fix(fire-target): Family/home targets monotonic (kills Family==Household)

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>

fire_planner/__main__.py

@@ -494,6 +494,16 @@ async def _recompute_fire_targets(
                 )
                 jur = jurisdiction_for_city(slug)
                 kids_cf = kids_annual_spend(ratios, kids_base=kids_base)
+                # 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 this guarantees
+                # Solo <= Household <= Family <= Family+home by construction —
+                # killing the Monte-Carlo-noise inversions where Family looked
+                # cheaper than Household. tol is tight (£1k) so the genuine but
+                # small kids/home increment (~£20k at the 99% bar) resolves
+                # instead of being quantised to the previous grid step.
+                prev_target = 0.0
                 for case in (Case.SOLO, Case.HOUSEHOLD, Case.FAMILY):
                     spend = case_base_spend(case, ratios)
                     home_variants = (False, True) if case is Case.FAMILY else (False,)
@@ -509,10 +519,13 @@ async def _recompute_fire_targets(
                             kids_start_year=KIDS_START_YEAR, kids_end_year=KIDS_END_YEAR,
                             with_home=with_home, home_amount_gbp=home_amount, home_year=home_year,
                         )
-                        # Bound the search to a sane SWR band (spend × 60 ≈
-                        # 1.67% floor) so the binary search converges fast.
+                        # hi = sane SWR band (spend × 60 ≈ 1.67% floor); lo =
+                        # previous (lighter) Case's target -> monotone chain +
+                        # a small band for the nested solves (fast).
+                        hi = min(5_000_000.0, spend * 60.0)
                         res = solve_target_nw(
-                            paths, inp, hi=min(5_000_000.0, spend * 60.0), tol=15_000.0)
+                            paths, inp, lo=min(prev_target, hi), hi=hi, tol=1_000.0)
+                        prev_target = float(res.target_nw_gbp)
                         await upsert_fire_target(sess, inp, res, n_paths)
                         written += 1
                         tag = "+home" if with_home else ""

tests/test_fire_target.py

@@ -112,3 +112,20 @@ def test_unreachable_bar_returns_not_reached() -> None:
     # Spend far above what any NW in range can sustain.
     res = solve_target_nw(_paths(), _inp(annual_spend_gbp=2_000_000.0), hi=1_000_000.0, tol=2_000.0)
     assert not res.reached_bar
+
+
+def test_nested_lo_bound_guarantees_case_monotonicity() -> None:
+    """The recompute solves Cases in increasing-cost order, lower-bounding each
+    by the previous target on the same paths. That must yield
+    Solo <= Household <= Family <= Family+home with NO inversions — the fix for
+    the 'Family == / < Household' Monte-Carlo-noise flaw."""
+    paths = _paths()
+    solo = solve_target_nw(paths, _inp(annual_spend_gbp=30_000.0), tol=1_000.0)
+    hh = solve_target_nw(paths, _inp(annual_spend_gbp=50_000.0),
+                         lo=solo.target_nw_gbp, tol=1_000.0)
+    fam = solve_target_nw(paths, _inp(annual_spend_gbp=50_000.0, kids_annual_gbp=12_000.0),
+                          lo=hh.target_nw_gbp, tol=1_000.0)
+    famh = solve_target_nw(paths, _inp(annual_spend_gbp=50_000.0, kids_annual_gbp=12_000.0,
+                                       with_home=True, home_amount_gbp=100_000.0),
+                           lo=fam.target_nw_gbp, tol=1_000.0)
+    assert solo.target_nw_gbp <= hh.target_nw_gbp <= fam.target_nw_gbp <= famh.target_nw_gbp