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}}.
| z | seed | copper_q10 | copper_q90 | draw_index | correct_q10 | correct_q90 |
|---|---|---|---|---|---|---|
| -0.9221885951 | 20260914 | -0.9909223007 | 0.9909223007 | 1 | -1.2815515655 | 1.2815515655 |
| -0.681267648 | 20260914 | -0.9909223007 | 0.9909223007 | 2 | -1.2815515655 | 1.2815515655 |
| -0.2560884528 | 20260914 | -0.9909223007 | 0.9909223007 | 3 | -1.2815515655 | 1.2815515655 |
| -0.2739142428 | 20260914 | -0.9909223007 | 0.9909223007 | 4 | -1.2815515655 | 1.2815515655 |
| 0.1829334182 | 20260914 | -0.9909223007 | 0.9909223007 | 5 | -1.2815515655 | 1.2815515655 |
| -0.9025269656 | 20260914 | -0.9909223007 | 0.9909223007 | 6 | -1.2815515655 | 1.2815515655 |
| -0.6065101657 | 20260914 | -0.9909223007 | 0.9909223007 | 7 | -1.2815515655 | 1.2815515655 |
| -1.5855326828 | 20260914 | -0.9909223007 | 0.9909223007 | 8 | -1.2815515655 | 1.2815515655 |
| 1.9381511026 | 20260914 | -0.9909223007 | 0.9909223007 | 9 | -1.2815515655 | 1.2815515655 |
| -0.1394198356 | 20260914 | -0.9909223007 | 0.9909223007 | 10 | -1.2815515655 | 1.2815515655 |
| -3.0739926503 | 20260914 | -0.9909223007 | 0.9909223007 | 11 | -1.2815515655 | 1.2815515655 |
| -1.728736898 | 20260914 | -0.9909223007 | 0.9909223007 | 12 | -1.2815515655 | 1.2815515655 |