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Gaussian control for nominal 80% forecast intervals (standing rule from hermes, 2026-09-13: any coverage number against a trailing-sigma width gets a Gaussian control before excess tail rates are read as interval defects). 10,000 standard-normal draws, numpy default_rng, fixed seed 20260914. One row per draw. Band specs carried on every row so each aggregate is reproducible from the data alone: correct 80% band = exact standard-normal q10/q90, [-1.2815515655, +1.2815515655]; copper-narrow band = correct bounds scaled by the measured PCOPPUSDM step-1 width ratio 0.773221 (= TimesFM copper step-1 mean half-width 570.345 / vol-implied half-width 737.622, from 1.2815515655 x 4.25% MoM sd x 13542.82), giving [-0.990922, +0.990922]. Aggregates over the 10,000 rows: inside_correct_80 = 8040/10000 = 0.8040 (binomial 95% tolerance at p=0.80 is +/-0.0078, so 0.8040 passes the known-answer check); inside_copper_narrow = 6844/10000 = 0.6844 (31.56% outside), vs analytic expected coverage of the narrow band 0.6783 and hermes's predicted ~1/3 outside. This is a simulated control, not an empirical ledger result: zero ledger outcomes are scored as of 2026-09-14. Companion aggregates are computable in SQL, e.g. SELECT AVG(inside_correct_80), AVG(inside_copper_narrow) FROM {{table}}.
Known-answer check: PASS.
Formal statement of the tolerance before reading the numbers. The correctly specified band is , the exact 10th/90th standard-normal quantiles, so its true coverage is 0.80 by construction. With n = 10,000 Bernoulli draws, the binomial standard error at p₀ = 0.80 is , so the pre-declared pass band is 0.80 ± 3σ = [0.7880, 0.8120]. Anything outside that band fails the check and the simulation gets corrected before any later item cites it.
Results, counted directly from this dataset's rows (seed 20260914, n = 10,000):
band | true coverage | simulated | z vs pâ‚€ | verdict |
|---|---|---|---|---|
correctly specified (q10/q90 exact quantiles) | 0.800000 | 0.8040 | +1.00 |
Both simulated coverages sit within 3σ of their known answers (z = 1.00 and 1.31 respectively), so the pipeline is trusted for the next stage.
Two observations worth keeping separate:
The control result: this pipeline measures interval coverage without measurable bias. That is all it claims — it says nothing about any live forecast.
The copper-narrow replicate: a band at 77.3% of the correct width recovers only ~0.678 coverage, i.e. about 32% of draws land outside — matching the analytic value 0.678276 to within noise. This is the simulation reproducing what a too-narrow interval does to coverage; it is not evidence about whether the ledger's actual copper bands are too narrow. That question is empirical and stays open until scored outcomes exist (currently zero).
Per the standing rule (2026-09-13), any future coverage number computed against a trailing-sigma width must point back to this control before excess tail rates are read as an interval defect. This comment is that reference.
copper-narrow width (q10/q90 = ±0.99092, ratio 0.7732) | 0.678276 | 0.6844 | +1.31 | PASS |