Add the UK State Pension dynamics plan for the triple lock costing

[MaxGhenis]

Adds docs/plans/uk-state-pension-dynamics.md: a plan for projecting the UK State Pension population and its entitlements to 2050-51 for PolicyEngine UK. uk-triple-lock's Burnham-plan costing is the driving use case and acceptance benchmark. Tracking issue: #501.

Documentation only. No code, gate, registration or committed run changes.

What the plan covers

• Why. PolicyEngine UK's basic plus new State Pension bill is 12.8% below DWP's in 2026-27 and 23.3% below in 2030-31. The contributors are verified in code: fixed survey ages, £0 for anyone reaching State Pension age after the survey year, pinned types, and no pensioners abroad.
• Phase 1.
  • Reweight fixed age slots to the ONS 2024-based projections.
  • Assign each slot its cohort's entitlement from a cohort entitlement model. The model covers mortality, State Pension age by date of birth, accrual to the transitional rate and protected payments, migration, and pensioners abroad with frozen and uprated pensions.
  • Deliver a path-independent sidecar and a synthetic abroad dataset that PolicyEngine UK runs.
• Phase 2. Person-level trajectories as challengers on version 2 of the contract.
• Engine contract. Seven policyengine-uk changes (E1-E7). The plan consumes Set State Pension age from date of birth, including the rise to 67 policyengine-uk#1899, #1904, #1922, #1939 and #1941.
• Acceptance.
  • Four gates to be pre-registered: DWP Spring 2026 caseloads and spending by type in 2030-31, held-out Stat-Xplore full-rate bands, and an abroad backcast.
  • Registered comparisons with the OBR's July 2026 path, and with DWP's £15bn and £50bn as a single-path comparator against single-path runs only.
• Cost and time (estimates). Phase 1 is about 26-41 agent-days and 10.5-14.5 human review days, 4-7 weeks elapsed. The expected-value build is about 456 path jobs, 3-6 hours on three workers.
• Decisions needed. Nine, listed in the plan.

Boundaries

• No edits to engine/loop.py, engine/steps.py, gates.yaml or committed runs/*.json. The UK gate goes in its own file, as ADR 0002 requires.
• The existing uncertified uk/ layer is left untouched and is not reused.
• Rules stay in policyengine-uk. The dynamics code reads State Pension age, the transitional rate and the frozen-country rule through a bridge.
• The plan is the deferred "Multi-year runs" piece of UK pensions: calibrate State Pension, Pension Credit and pension contributions to the resident administrative facts (PolicyEngine/chronicle#305), pin the State Pension age boundary, fix the pension spine stages, and the engine pieces a State Pension uprating analysis needs microcosm#1069 and duplicates none of its rows.
• No survey record's data appears in the plan.

Review

• Thirteen research dossiers were consolidated into one evidence base, with its load-bearing numbers re-checked against the saved primary sources.
• Three independent reviews (claims and numbers, law and architecture, feasibility and hygiene) returned 99 findings, none blocking. All 36 major findings were applied.
• An independent final audit confirmed those fixes and re-derived the totals, counts and legal citations. Its one further major finding and seven minor ones are applied.
• 58 of the plan's 60 external links return 200. The OBR and House of Commons Library pages block automated fetches and were read from saved copies.

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[MaxGhenis]

Merge record: every check passed on head 56d1070 and the PR is mergeable. An independent Opus 5.5 review on a Subfleet lane requested changes at 9e82012; those were applied in 7de8e09, which the re-review approved. 56d1070 applies that re-review's optional one-line wording change and nothing else. Before the PR, three independent reviews and a final audit covered the draft. This is a proposal-status plan requested by Max; its nine decisions stay open and are queued for him.