feat(granger): Bayesian Granger causality with Toda-Yamamoto robustness

[thomaspinder]

Summary

Stacked on feat/140-stationarity-diagnostics (#197) — it consumes the frozen IntegrationOrderResult.order / .d_max / .inconclusive contract pinned on the issue.

• FittedVAR.granger_causality(cause, effect, *, rope=None, standardize=True, test_lags=None): labelled posterior causal-strength summaries — per-lag coefficient posteriors and the headline posterior of the joint coefficient norm with median/HDI, standardised by sd(cause)/sd(effect) by default. The probability statement is p_rope = P(‖b‖ < rope | data) with a user-supplied region of practical equivalence and no default — the docstring states plainly why P(no causality) is unavailable under continuous priors and what would be needed to get one (spike-and-slab), per the issue's explicit honesty requirement. ADR-0010 records the stance (including why a Savage-Dickey Bayes factor was rejected: it exports the prior tightness into what reads as evidence).
• toda_yamamoto(data, cause, effect, ...): lag-augmented mode — fits ConjugateVAR(lags=p + d) (closed-form, milliseconds) but tests only the first p lags; n_lags_tested vs n_lags_fitted metadata makes the split explicit and the augmented block structurally cannot enter the statistic (single result-construction site). The integration-order decision is consumed per the contract: non-empty inconclusive → hard refusal naming the variables and explaining floor-vs-finding, with an explicit d= integer as the only override (recorded augmentation_source="user"); injectable integration_order_result=; works without statsmodels when d= is given.
• Docs: how-to with a CO2–temperature example whose limits section names the omitted forcings, the bidirectional physical coupling, and exactly what a small p_rope licenses; reference page; CONTEXT.md terms; ADR-0010.

Closes #154

Review

Planned by a Fable-tier planner; independently reviewed (verdict: approve). The reviewer re-derived the lag-major indexing and cross-checked it with an out-of-suite simulation, audited the honesty paragraph claim-by-claim against the implementation, and verified the refusal wording against _stationarity's actual inconclusive semantics. Its one P2 (a sentence conflating the event with its probability) is fixed in the final commit.

Note: the beartype forward-ref failure on FittedVAR methods that surfaced during testing is pre-existing and already fixed on main by #209 — it resolves when this stack rebases.

Tests

50 tests, 100% branch coverage on the engine: exact-index pins (including transposed-dims realignment and a lag_matrices cross-check), directionality (true edge p_rope 0.000 vs null edge 0.968), a 40-query null-calibration sweep, the full TY contract (refusal/override/injection/end-to-end on an I(1) system with statsmodels), and a slow NUTS smoke. Branch fast suite: 641 passed. ruff/ty/docs build clean.

🤖 Generated with Claude Code

https://claude.ai/code/session_01Egjd7ToFeb9TQqFnfRQZxV

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.4%. Comparing base (41e5234) to head (f69edaf).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

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  Lines       3317    3431    +114     
  Branches     420     437     +17     
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+ Hits        3161    3275    +114     
  Misses       111     111             
  Partials      45      45             

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