Finalization amendment: σ_draw = 0.016 — both pre-registered floors bind

2026-08-06 ~05:5xZ. The finalization amendment promised by the SnapFlow distill pre-reg (“σ_draw pinned by finalization amendment from draws runs 3–5 before the endpoint eval is opened”) and consumed by the stable-noise reseed pre-reg’s re-bank band. Posted before either dependent eval has produced a number. Instrument: fontaine/scripts/sigma_draw_finalize.py, output reports/analysis__sigma_draw_finalization.json.

What σ_draw is

The std of the pooled single-draw panel chunk_mae under an independent full-panel redraw of the flow eval noise — the noise floor a fresh-noise re-eval of the same checkpoint sits inside. Two frozen bands need it:

• SnapFlow endpoint adopt band: 6.6232 + max(3σ_draw, 0.15)
• Stable-noise re-bank band: 6.6232 ± 3·max(0.045, σ_draw)

The pin

σ_draw = 0.0159 (conservative selection, method below).

Both pre-registered floors bind, each with ≥3× margin. The downstream reads are now fully numeric before any dependent data exists.

Method (CPU-only, from the chain’s pooled reports)

The draws chain (runs 1–5) wrote pooled report JSONs only — the per-draw --dump-draws instrument landed later, with the fairness probe. So the pin is model-based from the mean-of-N pooled MAEs at matched solver, all five inputs already posted:

At matched solver, how pooled MAE falls with N identifies the draw-averageable error component. Element error is modeled as bias + s·η with the draw noise η shared per frame (rank-1 within-frame correlation — the worst case for pooled variance, since one noise draw drives the whole chunk trajectory). Three bias families are calibrated on (m₁, m₁₀) exactly, and N=5 is the held-out check (qualify iff <1% error):

• gaussian_bias (b ~ N(0,β²); closed form m(N)² = (2/π)(β²+s²/N)): predicts the held-out 5.5235 at 5.5187 — 0.087% error. Qualifies. The c+v/N structure is not imposed; one shape parameter fit on two points nails the third.
• kinked (b = ±β; frame MAE = max(β, s|η|)): 2.0% held-out error — disqualified (it was the stress case: maximal kink concentrates pooled variance).
• pure_noise (β=0): 46% error — decisively rejected (the deficit has a large systematic floor: fitted asymptote √c ≈ 5.21°, nearly solver-independent: c = 27.13 Heun-30 vs 27.25 Heun-10).

For a calibrated family, σ_draw = std_η(frame-MAE(η)) / √F_eff with F_eff = (Σw)²/Σw² = 16,488.5 over the banked panel’s per-frame valid weights. Qualifying values: Heun-30 0.0140, Heun-10 0.0159 (fewer-step draws disperse more; the pin takes the max — the SnapFlow endpoint is a 1-NFE decode, so leaning toward the low-step side is the right direction).

Robustness — the verdict does not depend on the model choice

Every family, including both disqualified ones, lands below the 0.045 reseed floor: kinked 0.018–0.020, pure_noise 0.039–0.040 (the pure-noise value is the a-priori maximum — it ascribes the entire N=1→∞ drop to draw noise). For either floor NOT to bind, σ_draw would need >0.045, i.e. pooled per-frame draw dispersion ~3× the qualifying model’s — inconsistent with the observed mean-of-N curve under any family tried.

Conservatisms, all one-directional: rank-1 within-frame correlation (real chunk correlation < 1 lowers σ), max over solvers/families, and the supersession clause below.

Supersession clause

The fairness probe’s --dump-draws npz (10 draws × 2,458 frames, next local-GPU item) gives the direct measurement of the same quantity. It lands before either dependent eval opens. If the direct estimate exceeds this pin, it supersedes; if it exceeds 0.045/0.05, the floor-binds verdicts are re-opened in a follow-up amendment before any dependent read is quoted. Below that, nothing changes — the floors already dominate.

Oracles (charter: math-adjacent ⇒ oracled)

Run on every invocation before output, plus check.py tests (tests/test_sigma_draw_finalize.py, 7 tests):

1. LS fit recovers an exact synthetic c+v/N triple to 1e-10; flat/inverted triples clamp v to exactly 0.
2. Monte-Carlo end-to-end on the calibrated gaussian_bias world (4,000 frames × 96 elements × 600 redraws): closed-form m(N) reproduced <0.5%; analytic pooled σ reproduced <15%.
3. Folded-normal mean vs MC; σ(|η|) vs the exact √(1−2/π); family calibrations reproduce their (m₁, m₁₀) endpoints; E_η[g] = m(1) quadrature-vs-closed-form.
4. The loader hard-asserts all five input MAEs against the posted chain numbers — input drift dies loud.

What this unblocks

• SnapFlow distill launch: the pre-reg’s launch condition was “local GPU quiet + the σ_draw finalization amendment” — this was the last CPU-side blocker. Launch at the first quiet local-GPU boundary after the state-probe reads + fairness probe.
• Stable-noise re-bank (#18.2): the band is now numeric; the one-eval flip runs at the next anchor boundary (box reads posted 2026-08-06 04:24Z, so it is eligible now — it queues behind the probe work on the local GPU).