Golden tickets, the whole story — a visual report (#1)

2026-08-08. Owner-requested consolidation (steering 08:42Z): the golden-ticket thread ran across a pre-registration, a results post, three frozen stage analyses, and a selector side-read — this page subsumes them into one chart-led report. Every number is read from the banked stage JSONs (analysis__goldenticket_stage{1,2,3}.json, analysis__noise_ladder_seating.json); charts are rendered by fontaine/scripts/goldenticket_report_charts.py from those files and nothing is re-computed.

Refreshed 2026-08-08 ~23:4xZ, the night the ladder’s second rung closed end-to-end: R3 is upgraded from record-only to CONFIRMED and seated on the leaderboard (paired re-run, CI entirely below zero), rung 2’s out-of-sample falsification of per-dataset routing is folded in, and the chart set is restyled to the dark eval-report theme.

The idea in one paragraph

A flow-matching policy turns a noise vector into an action chunk through a deterministic ODE. The Golden Ticket observation (banked on the noise-steering pages) is that some noise vectors are systematically better than others — not per-sample luck, but a reusable property of the vector. The screen asked, with every read pre-registered: draw 64 i.i.d. “tickets” (sha-pinned noise vectors), score them once on a probe, and check whether the winners are (R1) wider-spread than chance, (R2) real on held-out rows, (R3) still better inside the ensembling regime, and (R4) where the advantage lives. Total cost ~5.55 GPU-h, zero training.

Headline numbers

R1 — the spread is ~12× the i.i.d. null

If tickets were interchangeable, 64 probe scores would scatter with σ ≈ 0.067 (the frozen null, computed from banked per-draw variance before any data). Measured: sd 0.823, minimum 5.706 vs an expected-null-minimum of 6.587. The distribution isn’t a noisy constant — it has a long bad tail and a usable good tail.

R2 + R3 — real on held-out rows, and the searched ensemble is seated

R2 is the confirmatory read the screen lived or died on: the winner ticket, judged only on complement rows it was never selected on, paired per-frame against the banked stable-key default. It landed −0.924, eighteen times past the adopt floor.

R3 asked whether search survives ensembling — mean-of-top-10-tickets vs mean-of-10-random-draws. The screen’s first pass could only score it record-only (the banked comparator retained no per-frame npz), so the rung-2 pre-reg folded in a paired re-run: both ensembles decoded fresh on the full panel, same frames, same noise discipline. That read landed 2026-08-08 ~23:1xZ: paired Δ = −0.17358 [CI95 −0.19556, −0.15214] on 17,204 core frames, entirely below zero (the dataset-clustered CI [−0.202, −0.148] agrees; first-step mirror −0.041 [−0.047, −0.034]). R3 is confirmed, and the leaderboard row moved. (The read survived its own integrity gate the hard way — a base-equality abort that turned out to be kernel-order drift from the batched-ensembling merge, adjudicated at the npz level before any tolerance moved; the results post’s seating section has the full detour.)

The board, after seating

The seated row — chunk 5.1847, first-step 1.3831 — is the best chunk and the best first-step number measured on this panel by any config, and it costs nothing at train time: the tickets are ten sha-pinned noise vectors, found for ~5.5 GPU-h of one-off search. The gap to the ☆ bar (≤ 5.0) shrinks from 0.37 (random-10 family decode) to 0.18.

R4a — every ticket wins somewhere

The free stage-1 read that reframed the whole thread: per-dataset, the global winner is argmin in only 35/792 datasets (4.4%) — and it isn’t even the most task-general ticket (a blue top-10 ticket wins 62). The top-10 set contains the per-dataset argmin 29.8% of the time, ~2× the 15.6% null. The published analog (2603.11642): noise main effect 1.4%, context×noise interaction 39.4%, best shared noise optimal in 3.1% of contexts. Loud caveat, banked in advance: the median dataset has 2 probe frames — these per-dataset winners are hypotheses for the next rung, not results.

R4b — the ticket buys most where the decoder is least sure

Split the panel by draw dispersion (how much the 10 ticket decodes disagree per frame): the winner’s gain is monotone across quartiles, −0.35 on the tightest frames to −1.44 on the most dispersed. The ticket is not shaving uniform noise — it wins where the decoder’s noise-response is largest, which is exactly where any per-dataset or per-frame escalation has the most room.

R4c — horizon-wide, not a first-step artifact

Per-step MAE across the 50-step chunk, all three configs: the ordering stable-key → winner → ensemble holds at every step, and the gap grows with horizon.

The side-read that failed (and why that’s useful)

SDN’s smoothness selector (“pick the least jerky draw”, 2606.14084) was placed on the banked ticket-64 stack at table cost: null (agreement 1.5% vs 1.6% chance). Heun-30 ODE draws are uniformly smooth — the criterion has nothing to grip on this family. The family decode (mean-of-draws) stands.

Rung 2 — per-dataset routing, falsified out-of-sample

R4a’s “every ticket wins somewhere” begged the escalation: route each dataset to its own probe-picked ticket. The rung-2 pre-reg ran it honestly — a CPU reliability floor picked the 97 dataset cells that were even decidable, then one confirm eval on held-out complement rows. The answer was decisive, on the wrong side of zero: Δ_route +0.129 [CI95 +0.060, +0.205] — routing is significantly worse than the global ticket (34W/54L, sign p = 0.042). The in-sample −0.60 probe delta inverted out-of-sample: with a median of ~6–20 probe frames per cell, the per-dataset argmin memorizes its cell — exactly the R4a caveat cashing out. The golden-ticket effect itself stayed intact (routed still beats stable-key by −0.756); it’s the per-dataset selection that doesn’t transfer. Full readout: rung-2 results.

Where the ladder stands

Rung 2 is closed end-to-end, with one confirmation and one falsification — which is what a ladder is for:

• Adopted: the seated top-10 ticket ensemble is the flow board row (5.1847/1.3831). One global ticket set, no routing.
• Falsified: per-dataset ticket routing. The probe stack can rank tickets globally; it cannot pick per-dataset winners at 6–20 frames per cell.
• Named next candidates (each needs its own pre-reg): dispersion-gated draw allocation — R4b’s monotone gain-vs- dispersion curve is exactly the premise of ELASTIC, and the read is free on banked dumps; and a chunk-position noise policy — rung 2’s record-only lead that routing wins early chunk steps (~1–8) and loses late ones (~15+).
• Named unknown inherited by every ticket config: the panel cannot see chunk-boundary artifacts — a rollout-gated read (#16) stands between any ticket and a rig.