full-415(b) transported AIME + scheduled_amount baseline). PI/PPI reuse replication_ppi_mermin's reforms on the full-415(b) AIME; NRA/COLA reuse the Mermin-rows factors; the four caregiver plans reuse the caregiver credit encoding — all verbatim. Floors are the 5-seed person-disjoint half-split gaps.

Test outcomes vs pre-registered forecasts

Test	Forecast	Result	Met?
T1 sign agreement	100%	100% (8/8: four Mermin savings negative, four caregiver positive)	✅
T2 Kendall τ, Mermin quartet vs 75-yr payroll	τ = 1.0	τ = 0.667	❌
T3 Kendall τ, caregiver plans vs A-table cost	τ ≥ 0.8	τ = 0.913	✅

T2 (one adjacent swap, PPI ↔ NRA). Our order PI > NRA > PPI > COLA vs anchor PI > PPI > NRA > COLA. On our observed careers most AIME sits below the second bend, so progressive price indexing — which bites only above the 30th-percentile bend — cuts less (−11.0%) than the uniform NRA actuarial reduction (−20.2%), whereas DYNASIM's fuller projected careers rank PPI above NRA. The swap holds against both anchor columns: the payroll column and the direct "percent of scheduled 2050" cross-check both give τ = 0.667. This is the named compressed-careers delta the ppi_mermin artifact already documented, not a coding difference.

T3 (τ-b = 0.913). Our gain order Buttigieg > Warren > Klobuchar > Biden vs anchor Buttigieg > Warren > {Biden = Klobuchar}; the only difference is the Biden/Klobuchar pair, which the anchor ties at −0.12 (τ-b accounts for the tie).

Method notes

• Baseline — scheduled (not payable) denominator. PI/PPI/caregiver deltas are relative to the scheduled PIA (the claim-age factor cancels); NRA/COLA deltas are relative to the claim-adjusted scheduled benefit (the claim factor is those reforms' mechanism). Both are "% change vs current-law scheduled." Per-provision units-differ notes are carried in the artifact.
• Earnings sharing excluded with reason — intrinsically a couples provision (needs marriage episodes, spouse PIA records, 402(b)/(c)/(e)/(f) auxiliary benefits, actual eligibility year, and a package global-increase scalar — none on the single-person 2050-transport frame). Per the frozen spec it is recorded excluded-with-reason and scored on its own committed couples frame; its committed aggregate_cost_change supplies the T1 descriptive value (the anchor's packages are cost-balanced by design, so no strict sign to agree with).
• Anchors re-verified — every transcribed number checked against pdftotext output on 2026-07-09 per Replication anchors: DYNASIM-scored reforms and the minimum model surface for each #74 protocol note 3 (Mermin Table 1 payroll row, PDF p.15; Five-Approaches Table 3 caregiver row, printed p.19). Column mappings confirmed.

Files

• scripts/replication_cost_ordering.py — the synthesis (reuses every committed encoding verbatim).
• runs/replication_cost_ordering_v1.json — the artifact (reported_not_gated: true, registration pointer, per-provision rows with our delta + floor + anchor + PDF cite + units-differ note, T1/T2/T3 vs forecasts, named deltas).
• tests/test_replication_cost_ordering.py — always-runnable artifact-consistency tests (recompute T1/T2/T3 τ from the artifact rows; anchor re-transcription check) + a skipif-PSID reproduction pin on the PPI delta.

The orchestrator grades the forecasts on #42; this PR does not grade them.

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