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UK: bind the DWP benefit-cap rows to the UC cap the award actually loses #1349

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@juaristi22

From Vahid's first review of #1333 (item 2).

The gap

  • The fourteen dwp.benefit_cap.* amount bands and the total (uk/uk_population_targets.json) cite DWP's Benefit cap Table 4: Universal Credit households capped, by the amount capped per monthly assessment period.
  • They bind benefit_cap_reduction, which policyengine-uk 2.135.0 defines as uc_benefit_cap_reduction plus housing_benefit_benefit_cap_reduction. So the rows count units capped in either scheme, where DWP counts UC households only.
  • From 2.141.3, uc_benefit_cap_reduction stays the gross regulation 81 amount, and uc_benefit_cap_reduction_after_floor is what the award loses after the protected floor. For the amount bands, that is the closer concept.
  • Lock policyengine-uk 2.145.0, follow its bus fares and bind thin target rows #1333 binds the amount bands again under María's rule of 2026-10-21 (thin support alone leaves no row out), still on benefit_cap_reduction. Its A/B found no distortion: the shared rows' fit and the weight anatomy did not move, and binding the bands did not raise the share of their carriers' design weight that is stretched 9.5 times or more (experiments/1095-uk-thin-row-binding-receipts.md).
  • Lock policyengine-uk 2.145.0, follow its bus fares and bind thin target rows #1333 also gives the bands' measurement the Great Britain filter that their binding and the total already apply (item 9 of Vahid's second review). The grain still differs: the total is a household indicator and the bands count benefit units.

Proposed change

  • Bind every dwp.benefit_cap.* row, the total and the amount bands, to uc_benefit_cap_reduction_after_floor at benefit-unit grain, with the engine-neutral measurement on a UC-only concept.
  • Re-derive what the population contract feeds: the national target references, the compile-parity receipts and the battery digests.
  • Measure the rows on one arm before and after the rebinding.
  • Once the total and the bands count the same units, the total less the published bands gives back the withheld bands more closely. The build's complementary withholding (uk_withheld_row_sets) handles that, and the arm should confirm it.

Not changed

  • The OBR welfare-cap rows that filter on a zero cap reduction stay as they are.

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