# The fifth window: W = 2·10¹¹ scores the extinction law one decade blind, and it lands *(2026-08-19 night. Pre-registration committed alone at `4391c2c` before the producer existed: `foldL-window5-prereg.md`, same folder. Producer: `research/foldL-window5-01-extinction.js`, 1228.7 s at nice 15, formally embedded. The prereg fixed the anchor (A = 0), the sweep ceiling (2999, scored at the record's 1499), both predictions, all four criteria, and every consequence, before the run.)* ## 1. The verdict: HIT, all four criteria | criterion | prediction | measured | verdict | |---|---|---|---| | (a) last fold with L ≥ 2 | band [571, 877], median 683 | **631** | in band | | (b) N2(p ≥ 100) | 80.1, accept [51.2, 108.9] | 69 | in band | | (c) S1(p ≥ 100) | 80.1, accept [51.2, 108.9] | 70 | in band | | (d) the sequence | strictly increasing | 181 → 331 → 421 → 457 → **631** | holds | Crossing at the record's literal c = 1.22 predicted 653 against 631, ratio 0.966. The consequences were fixed in the prereg and apply mechanically: the rate law's support now spans **five windows and four decades of Y**, still MEASURED, H″ still UNPROVEN; `paper/proposals/prop-thinning-null.md` §5's "downgrade toward RETIRED if the rate law misses at a fifth window" does NOT fire; **the grade does not improve** — WEAKENED was set by found prior art and a fifth window says nothing about prior art. Writing this HIT up as an upgrade is the misreading the prereg names. ## 2. The secondary readings, none of which change the verdict - **D1, the hot systematic, now confirmed at five of five windows**: measured/predicted N2 = 0.75, 0.82, 0.87, 0.82, **0.86**. Per the prereg's own clause, this now belongs IN the law as a known ~20% overprediction on counts, not absorbed by the acceptance band a sixth time. Any future window prediction should quote both the raw and the ×0.82-corrected count. - **D3, the per-fold ±3√λ clause, FAILS**: 32 of 74 folds with E[X] ≥ 1 inside the band = 43.2% against the registered 90%. The aggregate lands while the per-fold dispersion is far wider than Poisson — overdispersion consistent with D1's systematic and with the anchor-offset spread the record and `null-limsup.md` both measure. A per-fold error model is the law's one missing piece; the aggregate statistics are what the law predicts well. - **D2**: the [300, 1000) decade measures 32 against 43 predicted — the hot bias concentrated where the counts are; [100, 300) is exact at 37. - **C3, the range check**: the full sweep to 2999 puts the last fold with θ ≤ G₂ at **1039 < 1499**, so the record's old ceiling was never binding and the extinction is arithmetic, not a sweep artifact. The §7-style disclaimer in the scaling record can be retired. - **D4, for the record only**: Σ X(p ≥ 100) = 190,961 against the fitted model's 2.004e5 (ratio 0.9527) and the Stein-derived pair's 1.917e5 (ratio **0.9961**). The prereg's §3.5 forbids reading this window as evidence between the fitted and derived pairs on the scored statistics, and D4's own caption notes the derived λ is not digit-comparable; the 0.9961 is recorded as a note, not a verdict. ## 3. Custody Stage A reproduced the whole embedded four-window tail byte for byte (`embed.js --check` on the scaling producer passed pre-launch), the copied engine passed 30 of 30 calibration assertions at the raised ceiling, and ceiling invariance was verified at Y = 2·10⁹ (identical restricted statistics across 428 folds). Stage B reproduced every prereg number with one disclosed fourth-significant-digit exception (B0a: the prereg used the published rounded constants; no scored figure moved). The raw log is `research/foldL-window5-01-extinction.raw.txt`; the formal embed carries the stdout stream (chunk progress went to stderr).