bench(worldmodel): raise n to 200, and refute the power claim behind it

[aurascoper]

Last item of the benchmark repair — plus ledger node 15, which refutes the power claim I made in #55.

n_episodes 20 → 200

Cost is nil: wall clock is flat at ~1.1 s from n=20 to n=200, because the run is dominated by training, not the MPC block. random_baseline_stderr falls 0.0761 → 0.0250 (√10 = 3.16 predicted, 3.04 measured). n was never a compute decision.

The power claim in #55 is refuted, by its own method

#55 reported "median n for |t|=2: binary ~248, log-ratio ~154", extrapolated from a paired ld32-vs-ld64 comparison at n=20. Scaling n directly:

n	20	50	100	200
log |t|	0.88	0.21	0.81	0.54

It does not grow. That is the null distribution — ld32 vs ld64 has no real effect, so no n reaches |t|=2 and a required-n extrapolated from it is meaningless. I computed a sample size from noise and put it in the ledger.

The 1.43× sensitivity ratio at fixed n stands — it compares two endpoints on identical data. The required-n figures do not, and node 15 says so.

Against a known effect, the endpoints separate sharply

2 epochs vs 22 — a real, large difference:

n	20	50	100	200	√n prediction (log)
log |t|	0.43	0.80	0.76	1.48	0.43 / 0.69 / 0.97 / 1.38
binary |t|	0.94	0.63	0.62	0.68	— flat

The continuous endpoint tracks √n. The binary endpoint does not respond to n at all — thresholding at goal_tol destroys the effect, so more episodes buy it nothing.

So raising n is nearly useless unless the continuous endpoint is adopted, not merely reported. That coupling was invisible before this measurement.

And the repaired benchmark is still underpowered

At n=200, against an eleven-fold difference in training, the continuous endpoint reaches only |t| = 1.48. On its own √n behaviour |t|=2 needs n ≈ 365 — and on 3 seeds that estimate is itself noisy.

Keep all six repairs — each removes a measured noise source and n=200 is free. Do not declare the benchmark repaired. The ceiling is now goal_tol and the horizon, not the sample size. A success criterion that discards the distance it is computed from cannot be fixed by more episodes.

Repair scorecard

	before	after
target encoder on restore	untrained	exact
baseline sampling sd	0.0750	0.0054
baseline across seeds	0.254–0.483	0.303 constant
episode sets across seeds	5 distinct	1, identical
planner noise	position-dependent	per-episode
n	20	200
can it adjudicate 0.07?	no	still no

Also outstanding

Nodes 10 and 11 swept CEM knobs under the shared-generator defect, so their paired reading did not hold. Re-running them is cheap and would either confirm "the planner is not the bottleneck" on sound footing or overturn it.

Verification

smoke test   3 consecutive runs, exit 0
ledger gate  PASS (0 warnings)    ADR gate  PASS
tests        OK