Fix ar()/grouped_ar() forward/inverse coefficient mismatch (partial fix for #232)

[microprediction]

Summary

Addresses part 1 of the fix plan laid out in the #232 discussion thread, plus an independent bug in _ar_spectral_radius identified there.

ar()/grouped_ar(): forward() emitted residuals using the raw, unconstrained RLS coefficients, while inverse_k() reconstructed the multi-step forecast using _ar_stationary(phi) (stationarity-projected). The leaf downstream learned errors from one predictor while forecasting used a different one -- a single ill-conditioned RLS update (e.g. a long zero run then a jump) could push phi non-stationary with nothing downstream any the wiser until inverse_k's reconstruction diverged.

Fixed by maintaining phi_used (re-projected after every RLS update) and using it consistently for BOTH the emitted residual and inverse_k's reconstruction; the raw RLS fit is untouched and still uses its own unconstrained prediction error.

Verified against the reproduction from the #232 thread:

from skaters.search import _build_from_recipe
f = _build_from_recipe(["ar(2)", "ar(5)", "pow(0.5)"], k=1)
state = None
for y in [0.0] * 2000 + [1e-8, 1.0, 0.0, 0.0]:
    ds, state = f(y, state)
print(ds[0].mean, ds[0].std)

Emitted std dropped from ~2.6e10 to ~0.31, matching the thread's own best-ablation number. On the original #232 FRED reproduction (NONFINGT80A2P2AMT, 6000 points), CRPS dropped from ~5.0e8 to ~400 -- now the same order of magnitude as laplace's own ~112 on the same (genuinely large-scale, spiky) series, rather than 6 orders of magnitude worse.

_ar_spectral_radius: the power-iteration branch (order >= 3) used a single all-ones seed, which can be exactly an eigenvector of a NON-dominant eigenvalue and never converge to the true spectral radius. Confirmed with the thread's exact counterexample: phi=[3,-2,0,0,0] (true radius 2) previously reported 1.0, and _ar_stationary then "damped" the coefficients to a result that was STILL non-stationary (true radius 1.998, not the intended 0.999 margin) -- the safety mechanism was silently failing on its own terms. Fixed with a second seed (alternating +-1) and taking the max; now correctly reports 2.0.

Fixed in Python, JS (docs/js/skaters/transform.mjs), and Rust (rust/src/transform.rs) -- rust/python's skaters_fast PyO3 backend picks the Rust fix up automatically, just needed a local rebuild (maturin develop --release -m rust/python/Cargo.toml) since its cross-backend parity test exercises ar/grouped_ar as part of laplace()'s standard candidate population.

NOT addressed here

Larger design changes flagged in the same thread, each needing its own scoping/discussion:

• Replacing the naive L1/power-iteration stationarity certificate with a proper Schur/reflection-coefficient test (statsmodels-style).
• Replacing the RLS covariance hard-reset with persistent regularization (a fading prior instead of a threshold reset).
• search.py-level candidate health checks / quarantine / recovery, so a degenerate singleton survivor isn't an absorbing search configuration.

Testing

• New regression tests: tests/test_ar_stability.py (4 tests, including the exact thread reproduction and the spectral-radius counterexample).
• node parity/check.mjs passes (JS); cargo test --test parity passes (Rust).
• Full Python suite: 1346 passed, 3 skipped.

🤖 Generated with Claude Code

https://claude.ai/code/session_011AwwectPicNyn6Wv5u43bf