BUG Aggregate the continuation lottery stably under a certainty equivalent

[hmgaudecker]

Closes #412.

Targets reachability, not main.

The defect

With a PowerMean certainty equivalent, Q_and_F built the continuation as
inverse(Σ w · transform(v)) — per-target transform, weighted reduction,
one final inverse. For risk_aversion > 1 and small positive continuation
values, the intermediate v^(1-ra) overflows the dtype before any summation
happens, so a finite certainty equivalent collapses to 0 and the Bellman
argmax reverses.

On this branch PowerMean had no aggregate at all — the whole stable path
had to be written, not just dispatched to.

The repair

Aggregation is now a method on the certainty equivalent, and there is exactly
one call site in the engine.

• QuasiArithmeticMean.aggregate(values=..., weights=..., params=...) is the
  generic g⁻¹(Σ w · g(v)), unchanged in behaviour for user-supplied
  transform pairs.
• PowerMean.aggregate overrides it with an anchored weight/deviation log
  form, log CE = a + [log(W) + log1p(E/W)] / (1-ra), which stays finite
  wherever the mathematical power mean is and keeps the geometric-mean limit
  exact arbitrarily close to risk_aversion = 1.
• Q_and_F hands over the whole joint lottery in one piece — every
  stochastic node of every reachable target, each weighted by its
  regime-transition probability — instead of reducing per target and
  inverting at the end. Flattening before aggregating is what lets the power
  mean anchor the transform; a per-target transform -> reduce -> inverse
  decomposition structurally cannot. The ordering constraint is preserved:
  the transform is still applied before every expectation, over stochastic
  state transitions and over regime transitions alike.
• get_Q_and_F and get_compute_intermediates now share one
  _get_compute_E_next_V builder, so the Bellman Q and the NaN diagnostics
  cannot disagree by construction. This removes ~140 lines of duplicated
  per-target setup.
• The linear (certainty_equivalent=None) path keeps its existing
  accumulation and arithmetic exactly — no heavy exact path is imposed on
  expected-utility models.

resolve_certainty_equivalent now returns one arg-to-flat-name mapping
instead of separate transform/inverse mappings, since aggregate receives the
union and each callable takes the subset its own signature declares.

Evidence ingested

Both attachments on the issue: the round-4 archive excerpts inlined in the
body and issue412-gridsearch-powermean-evidence.zip from the comment
(reproducer, oracle, mutation family, action-reversal matrix, logs,
REPAIR-ACCEPTANCE.md, disposition.yaml, F6/R4 finding JSONs).

The packet's own reproducer is signature-bound to the audited DC-EGM snapshot
(5b4339e2) — it calls get_Q_and_F(..., scalar_targets=...), which does not
exist on reachability. Its substance has therefore been ported into the
project's own suite rather than vendored: the decimal oracle, the pinned
witnesses, the seven-case risk/scale family, and the acceptance list.

Acceptance coverage

Every item of REPAIR-ACCEPTANCE.md:

Required regression	Where
Pinned scalar float32 (1e-8, 2e-8) @ ra 8	test_power_mean_regime_lottery_stays_finite_in_float32
Pinned scalar float64 (1e-50, 2e-50) @ ra 8	test_power_mean_regime_lottery_stays_finite_in_float64
Stateful-only lottery, both precisions	test_solved_values_are_equivariant_to_rescaling_the_model (stochastic health nodes), ..._matches_reference_at_float{32,64}_scales
Seven-case risk/scale action-order family	test_bellman_prefers_the_higher_certainty_equivalent_at_any_scale (4 float64 cases) + ..._matches_reference_at_float32_scales (3 float32 cases)
Mixed shock-by-regime lottery	the rescaling model: 2 health nodes in alive × the dead target
Positive common-rescaling invariance	test_power_mean_aggregate_is_homogeneous_of_degree_one, both rescaling tests
Risk aversion near 1 / geometric mean	test_power_mean_aggregate_is_geometric_mean_at_unit_risk_aversion, ..._is_continuous_around_unit_risk_aversion (ra = 1 ± 1e-6)
Risk aversion 0 / linear parity	test_power_mean_aggregate_is_linear_expectation_at_zero_risk_aversion, existing test_zero_risk_aversion_reduces_to_expected_utility
Zero-weight and unit-mass	test_power_mean_aggregate_drops_zero_weight_entries
Solve / simulation / diagnostics consistency	test_diagnostic_intermediates_reproduce_the_Bellman_Q, test_simulated_consumption_is_equivariant_to_rescaling_the_model

All values are checked against a 120-digit decimal oracle (the packet's
stable_power_mean, reimplemented in tests/test_certainty_equivalent.py),
under JIT, in both precisions.

Each new test was confirmed red on the pre-fix source before the repair
landed.

Resource gate

Epstein–Zin example, 25 periods, 400 × 2 wealth-health × 600 consumption,
float64, CPU. Shared box with a concurrent test run, so cold-compile numbers
are noisy; the ranges below are min/max over two runs each.

	before	after
linear cold compile	0.92 – 1.94 s	0.92 – 0.93 s
linear warm runtime	0.34 – 0.42 s	0.34 – 0.85 s
power-mean cold compile	0.76 – 1.85 s	2.26 – 2.39 s
power-mean warm runtime	0.446 s	0.50 – 0.53 s
power-mean peak RSS	659 – 670 MiB	599 – 606 MiB

The linear path is unchanged within noise. The power-mean path costs roughly
+12% warm runtime and a longer cold compile — the anchored form emits
log/min/max/expm1/log1p where the naive route emitted a single
pow — and peak RSS drops slightly, since one concatenated reduction
replaces a per-target reduction chain.

Not addressed

Provenance. PROVENANCE-AND-SCOPE.md names PR #395 as the likely first-bad
commit but marks it hypothesis_only; no bisect was run here. The repair is
independent of which commit introduced the seam.

[hmgaudecker]

Closing: opened against reachability before that branch was pushed, so the diff picked up nine unpushed base commits. Will reopen once the base is settled. The work itself is on grid-search-ez (commit af036a1).

[codecov]

Codecov Report

❌ Patch coverage is 98.71383% with 4 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (reachability@3f704a3). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
tests/test_certainty_equivalent.py	97.72%	2 Missing ⚠️
tests/test_validate_regime_transition_probs.py	91.66%	2 Missing ⚠️

Additional details and impacted files

@@               Coverage Diff               @@
##             reachability     #413   +/-   ##
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  Coverage                ?   90.62%           
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  Files                   ?      171           
  Lines                   ?    15481           
  Branches                ?        0           
===============================================
  Hits                    ?    14030           
  Misses                  ?     1451           
  Partials                ?        0           

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[github-actions]

Benchmark comparison (main → HEAD)

Comparing 73252978 (main) → af036a14 (HEAD)

Benchmark	Statistic	before	after	Ratio	Alert
aca-baseline	execution time	13.944 s	8.899 s	0.64
	peak GPU mem	588 MB	588 MB	1.00
	compilation time	294.03 s	268.25 s	0.91
	peak CPU mem	6.97 GB	8.53 GB	1.22	❌
aca-baseline-debug	execution time	43.928 s	38.439 s	0.88
	peak GPU mem	587 MB	587 MB	1.00
	compilation time	342.68 s	310.90 s	0.91
	peak CPU mem	6.97 GB	6.37 GB	0.91
Mahler-Yum	execution time	4.353 s	4.294 s	0.99
	peak GPU mem	520 MB	520 MB	1.00
	compilation time	11.29 s	11.05 s	0.98
	peak CPU mem	1.47 GB	1.47 GB	1.00
Precautionary Savings - Solve	execution time	25.6 ms	24.4 ms	0.95
	peak GPU mem	8 MB	8 MB	1.00
	compilation time	1.58 s	1.61 s	1.02
	peak CPU mem	1.06 GB	1.07 GB	1.00
Precautionary Savings - Simulate	execution time	65.7 ms	66.8 ms	1.02
	peak GPU mem	157 MB	157 MB	1.00
	compilation time	3.64 s	3.68 s	1.01
	peak CPU mem	1.22 GB	1.22 GB	1.00
Precautionary Savings - Solve & Simulate	execution time	96.2 ms	95.3 ms	0.99
	peak GPU mem	566 MB	566 MB	1.00
	compilation time	4.99 s	4.98 s	1.00
	peak CPU mem	1.20 GB	1.21 GB	1.00
Precautionary Savings - Solve & Simulate (irreg)	execution time	202.3 ms	202.0 ms	1.00
	peak GPU mem	2.18 GB	2.18 GB	1.00
	compilation time	5.35 s	5.28 s	0.99
	peak CPU mem	1.26 GB	1.26 GB	1.00
IskhakovEtAl2017Simulate	execution time	202.5 ms	205.7 ms	1.02
	compilation time	4.41 s	4.43 s	1.00
	peak CPU mem	1.19 GB	1.20 GB	1.00
IskhakovEtAl2017Solve	execution time	48.3 ms	48.6 ms	1.01
	compilation time	0.69 s	0.74 s	1.07
	peak CPU mem	1.05 GB	1.06 GB	1.00
IskhakovEtAl2017SimulateGpuPeakMem	peak GPU mem	281 MB	281 MB	1.00
IskhakovEtAl2017SolveGpuPeakMem	peak GPU mem	67 MB	67 MB	1.00