Tiny-expert capacity rung: prior CONFIRMED at the band — Δ_capacity@10k = +0.188 (#4/#16)

2026-08-10 05:4x–06:0xZ. The T1 rung (pre-reg, final amendment = matched-F 10k design) closed 05:06Z with train complete and its chained panel_v2 eval landing ~05:4xZ; this is the canonical frozen read — paired per-frame vs the banked F@10k npz via the oracle-gated attach_seam_results.py read-1 machinery pointed at explicit paths (per the pre-reg), analysis banked in analysis__tiny10k_delta_capacity.json. The “Δ_seam” decision branches in that machinery do NOT apply here — only the paired read, the state-copy execution oracle, and the record-only mirrors are consumed; interpretation runs on the tiny pre-reg’s own pinned bands.

The question

Is the flow expert over-provisioned at h1024/d12? The Decoupled Action Expert prior says task knowledge lives in the trunk’s residual streams, not the expert — a 5M MLP matched a 244M U-Net there. T1 tests the width direction on our stack: h256/d12 (~16× smaller transformer blocks; tap surface and adapters identical) on the same hard-frozen 60k trunk (sha e6ed783b verified at init and at upload), trained fully matched to F — 10k steps, eff-batch 48 (48×1 local vs F’s 12×4 box), same LR schedule, same save cadence.

Measured expert sizes (safetensors headers, record-only read): tiny 86.8M params vs F 367.5M — 4.2× smaller in total, not 16×, because the tap/adapter surface reading the h2048 trunk streams is held identical by design and is a fixed cost that dominates the tiny expert’s count. The width contrast is in the transformer blocks; the conditioning surface is the controlled variable.

The reads, in pre-reg order

Primary — Δ_capacity@10k (fully matched): paired per-frame chunk_mae, tiny@10000 − F@10000, panel-v2 core frames (n = 15,056), seeded 10k-resample bootstrap CI95: +0.18805 [+0.15527, +0.22139] — inside the |Δ| ≤ 0.3 band, and the CI excludes zero: the width cost is real but small (~2.0% of the panel number; median +0.149, tiny wins 43.2% of frames). Pooled panel numbers: tiny 9.6094 vs F 9.4157 (chunk); first_mae 3.0758 vs 2.9581 (mirror Δ +0.1176 [+0.1025, +0.1328] — same shape as the chunk read).

Execution oracle (state-copy): the tiny npz’s state-copy rows byte-match the banked F-side values (hard-abort guard in the read machinery — the PAIR_KEYS byte-equality check covers the shared state-copy column). Passed — byte-identical across the box (F) and local (tiny) eval machines, so the plan, frames, and state-copy column are provably the same rows. Both arms beat the state-copy pooled number (11.7639) by the pre-pinned VOID margin, so the read is live, not void.

Record-only: the step-matched probe ladder (chart, left panel) — tiny trailed F early (expected: same LR schedule on 16× fewer expert-block params), converged from ~step 6000, and finished 9.3469@10000 vs F’s 9.3798 probe-level; the panel read above is the one that counts. Per-step-in-horizon curves (chart, middle) — the tiny gap is late-horizon — Δ per step-in-horizon grows from +0.106 at step 1 to +0.374 at step 50, i.e. the small expert tracks F early in the chunk and cedes ground as the horizon extrapolates.

Interpretation (bands pinned pre-data)

The pre-reg froze: |Δ@10k| ≤ 0.3 → capacity prior CONFIRMED at this scale (tiny is a free ~16× shrink); Δ ≥ +1.0 → capacity binds, h1024 justified; between → gray zone. The prior is confirmed at the pinned band: +0.188 is deep inside |Δ| ≤ 0.3 and nowhere near the ≥ +1.0 capacity-binds line. Quoted honestly: the CI excludes zero, so this is not “within noise” — a 4.2× smaller expert (86.8M vs 367.5M) costs a real +0.19 chunk (+2.0%), concentrated late in the horizon. Width alone does not separate the experts at this scale; h1024 buys a small, measurable, probably-not-decision-relevant margin. One more datum for the probe-is-not-a-headline file: the 256-frame probe had tiny under F (9.3469 vs 9.3798, Δ −0.069) — the 15,056-frame panel flips the sign. Small-sample probes kill runs; panels make claims.

What this re-prices: the fjoint expert (#4) does not need h1024 to hold the frozen-trunk score — the cheap-expert pole is real capital for rig inference cost (#16, the north star’s deployment side). What this does NOT test (pre-reg’s own list): depth/tap-count (T2’s business), the joint pole (closed by the attachment decision memo), and trunk quality (frozen, shared).

Run record

Train 2026-08-09 20:1xZ → 2026-08-10 05:06Z on the local H100, ~8.7 GPU-h of the 15 gate including a host-RAM OOM at step ~9,060 (04:00:55Z, DataLoader-worker RSS class — the second host-RAM incident of this run, after the step-500 kill at launch workers 20; workers 10→6 on resume) and the resume-from-8750 replay (~310 steps, fresh shuffle seed 1 per the standing resume-seed policy, eval-seed 0 held so the probe ladder stays comparable). The resumed path converged back onto the pre-kill curve: 9.37@9000 pre-kill → 9.56/9.50 wobble → 9.35@10000. Chained panel_v2 @10000: pre-reg args verbatim, k4l2 panel_v2 plan sha-verified, heun30/draws1/stable, eval ~38 min / ~0.6 GPU-h at ~660 f/min single-GPU — run total ~9.3 of the 15 GPU-h gate.

Artifacts: panel report (tiny) · panel report (F comparator) · frozen analysis JSON · checkpoint fontaine_molmo2_flow_tiny_h256_10k_1xh100/step_010000 (weights-only, backbone deduplicated) on fontaine-checkpoints.