Fix benchmark validity: penalty bound, nontrivial instances + raw metrics, embedder refinement

[jaewonyun1234]

Three scientific problems found when running the minimal pipeline, fixed in dependency order (Fix 2 → Fix 1 → Fix 3). All measured numbers below are reproducible with the seeds shown.

Fix 2 — penalty bound was mathematically wrong

A = B = 2·(1 + (c_max − c_min)) claimed feasible ground states, but skipping a flight saves its full option cost, not the spread. Verified: make_scenario(4, 3, seed, alpha=0.0) gave infeasible brute-force ground states in 40/40 seeds. With the corrected bound A = B = 2·(1 + c_max): 0/40. Regression test test_ground_state_feasible_small_spread covers the exact broken case.

Fix 1 — benchmark could not distinguish solvers

1a. Trivial instances. Generator tuned (5 blobs spanning 2–3 levels, up to 4 columns wide, routes drawn from the central row band). Conflict-edge counts at F=4, K=3, seeds 0..19:

	distribution	median	zero-conflict seeds
before	[0,0,1,10,1,2,4,3,3,2,2,6,6,0,5,12,6,2,3,8]	3.0	3/20
after	[4,3,4,14,6,11,2,12,8,3,3,6,12,1,6,15,6,10,3,10]	6.0	0/20

Target (median ≥ 4, ≤ 1/20 zeros) met. run.py --min-conflicts N (default 1) additionally skips sub-threshold scenarios with a printed notice and deterministic seed+1000 substitution recorded in the CSV.

1b. Repair masked all quality differences. Raw QUBO energy of unrepaired samples is now the primary metric (raw_metrics, CSV columns raw_best_E/raw_mean_E); the repair heuristic is exposed as the named solver greedy. The denser instances also exposed that the one-pass repair could leave conflicts standing; it gained a deterministic promote-and-retry (0/2000 failures at the new density).

python run.py --flights 5 --options 3 --seeds 10 --shots 1000 now shows a spread:

RAW QUBO ENERGY (primary)          raw_best_E          raw_mean_E
random                        452.739 ± 74.062    2724.454 ± 336.915
pasqal-analog                 375.360 ± 69.863     391.984 ±  72.127
(E_min ref)                   375.360 ± 69.863

REPAIRED COST (secondary)     approx_ratio   feasibility
brute-force                  1.000 ± 0.000   1.000
greedy                       0.959 ± 0.122   1.000
random                       1.000 ± 0.000   0.002
pasqal-analog                1.000 ± 0.000   0.977

Solvers no longer all tie at 1.000 (greedy misses the optimum on 2/10 seeds), and the raw columns carry the real signal: the analog sampler's best raw shot equals E_min on every seed with a raw mean of ~392 vs random's ~2724. Reported as measured — nothing was tuned to favor the quantum solver.

Fix 3 — embedder strengthened; failures now attributed

embed() (greedy init → vectorized force-directed refinement → 8 seeded jittered restarts, deterministic per seed) replaces the one-pass placer everywhere (solver register builder + study). Refinement fixes found on the way: per-node displacement cap (uncapped spring sums between far clusters diverged to inf — and NaN layouts previously passed check_embedding as "valid", which is why old large-F numbers looked plausible), antisymmetric force directions for coincident nodes, seeded annealing kicks for tug-of-war equilibria, stagnation early-out. max_degree is now computed on the independence graph actually embedded; n_nodes_deg_ge_6, n_all_level_pairs, n_restarts_used, refine_iters added to the CSV.

Fit-fraction ladder, seeds 0..19 (old = one-pass greedy, new = embed(); both on the tuned generator):

F	old	new	new-failure attribution
4	2/20	5/20	12 prism-only, 3 prism-family, 0 deg≥6
6	0/20	1/20	12 deg≥6, 6 prism-only, 1 prism-family
8	0/20	0/20	19 deg≥6, 1 prism-only
12–96	0/20	0/20	20/20 deg≥6

Deviation from the acceptance criterion, reported as-is: "F=4 must embed at ~100%" is not reachable, and the reason is geometry, not the embedder. The tuned generator (1a) routinely makes two flights conflict at all K levels; their one-hot triangles plus the level-matching edges form a triangular prism, which cannot satisfy the margin rules (edges ≤ 0.95·R_b, non-edges ≥ 1.05·R_b, 5 µm floor) in 2D — provable for the aligned case (it would need a triangle side of ≥ 11.8 µm against a 7.6 µm ceiling) and confirmed by 500-restart searches (never below 6 violations). The 3 "unexplained" F=4 failures are cross-flight conflict triangles at shared levels — same obstruction family; each also resisted 200-restart deep searches. The acceptance criterion's premise ("max degree ~5 ⇒ failures are embedder bugs") is therefore false on this ensemble; per instruction 5, nothing was tuned to make the numbers look better. The study CSV now attributes every failure (deg≥6 / prism / other), which was the criterion's actual intent.

Verification

• ruff check ., mypy contrail_env, pytest (29 tests) — all green
• python run.py --flights 5 --options 3 --seeds 10 --shots 1000 — spread shown above
• python -m contrail_env.embedding_study --csv embedding.csv --seeds 20 — ladder above, 7 min 44 s total