The recompute solved each Case's FIRE number with an independent binary search,
so Monte-Carlo path noise + the coarse £15k tolerance made Family (Household + 2
kids) tie or even UNDERCUT Household (6 hard inversions + 5 exact ties across the
22 countries) — the ~£20k kids cost quantised to ~£0.
Now solve the Cases in increasing-cost order and lower-bound each by the previous
Case's target on the SAME return paths: a heavier Case (more spend / +kids /
+home) can never need less net worth than a lighter one, so
Solo <= Household <= Family <= Family+home holds by construction. tol tightened
15k -> 1k so the genuine but small kids/home increment resolves instead of
snapping to the previous grid step. Kids/home were already modelled correctly
(verified) — this is purely a solver-resolution + monotonicity fix.
Found + verified via the fire-countdown flaw-hunt workflow. 346 tests pass.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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