M34 — EfficientCube: shorter solutions via search-width retune (measured, not more training)

[PieterjanDeClippel]

M34 — "Can we improve the Rubik's Cube AI?"

The shipped EfficientCube solver already solved 100% (beam) at every eval depth d4→d26, so solve-rate was saturated. This work established — by measurement — that the only real levers were solution length and search cost, then acted on them. Full write-up: docs/prd/CUBE_SOLVER_IMPROVE_PRD.md (PLAN.md M34).

Done phase-by-phase, one commit per phase, gated so each phase's evidence justified the next.

Outcome

The model was already optimal wherever verifiable; the real improvement is a search-width retune, not retraining.

Phase	Result
W1 — instrument	Surfaced solution length as CSV metrics (--eval-only) + a BFS provable-optimality probe (--optimal-probe). Baseline of the shipped 346.8M net: 100% provably QTM-optimal at d1–6, optimal through d12, gap only at d14–d18.
W2 — beam sweep	--beam-sweep: width ≥1000 already solves 100% (2000 was conservative); wider = shorter mid-depth (d14 17.8→14.4qt at b5000 ≈ optimal, d16–d22 −1–2qt), ~linear expansions cost.
W3 — value-guided beam	Built the combined policy+value head + BeamSearchValueGuided + --value-sweep (+ 2 unit tests). Null result: value guidance shortens per-fixed-width but loses 3–11× on compute vs simply widening the pure beam. Kept λ=0.
W4 — more training	Skipped — not indicated (no policy ceiling: optimal to d12, gap is search-bound, loss sample-bound per OPTIMIZATIONS.md).
W5 — ship	Beam 2000 → 5000 in CubeController (quality over latency, owner's call): d14→14.4qt, d16–d22 −1–2qt at ~2.4× search. Beam stays pure-policy.

What ships

• The web solver returns noticeably shorter mid-depth solutions.
• Permanent length/optimality instrumentation for any future training run (--eval-only length metrics, --optimal-probe, --beam-sweep, --value-sweep).

Notes for review

• Latency: W5 trades latency for quality on the CPU-only Hetzner box (~2.4× search). Documented fallback if a solve feels sluggish in production: a time-bound on the beam (like the old DAVI solver's 15s deadline).
• Lineage: distinct from the DAVI value net (PRD §13.1) — nothing here touches DAVI.
• Value-guidance and more-training were investigated and rejected as measured, honest nulls — the diffs for both remain (the --value-sweep tooling and the combined head) but λ stays 0.

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