UC residual after the pension-wealth split: support 4.24m vs 6.76m — re-draw undershoot, the 0.55 take-up freeze, and composition shape

[juaristi22]

What

First calibrated measurement of the #750 pension-wealth split (v11: spine-j through the main seam, 1500 epochs / family_equal, 408-spec register): the lever works — UC initial support 3,128,938 → 4,242,978 benefit units (+1.11m freed from the capital test), UC caseload calibrates −25.6% → −20.8%, with every non-UC target's initial estimate byte-identical (clean isolation). Receipts: runs/uk-623-first-calibrated/spine-assessment-{v10,v11}/.

This issue is the residual: what remains after M2, so uk-data#452's "~40% below admin" has a live decomposition and #796's blocked-cell queue has an owner for the UC composition cells.

The residual, measured (v11)

cell	published	initial	calibrated	error
dwp.uc.households	6,758,889	4,242,978	5,352,146*	−20.8%
dwp.uc.households_single_no_children	3,191,316	1,799,310	2,347,653	−26.4%
dwp.uc.households_children_2	1,103,880	612,437	687,483	−37.7%
dwp.uc.households_children_5_or_more	77,894	41,585	55,385	−28.9%

*caseload final derived from error. The 1-child and 3/4-children cells fit; the 2-children cell specifically does not — a composition shape, not a level, problem.

Three candidate mechanisms, in evidence order

1. The wealth-block re-draw undershoot already registered in UK WAS stage: split private pension wealth out of corporate_wealth (uk-data#452 M2) #750's follow-ups: the microcosm QRF re-draw sits ~1.15m UC benefit units below the incumbent on the same households with the old arithmetic (continuous-quantile full-leaf draws vs microimpute's 10-point grid; predictor surface — the Port UK compact source stages and 2024-25 refresh from uk-data #145 predictor-quality revisit). That bullet deserves promotion to its own workstream now that it is the largest identified residual mechanism.
2. The U8 would_claim_uc lever, frozen at 0.55 with disposition "UK WAS stage: split private pension wealth out of corporate_wealth (uk-data#452 M2) #750; do not re-raise without new evidence" (WS-E spine deferrals: known bugs and signed inconsistencies awaiting their increment #796 standing record). UK WAS stage: split private pension wealth out of corporate_wealth (uk-data#452 M2) #750 has now landed and been measured: caseload still −20.8% with support at 4.24m vs 6.76m. That is the new evidence the freeze asked for — the lever's re-measurement is due, on post-split spines where it no longer masks the capital defect.
3. Family-composition shape: single-childless (the lowest-take-up UC group) and exactly-2-children run low while neighbours fit — pointing at composition-conditional take-up rather than a uniform rate.

Also in this cell family

dwp/uc_payment_dist/COUPLE_WITH_CHILDREN_annual_payment_26_400_to_27_600 (−46.4%, target 17,650, support 946) newly fails post-split; its LONE_PARENT/SINGLE analogues are already among the 16 adjudicated band exclusions (uk-data#452) — needs either the same adjudication or coverage by whatever fixes mechanisms 1–3.

Refs: #750 (mechanism M2, landed via #755), uk-data#452 (parent defect), #796 (capstone queue: these are 4 of the 8 blocking cells), #145 (predictor-quality revisit), #808 (the two TCL disability cells, filed separately).

[juaristi22]

Mechanism 2 measured — the three-point would_claim_uc probe on post-split spines. Three full spine builds (0.55 control / 0.70 / 0.85) on identical code (the #813 re-bind branch, policyengine-uk 2.92.1), each through the seam at 1500 epochs / family_equal. Receipts: data/ukds/acceptance/809-lever-probes/ (spines + sidecars), runs/uk-623-first-calibrated/spine-assessment-l{055,070,085}/. Full-rebuild probes, not column patches — the g-vs-h precedent showed the flag feeds engine-materialised predictors downstream.

cell	0.55	0.70	0.85
dwp.uc.households (init support)	−18.3% (4.26m)	−15.7% (4.80m)	−14.0% (5.36m)
households_single_no_children	−7.0%	−2.4%	−0.1%
households_couple_no_children	+0.0%	−0.0%	+0.0%
households_couple_with_children	−5.9%	−2.0%	−1.5%
households_single_with_children	−35.6%	−35.6%	−34.2%
households_children_1	−29.6%	−29.0%	−27.6%
households_children_2	−35.7%	−32.7%	−32.4%
households_children_5_or_more	−29.1%	−29.0%	−29.0%
obr.housing_benefit	−0.1%	+0.1%	−44.9%
loss	0.0254	0.0257	0.0265

Findings:

1. The lever's marginal claimants are overwhelmingly childless. Raising 0.55 → 0.85 adds +0.73m single-childless initial claims but only +0.07m lone-parent claims — the eligible-non-claiming pool is ~10:1 childless (FRS-reported family claims are already anchored true; eligible-but-unclaiming families barely exist on the spine). No take-up rate — uniform or composition-conditional — can manufacture the missing ~0.8m lone-parent claims. Mechanism 3 is not a take-up shape problem; it is a support/eligibility gap in with-children claims, now cleanly isolated by the Re-bind the DWP UC composition and TCL disability-children targets to the publisher's grain (#808, #809) #813 grain fix.
2. The legacy trade-off reappears at 0.85: housing benefit's initial support drains £2.67bn → £0.90bn as claimants move off legacy benefits, and the solver can no longer recover it (−44.9%, the same signature as the pre-split probe). At 0.70 the solver still holds HB green.
3. The blocking cells do not clear at any rate — the four with-children composition cells stay −27.6% to −35.6% across the sweep. Per the freeze's own standard (re-raise only on evidence it moves the failing cells), 0.55 stands. Noted for adjudication: 0.70 is a strict fidelity improvement everywhere else (headline −15.7%, childless singles −2.4%, HB green, loss flat) — but choosing a rate should come from DWP take-up evidence, not from tuning to fit, so this is recorded rather than proposed.
4. The UK spine: child disability under-identification blocks the TCL disability cells (−56.5% / −40.0% across three spine vintages) #808 cells stay green at every rate (+0.1%/−0.4%), and the marginal hmrc drifts (state_pension 50–70k ~+25.5%, private_pension count ~+25.3%, CGT ~−25%) ride just at the band on all three runs — solver-pressure marginals independent of the lever.

Where this leaves the residual: with-children claims are short ~0.8m at the support level — either the FRS under-carries eligible lone-parent benunits at DWP's volume, or entitlement modelling zeroes claims that should be positive (childcare/element interactions), or the wealth re-draw pushes family claims over the capital threshold (mechanism 1, the remaining unmeasured decomposition). Mechanism 1's controlled re-draw comparison is the next measurement.

[juaristi22]

Mechanism 1 measured — the £16k threshold-crossing share against WAS donor truth (the E5-consistent benchmark: donor faithfulness, not incumbent-matching). Countable capital = the engine's UC assessable set (savings + other_residential_property_value + non_residential_property_value + corporate_wealth); donor cleaned with the stage's own clean_was_household_table, donor weights; spine-l055 (current main + #813) at design weights.

surface	households with countable capital > £16,000
WAS round-8 donor, post-split arithmetic	28.6% (n=15,128)
spine-l055 re-draw	38.3% (n=52,846)
WAS donor, pre-split arithmetic (pension folded in)	63.7%

The re-draw puts ~10pp more households (~2.9m) over the capital threshold than the donor it draws from — a ~34% relative overshoot on exactly the statistic the UC caseload depends on. This is the concrete, donor-anchored defect signature behind the "~1.15m below incumbent" observation, now separated from the incumbent's own inflation (E5) and from the predictor-surface confounds of the 452 receipt: the continuous full-leaf draw spreads mid-mass — it rarely reproduces the donor's zeros and small balances, so the >£16k share inflates even while aggregates stay donor-faithful.

The pre-split row also sizes M2 cleanly: the pension fold alone had 63.7% of donor households over the threshold.

Where this points: the fix is in the draw's zero/small-balance behaviour (regime-gate the zero class per column, or donor-atom faithfulness in the mid-range), which is the #145 draw-quality workstream — promoting it from "registered revisit" to a measured defect with an acceptance statistic: the spine's countable->£16k share should land near the donor's 28.6%. Closing that ~10pp gap frees capital-test-failing claims across all family types — including the with-children claims the take-up lever cannot reach (see the lever readout above).

Caveats recorded: donor is GB round-8 (2018–20) households vs the 2024 FRS spine (population drift is real but far smaller than 10pp); nominal-pound threshold applied to both sides consistently since draws are donor-scale.