Alignment Workspace

Item 121: Transitive retirement, and the closure a settlement must carry

Deference line — second wave · difficulty entry · project normativity.seed · closed · node item-121

— *answered 2026-10-22: the grounded rule propagates retirement, vacuity, rebuttal and undercut along citation chains of every length without a closure on the settlement (mem_survivors)*

The rule settleForm (lean/Workspace/Normativity/Contrib/WarrantEntitlement.lean, Grounds.survivors) retires a premise whose sentence is pinned false and removes, one step along cites, the occurrences that cite it; conditional forms further down a chain leave only when the settlement's closure pins their antecedent false. The round's fixtures carry their closure (X false pins X∧A, X∧A∧Y false) and the rule reaches the whole warrant; without closure a chain of three keeps its last link (projects/normativity/rounds/2026-10-21-rebuttal-and-end-to-end/tests/test_rebuttal.py::test_retirement_needs_closure). Wanted: either the transitive closure of citation as the retirement rule (a terminating recursion on the finite grounds, with survivors_anti re-proved), or the closure requirement on settlements as a stated hypothesis of the statics, with the theorem that a propositionally closed settlement makes the one-step rule complete.

Deliverable shape: the chosen rule as a def, the re-proved monotonicity lemmas, and the chain-of-three fixture under it. Acceptance check: Lean green; the round's tests/run.py extended and green. Context: projects/normativity/rounds/2026-10-21-rebuttal-and-end-to-end/REBUTTAL.md A1; DECISIONS.md 2026-10-21 (M2).

Deliverable shape: the chosen rule as a def, the re-proved monotonicity lemmas, and the chain-of-three fixture under it.

Acceptance check: Lean green; the round's tests/run.py extended and green.

Context: DECISIONS.md; projects/normativity/rounds/2026-10-21-rebuttal-and-end-to-end/REBUTTAL.md

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