# Per-fold error model — pre-registration of the blind fold-factor band test at a fresh anchor *Staging note, pre-registration only. Nothing here is a measurement and nothing here is integrated into a live document. Written and committed alone, before the producer `research/attack-perfold-02-blindwindow.js` exists, so the commit graph carries the order. Calibration marked on every claim: PROVEN, VERIFIED by exact computation, MEASURED, PREDICTED.* ## 0. What fires, and what is being tested The extinction law's per-fold `±3√λ` clause FAILED at the fifth window (32 of 74 folds inside = 43.2% against the registered 90%, `foldL-window5.md` D3), while every aggregate clause landed. `research/attack-perfold-01-error-model.js` (formally embedded, 2026-08-20) identified the surviving per-fold error model against three calibrated synthetic controls and two held-out windows: > **X_p ~ Poisson(λ_model(p, Y) · M_p)**, with **M_p a deterministic factor of > the fold** — identical across window lengths (fold-factor deviance > G/df = 0.98 on six windows) and across anchors (anchor-replicate > χ²/df = 1.17 on the 2e9 pair, against 11.6 under window-level mixing) — > MEASURED, not derived. `M_p = λ_derived/λ_model` at all 8 comparable folds of > `import-stein.md` §2.4, so the per-fold failure is first-moment roughness the > smooth law misses, not super-Poisson noise. sd(ln M) = 0.56 over the 43 > best-measured folds; range [0.19, 2.23]. The model's predictive for a window that has never been run is a negative binomial with the fold's own pooled exposure over the six embedded windows: > `X_p ~ NB(r = Sx_p + 1/2, q = λ_h/(λ_h + Sλ_p))`, > `Sx_p = Σ X_p` and `Sλ_p = Σ λ_model` over the six embedded windows, > `λ_h = λ_model(p, 2·10⁹)`. This note fixes the blind test of those bands at a window that does not exist anywhere in the corpus, and writes every number the run will be scored against before the producer exists. Units on both sides: counts of adjacent kill pairs per fold (dimensionless integers); λ is the expected count. ## 1. The window, stated before the run **Anchor `A = 66,000,000,000` (= 6.6·10¹⁰, a multiple of 6), length `Y = 2·10⁹`, fold ceiling 1499, engine conventions of `attack-foldL-06-scaling.js` verbatim.** No window in the corpus has used this anchor. The window is run at this anchor and scored at this anchor. No second anchor is run before the verdict is written, and no second anchor may be used to overturn a miss. The producer is a copy of the scaling record's chunked streaming engine. Its Stage A must reproduce, digit for digit, the embedded `[0, 2·10⁹)` calibration figures of `attack-foldL-06-scaling.js` (X at folds 7, 23, 29, 421; N2 = 37; Σ X = 20,317,943; last L ≥ 2 fold = 421) and abort on any mismatch, and its Stage B must reproduce this note's prediction table from the embedded artifacts before Stage C measures anything. PREDICTED wall time: ~10 s sieve at an idle machine, up to ~60 s under load. ## 2. The predictions, verbatim from the embedded Stage 4 of `attack-perfold-01-error-model.js` The population is fixed in advance: the 37 folds `p ≥ 100` with predictive mean ≥ 1 or `λ_model ≥ 1`. The bands are central intervals of the NB predictive (discrete, so nominal coverage is ≥ the stated level). `P(old clause)` is this model's own predicted probability that the fold lands inside the REGISTERED Poisson clause band `λ_model ± 3√λ_model` — printed as contrast, not scored. ``` p lam_model Sx Slam pred.mean 90% band 99.73% band P(old +-3sqrt clause) 101 269.37 29454 30199.0 262.73 [236, 290] [215, 313] 1.00 103 281.59 31072 31569.2 277.16 [250, 305] [228, 329] 1.00 107 226.77 14490 25423.6 129.25 [111, 148] [96, 165] 0.00 109 236.81 15451 26548.7 137.82 [119, 158] [104, 175] 0.00 113 192.42 29916 21572.3 266.85 [240, 294] [219, 317] 0.02 127 115.64 22880 12964.4 204.09 [181, 228] [162, 248] 0.00 131 95.20 8096 10672.4 72.22 [58, 87] [48, 99] 0.78 137 77.56 6174 8695.5 55.08 [43, 68] [34, 79] 0.68 139 81.09 6796 9091.5 60.62 [48, 74] [39, 85] 0.78 149 52.33 8135 5867.1 72.57 [59, 87] [48, 100] 0.60 151 54.72 8742 6134.5 77.98 [64, 93] [53, 106] 0.44 157 45.25 4880 5073.2 43.53 [33, 55] [25, 65] 1.00 163 37.57 2407 4211.6 21.47 [14, 29] [9, 37] 0.65 167 31.67 2885 3550.5 25.74 [18, 34] [12, 42] 0.99 173 26.48 4822 2968.3 43.02 [32, 54] [25, 64] 0.42 179 22.22 4061 2490.7 36.23 [27, 46] [20, 56] 0.53 181 23.20 4253 2601.5 37.94 [28, 48] [21, 58] 0.48 191 15.78 627 1769.2 5.60 [2, 10] [0, 14] 0.81 193 16.50 715 1849.3 6.38 [3, 11] [0, 15] 0.76 197 14.10 868 1581.1 7.75 [3, 13] [1, 17] 0.98 199 14.73 877 1651.2 7.83 [4, 13] [1, 17] 0.95 211 10.11 2521 1133.2 22.49 [15, 31] [10, 38] 0.27 223 6.98 339 782.7 3.03 [1, 6] [0, 9] 1.00 227 6.00 237 673.0 2.12 [0, 5] [0, 8] 1.00 229 6.30 249 705.8 2.23 [0, 5] [0, 8] 1.00 233 5.45 428 610.9 3.82 [1, 7] [0, 11] 1.00 239 4.68 442 525.2 3.95 [1, 7] [0, 11] 1.00 241 4.89 520 548.0 4.64 [1, 8] [0, 12] 1.00 251 3.49 208 390.9 1.86 [0, 4] [0, 7] 1.00 257 3.01 189 337.8 1.69 [0, 4] [0, 7] 1.00 263 2.61 309 292.4 2.76 [0, 6] [0, 9] 0.99 269 2.26 201 253.7 1.80 [0, 4] [0, 7] 1.00 271 2.36 237 264.5 2.12 [0, 5] [0, 8] 0.99 277 2.05 141 229.8 1.26 [0, 3] [0, 6] 1.00 281 1.80 38 201.4 0.34 [0, 1] [0, 3] 1.00 283 1.86 59 208.7 0.53 [0, 2] [0, 4] 1.00 293 1.36 158 152.3 1.41 [0, 4] [0, 6] 0.98 expected count inside the 90% predictive bands = 34.6 of 37 ``` **Expected counts under the model, fixed here:** 34.6 of 37 inside the 90% bands; 28.1 of 37 inside the old Poisson clause (76%, still below the 90% that clause demands). **Expected under the refuted rival** (i.i.d. NB mixing per window, k ≈ 3.5): the fold-factor bands are then mis-centred and Poisson-narrow, and control C of the embedded battery measured their coverage at 56–59%, i.e. ≈ 21.5 of 37. The test separates the two by ~13 folds. ## 3. The scoring rule, stated before the data exists Read off the 37 listed folds at anchor A = 6.6·10¹⁰ only. - **(a)** at least **28 of 37** folds lie inside their listed 90% band; - **(b)** at most **1 of 37** folds lies outside its listed 99.73% band. **HIT** requires both. **MISS** is either failing. Under the model, (a) fails with probability < 0.2% (binomial, 37 trials at ≥ 0.90 each) and (b) fails with probability ≈ 0.5%; under the rival, (a) holds with probability < 2%. So a HIT is evidence for anchor-transferability of the fold factor at Poisson precision, and a MISS is a real miss, not band luck. ### What HIT does - The fold-factor error model moves from held-out-validated (windows 2e10 and 2e11 scored by an estimator fitted on the smaller windows) to **blind-validated at a fresh anchor**. It stays MEASURED; M_p has no derivation, only the comb-weight correlation (0.654) as a mechanism lead. - The per-fold clause of the extinction law should be REPLACED in any future window prereg by the NB predictive bands of §0, with the old `±3√λ_model` clause retired as REFUTED (it was scored at window 5 and failed; this note predicts it keeps failing). - Nothing about the law's aggregate statistics, its grade (WEAKENED, set by prior art), or H″ moves. This is an error model, not progress on the target. ### What MISS does - **(a) fails**: the fold factor is not anchor-transferable at Poisson precision; the surviving description falls back to i.i.d. NB with k ≈ 3.5, and `perfold-error-model.md` must say so in its verdict block. - **(b) fails alone** (two or more 99.73% escapes with (a) holding): a heavy tail the mixture candidates would own; the PLN/NB comparison of the embedded battery is then re-read on the new window before anything is written. - A MISS says nothing about the aggregate law, whose five-window record is untouched by any outcome here. ### What is registered as not scored The old Poisson clause count (expected 28.1 of 37, printed for contrast). The folds below p = 100 (alternation-capped, the record refuses to predict them). All aggregate statistics (N2, S1, ΣX, extinction fold) — this window is a per-fold test only; its aggregates are printed for the record. Everything above p = 293. ## 4. Reproduction ``` node research/qc/embed.js --check --timeout 400 research/attack-perfold-01-error-model.js node research/attack-perfold-02-blindwindow.js # the producer; does not exist at commit time ``` --- *This document states current understanding. Superseded claims, retired numbers and the reasons they changed are in [../CHANGELOG.md](../CHANGELOG.md), indexed by document.*