Validate uncertainty inference across Domino, Fan, Boil, Balloons, and Bridge

[yichao-liang]

Third of four stacked PRs splitting bridge-learning (commits ffdd1d940..86431fa58, 87 commits).

Summary

Extends and validates offline uncertainty inference across the physics domains:

• Sequential density weighting for stochastic histories, defensive and density-corrected fixture proposals, box and prior-preserving categorical guidance.
• Ordered process-safe target batches, mixed global/local block refreshes, budgeted joint-support initialization.
• Shared variance inference, constant-output likelihoods with correlated error, and independent prior factorization.
• Unobserved joint uncertainty, threshold joints, and evaluation helpers.
• Validation records for Domino, Fan, Boil, Balloons and Bridge: budget and proposal comparisons, repeated-dataset coverage, incumbent comparisons, weighted forecasts, and the diagnosed model and inference failures that remain open.

Checks

yapf, docformatter, isort, mypy and pylint pass locally on this tree.
The full unit test suite was run locally in file shards; the only failures are test_bilevel_sketch_samplers::test_refine_and_validate_report_returns_plan, test_pg3_analogy_approach and test_boil_sketch_refinement, which fail identically on origin/master when run outside CI's shard order.

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