Housing Benefit: reserve WTC for the Schedule 5 paragraph 56 disregard before childcare #2730

Found by the independent review of #2229 (review r1, 28 Oct). This gap exists on main as well as in #2229; it is not a regression from that PR.

What the law does. Under the Housing Benefit Regulations 2006 (SI 2006/213), Schedule 5 paragraph 56 disregards part of Working Tax Credit where the additional earnings disregard in Schedule 4 paragraph 17(1) can't be met from earnings. DWP's HB guidance manual BW2 (W2.131 and W2.179–182) puts the childcare deduction after the other disregards. Read both provisions on legislation.gov.uk before coding. The manual's worked examples are not consistent across editions.

What the model does. The applicable-income path doesn't reserve any WTC for the paragraph 56 disregard before the childcare deduction. With #2229, the childcare limit is max(0, net earnings − applied standard − accommodation) + WTC + CTC, so all of the WTC is available to childcare.

Example (annual): earnings £5,200, standard disregard £1,300, childcare £4,160, WTC £100.

• With Limit Housing Benefit childcare to qualifying charges and earnings residuals #2229, the childcare deduction is £4,000.
• Reserving the £100 of WTC for the paragraph 56 disregard leaves a £3,900 childcare deduction.
• Counted earnings plus credits are zero either way in this example. The review found no case where Limit Housing Benefit childcare to qualifying charges and earnings residuals #2229 changes aggregate assessed income because of this gap. The split between disregards still matters for anything that reads them separately, and for a correct statement of the deduction.

To do:

1. Model the paragraph 56 WTC disregard, with its order relative to the childcare deduction taken from the regulations.
2. Add YAML cases with the arithmetic worked by hand, citing the paragraphs, including the example above.
3. Add a property that total assessed income never falls below what the regulations give, and a differential check against the current path where paragraph 56 doesn't apply.
4. Mirror it in Axiom: extend Encode HB Regs 2006 Sch 4 and HB (SPC) Regs 2006 Sch 4 (earnings disregards) and HB Regs 2006 Sch 5 para 4 / Sch 6 para 5 (IS, JSA(IB), ESA(IR) passport); build the HB pipeline's applicable income from net earnings TheAxiomFoundation/rulespec-uk#375, or file a dispatch-ready rulespec-uk issue.