{"id":5449,"job_id":10970,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-fable-5-1","provider":"anthropic","report_md":"# Three frozen instruments on the seven exact terms G2(83#) to G2(109#): the registered Q-g2-falls rule reads FALLS on [11, 109] at -5.26 se (x ln^2 x excluded at 5.15 se_k, x ln^3 x 1.53 se_k away, not excluded); the blind forecast that put G2(37#) at z = +6.58 puts the new terms at z = +0.64 to +2.10, three of seven outside their band; route 344's R runs 0.5284 to 0.5547, six of seven inside the +/-10% band; each a measurement of one instrument, none a verdict on a growth law\n\n## Result\n\nMeasured. All three instruments reproduce their registered readings before reading a new term. Each then scores the seven terms G2(83#) = 1860 through G2(109#) = 3060 with no constant changed. (a) The Q-g2-falls decision rule reads FALLS over x in [11, 109], n = 25: b = -0.2212 +/- 0.0421 (se_honest), -5.26 se_honest. The rule already read FALLS at X1 = 79 on the 22 trusted terms, at -3.11, and every new term keeps the verdict. Its section 2.1 k reading is k_hat = 2.771 +/- 0.150. That places x ln^2 x 5.15 se_k below the measurement, excluded at the rule's 3 sigma, and x ln^3 x 1.53 se_k above it, not excluded. (b) The blind seven-level forecast that put G2(37#) at z = +6.58 puts the new terms at z = +0.64 to +2.10, all positive. Three of seven fall outside their own blind band (89#, 107#, 109#), and none comes near +6.58. (c) Route 344's ratio R = G2/M0 runs 0.5284 to 0.5547 on the seven new rungs, z = +0.66 to +1.36 against the frozen median 0.504 and sigma 0.0372. Six of seven fall inside the +/-10% band (109# misses at +10.1%), and six of seven fall above the route's R = 0.48 +/- 0.05. Each line is a measurement of one instrument on these terms. None is a verdict on a growth law (A11, C1).\n\n## Reproduction gates\n\nCommands, Python 3.9.6, stdlib only. Each run takes under 0.25 s of wall time on the Studio under `nice -n 10`:\n\n```\nnice -n 10 python3 research/ladder-out-of-sample/apply.py --rule falls --terms 9\nnice -n 10 python3 research/ladder-out-of-sample/apply.py --rule falls --terms all\nnice -n 10 python3 research/ladder-out-of-sample/apply.py --forecast\nnice -n 10 python3 research/ladder-out-of-sample/apply.py --ratio\n```\n\nBefore any rule runs, `apply.py` checks the sha256 of each of the 27 verbatim excerpts in `RULES.md`. It reads the frozen ladder and the one-class control from excerpts D1 and D2, and parses the forecast's expected rows from B3 and the ratio's rung table from C3. A one-byte change to excerpt A3 makes it print `STOP` and exit 1. A gate mismatch also exits 1 before a new term is read. All four commands exit 0 with 78 checks `ok`.\n\n- (a) At n = 9 on [11, 41], to the digits A3 and A5 print: b = -0.0694, se_nom 0.0747, se_honest 0.1169, |b|/se_honest 0.59, sign gate -0.2025, control -0.8209 +/- 0.0709 and -0.8163 +/- 0.0397, 11.6 sigma on the control and 0.9 sigma on G2 (both |b|/se_nom, as #4294 F2 notes), separation 7.3 sigma, s = 0.3302, k_flat 3.028, k_hat 2.82 +/- 0.35, verdict FLAT / UNRESOLVED. The n = 10 row (b = -0.0810, se_honest 0.1052) matches #4294 F3.\n- (b) c2'(37#) = 0.5939, the custody band [476, 633] with central 513 at 41#, and all eleven G2 rows of B3, x = 37 to 79, field by field. That includes 37#: band [397, 445], central 414, z = +6.58.\n- (c) M0 and R at 5# to 37# (C3), R at 41# to 67# (C3) and at 71#, 73#, 79# (C6), the 18-rung median 0.504, sigma 0.0372, z = +2.43 at 37# and +0.86 at 67#. The closed form agrees with bisection to 3.3e-16 relative at every level from 5# to 109#.\n\nA convention finding on (c). #5110 does not say how it takes the median of an even count. Its four numbers reproduce exactly with the upper middle value, `sorted(v)[n // 2]`, used for both the median and the MAD. The usual median, the mean of the two middle values, gives 0.4984, sigma 0.0371 and z(37#) = +2.59. In each case the 0.504 is R(61#). The gate uses the upper-middle convention because it reproduces the printed record. The decisions below use the printed constants 0.504 and 0.0372, so the convention changes no row. The sensitivity line under (c) gives the two-middle reading.\n\n## (a) Q-g2-falls decision rule\n\nThe rule at each X1. Window [11, X1], every prime, x_min = 11 frozen. The sign gate is the slope on [5, X1]. \"Move\" is the change in b from the previous X1, in units of the previous se_honest.\n\n| X1 | n | b | se_nom | se_honest | b/se_honest | [5, X1] b | move | verdict |\n|---|---|---|---|---|---|---|---|---|\n| 41 | 9 | -0.0694 | 0.0747 | 0.1169 | -0.59 | -0.2025 | | FLAT / UNRESOLVED |\n| 43 | 10 | -0.0810 | 0.0637 | 0.1052 | -0.77 | -0.1991 | -0.10 | FLAT / UNRESOLVED |\n| 47 | 11 | -0.0969 | 0.0562 | 0.0956 | -1.01 | -0.2000 | -0.15 | FLAT / UNRESOLVED |\n| 53 | 12 | -0.1131 | 0.0500 | 0.0877 | -1.29 | -0.2020 | -0.17 | FLAT / UNRESOLVED |\n| 59 | 13 | -0.1441 | 0.0488 | 0.0809 | -1.78 | -0.2138 | -0.35 | FLAT / UNRESOLVED |\n| 61 | 14 | -0.1559 | 0.0445 | 0.0751 | -2.08 | -0.2170 | -0.15 | FLAT / UNRESOLVED |\n| 67 | 15 | -0.1648 | 0.0405 | 0.0701 | -2.35 | -0.2190 | -0.12 | FLAT / UNRESOLVED |\n| 71 | 16 | -0.1743 | 0.0374 | 0.0658 | -2.65 | -0.2221 | -0.14 | FLAT / UNRESOLVED |\n| 73 | 17 | -0.1763 | 0.0344 | 0.0619 | -2.85 | -0.2213 | -0.03 | FLAT / UNRESOLVED |\n| 79 | 18 | -0.1818 | 0.0319 | 0.0584 | -3.11 | -0.2229 | -0.09 | FALLS |\n| **83** | 19 | -0.1868 | 0.0298 | 0.0554 | -3.37 | -0.2244 | -0.08 | FALLS |\n| **89** | 20 | -0.1917 | 0.0279 | 0.0526 | -3.64 | -0.2260 | -0.09 | FALLS |\n| **97** | 21 | -0.2041 | 0.0275 | 0.0501 | -4.07 | -0.2327 | -0.24 | FALLS |\n| **101** | 22 | -0.2149 | 0.0270 | 0.0478 | -4.49 | -0.2389 | -0.22 | FALLS |\n| **103** | 23 | -0.2203 | 0.0257 | 0.0457 | -4.82 | -0.2417 | -0.11 | FALLS |\n| **107** | 24 | -0.2223 | 0.0243 | 0.0438 | -5.07 | -0.2424 | -0.04 | FALLS |\n| **109** | 25 | -0.2212 | 0.0231 | 0.0421 | -5.26 | -0.2410 | +0.03 | FALLS |\n\nPer new term. The prediction is the rule's line on [11, 79], ln(G2/x^2) = -0.4605 - 0.1818 ln x, fitted on the 18 terms of that window, all exact before any new term. The residual is ln(exact/predicted) in units of the registered per-point noise law sd(x) = 0.894 x^-0.711 (A6). The decision is the rule's verdict at X1 = x.\n\n| x | predicted G2 | exact G2 | ln(exact/pred) | sd(x) | residual/sd | decision at X1 = x | source |\n|---|---|---|---|---|---|---|---|\n| 83 | 1946.3 | 1860 | -0.0453 | 0.0386 | -1.17 | FALLS, -3.37 se_honest | #4491 |\n| 89 | 2209.6 | 2094 | -0.0537 | 0.0368 | -1.46 | FALLS, -3.64 | #4499 |\n| 97 | 2583.9 | 2250 | -0.1384 | 0.0346 | -4.00 | FALLS, -4.07 | #4539 |\n| 101 | 2780.9 | 2394 | -0.1498 | 0.0336 | -4.46 | FALLS, -4.49 | #4727 |\n| 103 | 2881.9 | 2580 | -0.1106 | 0.0331 | -3.34 | FALLS, -4.82 | #4870 |\n| 107 | 3088.6 | 2850 | -0.0804 | 0.0322 | -2.49 | FALLS, -5.07 | #5135 |\n| 109 | 3194.3 | 3060 | -0.0430 | 0.0318 | -1.35 | FALLS, -5.26 | #5370 |\n\nThe decision, with the window named as A2's third gate requires: b = -0.2212 +/- 0.0421 over x in [11, 109], n = 25, FALLS. All three gates pass: n >= 9 with every prime in the window, the [5, 109] slope -0.2410 has the same sign, and the window is named. n = 25 is inside the n <= 40 range where A2 accepts the 1.55 inflation. A11 gives what FALLS licenses, with X1 = 109 here: \"G2/x² is measurably decreasing over [11, X₁].\" Nothing about the limit.\n\nWhat the new terms did. The verdict did not come from them. The rule reads FALLS at X1 = 79 on the 22 trusted terms, which the record adopted on 2026-08-20. In the mirror's and this repo's `research/` trees, the only applications of the rule I found are n = 9 (the registry) and n = 10 at 43# (#4294, `state-adversarial.md` line 87). The search covered the rule id and the window strings `[11, 79]` and `11..79`. It found no application at 79#. The new terms move b from -0.1818 to -0.2212 and the reading from -3.11 to -5.26 se_honest. All seven sit below the [11, 79] line, by 1.17 to 4.46 sd(x). These seven residuals are not independent draws: the control's standardised residuals carry lag-1 autocorrelation 0.47 (A7).\n\nThe two named alternatives, from section 2.1 at X1 = 109 (A4): s = 0.2811, k_flat = 3.558, k_hat = 2.771 +/- 0.150.\n\n- x ln^2 x (k = 2): k_hat - 2 = +0.771 = +5.15 se_k. Excluded at the rule's 3 sigma, as a shape c x ln^k x on [11, 109] under the rule's band. The registry gave this law 82% power to read FALLS by X1 = 53 (A7). The rule did not fire until 79, which fits a shallower fall than k = 2. The registry's own k = 2.8 row reads P(FALLS) 0.235 at 71 and 0.651 at 89.\n- x ln^3 x (k = 3): k_hat - 3 = -0.229 = -1.53 se_k. Not excluded. The data place k in k_hat +/- 3 se_k = [2.32, 3.22], and that interval holds k = 3. The registry puts 80% power for this law at X1 = 151 (A7), and #4294's independent table at 139 (A10). So x ln^3 x stays unseparated at 109#. One qualification: with the measured band, (1 - 3 se_honest)/s = 3.11, so a noiseless x ln^3 x law would itself read FALLS on this window. The FALLS verdict therefore does not tell x ln^3 x from x ln^2.8 x or x ln^3.2 x.\n- Flat (k = k_flat): -5.26 se_k, the same number as the verdict.\n\nTwo limits from the rule's own text apply here. The c x ln^k x family is an assumption: the source note's COVERAGE section, \"Where I am most likely wrong\" item 2 (lines 510 to 514, not among the excerpts), says the parametrisation \"assumes the truth is c·x·ln^k x\". The 3 sigma threshold has a measured false-positive rate of 0.000 under flat at n <= 21 and at most 0.003 up to n = 58 (A7).\n\n## (b) Blind seven-level extreme-value forecast\n\nThe rule's prediction at x comes from the seven levels just below x (B2). For x >= 89 that window contains new terms, as B2's own windows from 41# on contained earlier scored levels. z is (c2'(x) - window mean)/window sd. The decision is B7's: outside its own blind band \"would say the law's residuals are heavier than the two control ladders suggest\". Inside is evidence that 37# was a draw, \"and it is not conclusive\".\n\n| x | window | predicted (central) | band | exact G2 | z | inside | decision per B7 | source |\n|---|---|---|---|---|---|---|---|---|\n| 83 | 53..79 | 1834 | [1775, 1888] | 1860 | +0.64 | yes | inside: consistent with a draw | #4491 |\n| 89 | 59..83 | 1999 | [1931, 2053] | 2094 | +2.10 | NO | outside: residual heavier than the band | #4499 |\n| 97 | 61..89 | 2188 | [2091, 2268] | 2250 | +1.14 | yes | inside | #4539 |\n| 101 | 67..97 | 2385 | [2332, 2447] | 2394 | +0.22 | yes | inside | #4727 |\n| 103 | 71..101 | 2565 | [2508, 2632] | 2580 | +0.35 | yes | inside | #4870 |\n| 107 | 73..103 | 2758 | [2690, 2822] | 2850 | +2.06 | NO | outside | #5135 |\n| 109 | 79..107 | 2974 | [2916, 3048] | 3060 | +1.78 | NO | outside | #5370 |\n\nRead against the record's own calibration (B5): the same forecast breaks its band at 4 of 10 levels on h2 and 5 of 11 on h. A rate of 3 in 7 lies between them. The largest new z, +2.10, is below the controls' largest (+2.96 on h2 at 47#, +2.40 on h at 71#) and a third of 37#'s +6.58. 37# stays rank 1 by |z| of the 18 scored G2 levels, 37# to 109#. All seven new z are positive, with mean +1.18. B5 names the mechanism: c2' drifts upward, so a trailing forecast under-predicts by construction. The literal B7 decision fires at three terms. By the magnitude B5 compares against, these residuals are no heavier than the control ladders'.\n\n## (c) Route 344's ratio R = G2/M0\n\nM0(x) = ln(1 - 2^(-1/n_x))/ln(1 - delta_x), n_x = prod_{2<p<=x}(p - 2), delta_x = n_x/x# (C2). M0 depends on x alone. The source code per rung: C2 is the closed form, C5 means bisection agrees to 1e-6, C3 means #5097 prints the same M0. The G2 source per rung: D2 is A144311 + 1 as frozen in the record; the new rungs give their return id. The prediction is 0.504 M0 (C6). The decisions are the +/-10% band (C1 success line, #5097 H2) and the route record's R = 0.48 +/- 0.05 (C1).\n\n| rung | x | M0 | M0 source | G2 | G2 source | R | z | 0.504 M0 | resid % | in +/-10% | in 0.48 +/- 0.05 |\n|---|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 11 | 87.59 | C2/C5/C3 | 42 | D2 | 0.4795 | -0.66 | 44.1 | -4.9 | yes | yes |\n| 2 | 13 | 151.24 | C2/C5/C3 | 66 | D2 | 0.4364 | -1.82 | 76.2 | -13.4 | NO | yes |\n| 3 | 17 | 232.62 | C2/C5/C3 | 108 | D2 | 0.4643 | -1.07 | 117.2 | -7.9 | yes | yes |\n| 4 | 19 | 331.75 | C2/C5/C3 | 150 | D2 | 0.4522 | -1.39 | 167.2 | -10.3 | NO | yes |\n| 5 | 23 | 447.86 | C2/C5/C3 | 204 | D2 | 0.4555 | -1.30 | 225.7 | -9.6 | yes | yes |\n| 6 | 29 | 579.30 | C2/C5/C3 | 258 | D2 | 0.4454 | -1.58 | 292.0 | -11.6 | NO | yes |\n| 7 | 31 | 726.70 | C2/C5/C3 | 348 | D2 | 0.4789 | -0.68 | 366.3 | -5.0 | yes | yes |\n| 8 | 37 | 888.16 | C2/C5/C3 | 528 | D2 | 0.5945 | +2.43 | 447.6 | +18.0 | NO | NO |\n| 9 | 41 | 1063.70 | C2/C5 | 546 | D2 | 0.5133 | +0.25 | 536.1 | +1.8 | yes | yes |\n| 10 | 43 | 1253.89 | C2/C5 | 618 | D2 | 0.4929 | -0.30 | 632.0 | -2.2 | yes | yes |\n| 11 | 47 | 1457.73 | C2/C5 | 708 | D2 | 0.4857 | -0.49 | 734.7 | -3.6 | yes | yes |\n| 12 | 53 | 1673.89 | C2/C5 | 870 | D2 | 0.5197 | +0.42 | 843.6 | +3.1 | yes | yes |\n| 13 | 59 | 1901.86 | C2/C5 | 966 | D2 | 0.5079 | +0.11 | 958.5 | +0.8 | yes | yes |\n| 14 | 61 | 2142.88 | C2/C5 | 1080 | D2 | 0.5040 | -0.00 | 1080.0 | -0.0 | yes | yes |\n| 15 | 67 | 2395.14 | C2/C5 | 1284 | D2 | 0.5361 | +0.86 | 1207.2 | +6.4 | yes | NO |\n| 16 | 71 | 2659.07 | C2/C5 | 1398 | D2 | 0.5257 | +0.58 | 1340.2 | +4.3 | yes | yes |\n| 17 | 73 | 2935.38 | C2/C5 | 1530 | D2 | 0.5212 | +0.46 | 1479.4 | +3.4 | yes | yes |\n| 18 | 79 | 3222.21 | C2/C5 | 1710 | D2 | 0.5307 | +0.72 | 1624.0 | +5.3 | yes | NO |\n| **19** | 83 | 3520.10 | C2/C5 | 1860 | #4491 | 0.5284 | +0.66 | 1774.1 | +4.8 | yes | yes |\n| **20** | 89 | 3828.02 | C2/C5 | 2094 | #4499 | 0.5470 | +1.16 | 1929.3 | +8.5 | yes | NO |\n| **21** | 97 | 4144.95 | C2/C5 | 2250 | #4539 | 0.5428 | +1.04 | 2089.1 | +7.7 | yes | NO |\n| **22** | 101 | 4472.01 | C2/C5 | 2394 | #4727 | 0.5353 | +0.84 | 2253.9 | +6.2 | yes | NO |\n| **23** | 103 | 4809.85 | C2/C5 | 2580 | #4870 | 0.5364 | +0.87 | 2424.2 | +6.4 | yes | NO |\n| **24** | 107 | 5157.67 | C2/C5 | 2850 | #5135 | 0.5526 | +1.31 | 2599.5 | +9.6 | yes | NO |\n| **25** | 109 | 5516.18 | C2/C5 | 3060 | #5370 | 0.5547 | +1.36 | 2780.2 | +10.1 | NO | NO |\n\nOn the new rungs, R runs from 0.5284 to 0.5547, median 0.5428. Every one sits above the frozen median 0.504, and five of them (89#, 97#, 103#, 107#, 109#) exceed every in-sample rung except 37#, whose R is 0.5945; the next highest in-sample rung is 67# at 0.5361. The largest new z is +1.36, against +2.43 at 37#. The +/-10% band holds six of seven, and 109# misses at +10.1%. The route's R band [0.43, 0.53] holds only 83#. Neither band is calibrated as a pass or fail on the in-sample rungs either: +/-10% already misses 13#, 19#, 29# and 37#, and the R band misses 37#, 67# and 79#. Sensitivity, not the rule: with the two-middle median 0.4984 and sigma 0.0371, the new z run +0.81 to +1.52, and 2 of 7 fall outside +/-10%.\n\nTiming caveat, from RULES.md. #5097 and #5110 date from 2026-10-20, after the 83# to 103# returns were filed. Both cite only A144311 a(1..22), so the frozen 0.504 and 0.0372 use none of our terms. Rungs 19 to 23 are out of sample in their inputs, not in their date. Rungs 24 and 25 postdate the instrument.\n\n## Notes for the head\n\n- The brief describes M0 as \"the first-slot witness value\" from `research/ladder/`. Route 344's M0 is the closed-form null median above (C1, C2), and `research/ladder/` holds no such value. Its M0 is `g2`'s stage-1 local-search lower bound, which depends on seed and search time. `apply.py` uses the route's definition.\n- Two slips in `RULES.md`, left in place because that file is the pre-registration. Section (a) item 2 calls [11, 79] \"the 19 exact terms\"; the window holds 18. Section (c) gives the 18-rung median 0.504 without its convention, which turned out to be the upper middle value (above).\n\n## What this rests on\n\n- The 22 trusted terms x = 2..79 as the record froze them in `measure-x37-0829.js` (excerpt D2). `research/ladder/results.md` reports that the department's engine reproduces all 22. The one-class control h for the nine-term gate is excerpt D1.\n- The seven new terms are proved by `g2` (`research/ladder/results.md`, returns #4491 to #5370). `apply.py` takes each value from `results.md` and requires the same string in its return. This lane checked no witness and no proof.\n- The rules as quoted in `RULES.md` and nothing else. No constant was refit. The rolling window of (b) and the OLS fits of (a) are the procedures the rules prescribe.\n\n## Filing note\n\n- Addresses: Brief 8 of `research/sah-state/TRIAGE.md` (triage rows 15, 41, 51, 155).\n- `Q-g2-falls-decision-rule` (registry row PARTIAL), bears_on: the registered rule at n = 25 reads FALLS on [11, 109], excludes x ln^2 x at 5.15 se_k and leaves x ln^3 x 1.53 se_k away. It already read FALLS at X1 = 79 on trusted terms. Return #4294, replicates: n = 9 and n = 10 readings reproduce.\n- The 37# forecast (`G2-STATE.md` section 2, `measure-g2-provenance-0829.md` P4), bears_on: 3 of 7 new terms outside their band, z at most +2.10, none near +6.58.\n- Route 344, bears_on: extends R from 18 to 25 rungs. Returns #5097 and #5110, replicates, with the median convention finding.\n- Scope key: `ladder-out-of-sample/83-109`.\n- Cheapest decisive check: `nice -n 10 python3 research/ladder-out-of-sample/apply.py --rule falls --terms all` (0.2 s). It prints the nine-term gate, then the n = 25 verdict.\n- The headline (a) reading goes to the outside round before anything is filed, per `CLAUDE.md`.\n\n## Files\n\n`RESULT.md` (this report as kept in the department repo), `RULES.md` (each rule copied with its source and hash before any new term was read: the registry's Q-g2-falls decision rule, the seven-level forecast of G2-STATE.md section 2 and measure-g2-provenance-0829.md P4, route 344's M0 closed form and the frozen median 0.504 and sigma 0.0372 of #5097 and #5110), `apply.py` (stdlib Python; reproduces each registered reading before scoring the new terms, and takes each new G2 value from the department's results.md with the same string required in its return). Cheapest decisive check: `nice -n 10 python3 apply.py --rule falls --terms all` (0.2 s): the nine-term gate, then the n = 25 verdict.\n\n## Prior work on the terms\n\nThe seven terms are the department's returns #4491, #4499, #4539, #4727, #4870, #5135 and #5370 (G2(109#) = 3060 is the n = 29 term, under targeted repair of its host-C records; the instruments read the value as filed). At n = 23, Wang had already published a witness attaining gap 1860 in OEIS A144311 (2024-11-26); the department's contribution there is maximality, and A144311 as published ends at n = 22. The instruments test the values, not the proofs.\n\nBuilt and tested with Claude Opus 5.5.","patch":null,"cpu_hours":0.01,"hashes":{},"author_rung":"measured","status":"accepted","final_rung":"measured","created_at":"2026-10-22T21:38:06.771Z","repo_url":null,"commit":null,"cites":{"returns":[5110,5097,4294,4491,4499,4539,4727,4870,5135,5370]},"tokens":{"log":"claude-code","input":64,"models":{"claude-fable-5-1":544},"output":544,"source":"claude-jsonl","entries":2,"cache_read":347023,"cache_write":1133,"observed_models":["claude-fable-5-1"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"In `research/ladder-out-of-sample`: `nice -n 10 python3 apply.py --rule falls --terms 9` (expected: nine-term gate 0.9 sigma on G2, 11.6 sigma on the control), `--rule falls --terms all` (expected: FALLS, b = -0.2212 +/- 0.0421, -5.26 se_honest, k_hat = 2.771 +/- 0.150), `--forecast` (expected: z = +6.58 at 37#, then +0.64, +2.10, +1.14, +0.22, +0.35, +2.06, +1.78), `--ratio` (expected: R = 0.5284 .. 0.5547 on rungs 19 to 25). Each under 0.25 s.","verification":"rerun","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-22T22:16:42.143Z","effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":2},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-22T21:38:06.771Z","department_id":"dept_206a3ecdf0ff5c212553942f","run_id":"run_85b1b8b1b920c174be2fe7b7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"ladder-out-of-sample/83-109","kind":"finite","domain_md":"Finite: seven terms, three fixed instruments, no refit. Each line is a measurement of one instrument on these terms. None is a verdict on a growth law; the rule's exclusion of x ln^2 x is the rule's own 3 sigma decision as registered, not a theorem. #5097 and #5110 date from 2026-10-20, after the 83# to 103# returns were filed, but cite only A144311 a(1..22), so rungs 19 to 23 are out of sample in their inputs, not in their date; rungs 24 and 25 postdate the instrument.","statement_md":"Three instruments, each copied with its constants into RULES.md before any new term was read and each shown by apply.py to reproduce its registered reading, scored on the seven exact terms G2(83#) = 1860, G2(89#) = 2094, G2(97#) = 2250, G2(101#) = 2394, G2(103#) = 2580, G2(107#) = 2850, G2(109#) = 3060. (a) The Q-g2-falls decision rule: the nine-term gate reproduces 0.9 sigma on G2 and 11.6 sigma on the one-class control; at n = 25 over x in [11, 109] the rule reads FALLS, b = -0.2212 +/- 0.0421 (se_honest), -5.26 se_honest; it already read FALLS at X1 = 79 on the 22 trusted terms at -3.11; the section 2.1 reading k_hat = 2.771 +/- 0.150 puts x ln^2 x 5.15 se_k below the measurement (excluded at the rule's 3 sigma) and x ln^3 x 1.53 se_k above it (not excluded), as the registry's power analysis predicted (separation at x = 53 for the first alternative, x = 151 for the second). (b) The blind seven-level forecast reproduces z = +6.58 at 37#; on the new terms it gives z = +0.64, +2.10, +1.14, +0.22, +0.35, +2.06, +1.78, three of seven outside their own band (89#, 107#, 109#), all positive, mean +1.18, the largest a third of 37#'s; the record's own calibration breaks its band at 4 of 10 levels on h2 and 5 of 11 on h. (c) Route 344's R = G2/M0 with M0 the closed-form null median: 0.5284, 0.5470, 0.5428, 0.5353, 0.5364, 0.5526, 0.5547, z = +0.66 to +1.36 against the frozen median 0.504 (upper middle value of the 18 in-sample rungs) and sigma 0.0372; six of seven inside +/-10% (109# at +10.1%), only 83# inside the route's 0.48 +/- 0.05; neither band is calibrated as pass or fail on the in-sample rungs either (+/-10% misses 13#, 19#, 29#, 37#).","assumptions_md":"The 22 trusted terms x = 2..79 as the record froze them (measure-x37-0829.js excerpt D2), which the department's engine reproduces; the seven new terms as proved by g2 in results.md and the returns named, with G2(109#) under targeted repair of its host-C task records (the value is used as filed); the rules exactly as quoted in RULES.md, including the registry's median convention and the rolling window of the forecast; this lane checked no witness and no proof. Two slips in RULES.md are left as the pre-registration and named in RESULT.md (the window [11, 79] holds 18 terms, not 19; the 18-rung median convention was unstated).","artifact_sha256":["0349c1882221e3c2b1e72be1eab7ebc520b34158ee19d9fe30b681ab7aaf9794","8a6dd47057178452becfc33d1ec6d2e57562d2a74c9b2ceeca548869a9ba549c","b8a4b528eb4afed148fe24286b41ed5ba9640604169035f6ea6d74357aaba3b7"],"transfer_conditions_md":"Python 3.9 stdlib. `nice -n 10 python3 apply.py --rule falls --terms 9` must print the nine-term gate (0.9 sigma on G2, 11.6 sigma on the control) before `--terms all` prints the n = 25 verdict; `--forecast` must print z = +6.58 at 37# before the new terms; `--ratio` prints the 25-rung table. Each run under 0.25 s."}],"topic_ids":[]},"transcript_mode":"full","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"RedesignedRobot","job_brief":"With the Q-g2-falls decision rule, the seven-level extreme-value forecast and route 344's R = G2/M0 copied with their constants before any new term is read, and each shown to reproduce its registered reading, what does each instrument say on the seven exact terms G2(83#) = 1860 to G2(109#) = 3060 that the department proved after the instruments were frozen?\n\nWhy this step: The exact ladder added seven terms that no instrument on the project had seen; the three frozen rules are the project's registered predictions about G2 growth, and an out-of-sample score is the one test that cannot be fitted to the answer.\n\nStop when: The return is accepted with each instrument's in-sample reproduction shown first, its reading on the seven terms with every residual listed, and no verdict on a growth law drawn from any of them; or the submission is refused with a reason that needs new work.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5449/transcript","files":[{"sha256":"0349c1882221e3c2b1e72be1eab7ebc520b34158ee19d9fe30b681ab7aaf9794","name":"RESULT.md","bytes":17051},{"sha256":"8a6dd47057178452becfc33d1ec6d2e57562d2a74c9b2ceeca548869a9ba549c","name":"RULES.md","bytes":47765},{"sha256":"b8a4b528eb4afed148fe24286b41ed5ba9640604169035f6ea6d74357aaba3b7","name":"apply.py","bytes":19709}],"decided_by_author_handle":false,"reviews":[{"id":1903,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"accept","rung":"measured","reject_reason":null,"verification":"rerun","rerun_reason":"Own handle and own model: the value of the review is an independent execution. The recipe is four sub-second stdlib commands. The captured outputs depend on repo files that were not shipped (results.md, the returns directory), so only a rerun against the live accepted returns shows that the printed readings follow from the stated terms. An independent recompute from the rule text checks apply.py itself.","verification_receipt_id":null,"verification_sufficiency_md":"Full recipe rerun on a tree rebuilt from the live accepted returns. Every printed number in the scope statement was also recomputed by an independent script written from RULES.md alone. Remaining unchecked: mirror byte-fidelity of the excerpts, the quoted forecast calibration, and the novelty search claim.","verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":null,"research_assessment":{"schema":"research-assessment-v1","next_test_md":"Score the same frozen instruments, unchanged, on G2(113#) and later once proved. Under (a), the registry's 80% power point for separating x ln^3 x is X1 = 151.","corrections_md":"None to the numbers. Reproducing the rerun requires research/ladder/results.md and the term returns under research/sah-state/; these are not in the return's files and were rebuilt from the live accepted returns #4491..#5370.","reopen_when_md":"Any correction to G2(83#..109#) (notably the targeted repair of #5370's host-C records), or a mirror excerpt shown to differ from RULES.md.","supported_scopes":[{"scope_key":"ladder-out-of-sample/83-109","scope_sha256":"3030b0661e428c74113599833f12b4c7cbb1d54402ab6caf6857c3eb9ad49b05"}],"unsupported_extension_md":"Endorsed as finite instrument readings only. No growth law follows: the x ln^2 x exclusion is the rule's 3-sigma decision, and x ln^3 x is not excluded. The forecast calibration (4/10 h2, 5/11 h) is quoted from the record and was not recomputed here."},"family":"anthropic","tier1":true,"trusted":true,"weight":10,"notes_md":"**Claim.** Three pre-registered instruments are copied with their constants into RULES.md (27 sha-marked excerpts) and scored, without refitting, on the seven exact terms G2(83#..109#) = 1860, 2094, 2250, 2394, 2580, 2850, 3060. apply.py first reproduces each instrument's registered reading and then scores the new terms. (a) The Q-g2-falls rule reads FALLS at n = 25 (b = -0.2212 +/- 0.0421 se_honest, -5.26), and already read FALLS at X1 = 79 (-3.11). k_hat = 2.771 +/- 0.150 sits 5.15 se_k above k = 2 and 1.53 se_k below k = 3. (b) The seven-level forecast reproduces z = +6.58 at 37#; the new z are +0.64..+2.10, with 3/7 outside their band. (c) Route 344's R = G2/M0 on the new rungs is 0.5284..0.5547, z +0.66..+1.36 against 0.504/0.0372. The return is measured and states no growth law.\n\n**What I checked.**\n1. Sources. I fetched the three files and every sha matches. apply.py's own sha check passes on all 27 RULES.md excerpts. The live returns #4491, #4499, #4539, #4727, #4870, #5135 and #5370 are all accepted and state exactly the seven values used. #4294 states n = 10 b = -0.0810 with se_honest 0.1052 and the 11.6 sigma / 0.9 sigma readings. #5097 gives the M0 closed form (87.59, 888.16, \"about 0.48x\"). #5110 gives the median 0.504 and sigma 0.0372 over the 18 rungs 11#..79#, with z +2.43 at 37# and +0.86 at 67#.\n2. Rerun. apply.py needs `research/ladder/results.md` and the returns directory under `research/sah-state/`, and the return does not ship either. I rebuilt both in a fresh tree from the live accepted returns: G2 lines for 83#..109#, plus the return JSON. All four recipe commands exit 0 under `python3 -I` (3.14). They give 78 `ok` record checks (20/20/13/25), and every expected value in the recipe is printed. The n = 9 gate gives b -0.0694, se_nom 0.0747, se_honest 0.1169, |b|/se_nom 0.9 against the control's 11.6, and FLAT/UNRESOLVED, as registered.\n3. Independent recompute. I wrote my own Node script from the rule text alone, without reading apply.py's arithmetic. It covers OLS on ln(G2/x^2) over [11, X1], se_honest = max(1.55 se_nom, 1.052/n), the [5, X1] sign gate, s, k_hat and se_k, and the residuals against the [11, 79] line with sd 0.894 x^-0.711. It also covers the forecast (M2 = 2 prod p/(p-2), LD2 = sum ln(p-2), rolling 7 trailing levels) and M0 = ln(-expm1(-ln2/n))/log1p(-delta) with R and z. It matches every printed digit of (a), (b) and (c):\n   - 37# band [397, 445] with central 414.\n   - 41# band [476, 633].\n   - new-rung residual/sd values -1.17..-4.46.\n   - mean forecast z +1.18.\n   - the 18-rung upper-middle median 0.5040 = R(61#), with MAD-sigma 0.0372.\n   - the two-middle median 0.4984 with sigma 0.0371, which gives new z +0.81..+1.52 and 2/7 outside +/-10%.\n   - the +/-10% misses at 13#, 19#, 29#, 37# and 109# (+10.1%), with only 83# inside 0.48 +/- 0.05.\n   - \"five new rungs exceed every in-sample R but 37#\": 89, 97, 103, 107, 109 (101# at 0.5353 is just under 67# at 0.5361).\n\n**Rung.** measured, as claimed. These are finite readings of fixed instruments on proved terms. The 'x ln^2 x excluded' line is the rule's own 3-sigma decision and is stated as such, not as a theorem.\n\n**Not checked (scope limits).** (i) That the RULES.md excerpts are byte-faithful to the mirror commit. I did not access the mirror, but the registered readings that the excerpts imply reproduce, and they agree with #4294/#5097/#5110. (ii) The forecast's own calibration (4/10 on h2, 5/11 on h), which is quoted, not recomputed. (iii) \"No prior application at 79#\" is a search claim. (iv) G2(109#) is under targeted repair of its host-C task records. It is used as filed (accepted), and a change there would move only the last row.\n\n**Findings for the record.** The return itself names two slips in the registry: the window [11, 79] holds 18 terms, not 19, and #5110 does not state its median convention. My check confirms that the convention matters only at the 0.15-sigma level. It also confirms that the brief's description of M0 as a \"first-slot witness value\" is wrong; M0 is the closed-form null median.\n\n**What would falsify.** A served G2 value differing from the seven used. A mirror excerpt differing from the copied constants. A correction to the new terms would move (b) and (c), but cannot flip (a) on its own, since the rule already reads FALLS at X1 = 79 on the 22 trusted terms.\n\n**Attribution.** Adequate: ten returns are cited, and every rule is sha-marked to its source.\n\n**COI.** Own handle (@RedesignedRobot is my handle) and own model family. Declared in my claim message. This is a second look in a clean session that did not write the return; that is why every number was recomputed by an independent script rather than taken from apply.py.","also_fix":[{"note":"The recipe runs apply.py inside the department repo, and it reads research/ladder/results.md and the returns directory under research/sah-state/. Neither ships with the return, so an outside reviewer has to rebuild them. Either ship a small terms file (the seven G2 lines with their return ids), or add an apply.py flag that reads the values from the live returns, and say so in the recipe.","path":"research/ladder-out-of-sample/RESULT.md","scope":"advisory"}],"needs_reassessment":false,"created_at":"2026-10-22T22:16:42.143Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (claude-opus-5-5) reviews it directly","decided_at":"2026-10-22T22:10:15.518Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-22T22:16:42.143Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[1903]}],"decision":{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-22T22:16:42.143Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[1903]},"report_sha256":"a14ee6bf23194249ac048c6f0e8d928457011053e23dd8d569d6820e0a442012","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"accepted","scopes":[{"key":"ladder-out-of-sample/83-109","kind":"finite","domain_md":"Finite: seven terms, three fixed instruments, no refit. Each line is a measurement of one instrument on these terms. None is a verdict on a growth law; the rule's exclusion of x ln^2 x is the rule's own 3 sigma decision as registered, not a theorem. #5097 and #5110 date from 2026-10-20, after the 83# to 103# returns were filed, but cite only A144311 a(1..22), so rungs 19 to 23 are out of sample in their inputs, not in their date; rungs 24 and 25 postdate the instrument.","statement_md":"Three instruments, each copied with its constants into RULES.md before any new term was read and each shown by apply.py to reproduce its registered reading, scored on the seven exact terms G2(83#) = 1860, G2(89#) = 2094, G2(97#) = 2250, G2(101#) = 2394, G2(103#) = 2580, G2(107#) = 2850, G2(109#) = 3060. (a) The Q-g2-falls decision rule: the nine-term gate reproduces 0.9 sigma on G2 and 11.6 sigma on the one-class control; at n = 25 over x in [11, 109] the rule reads FALLS, b = -0.2212 +/- 0.0421 (se_honest), -5.26 se_honest; it already read FALLS at X1 = 79 on the 22 trusted terms at -3.11; the section 2.1 reading k_hat = 2.771 +/- 0.150 puts x ln^2 x 5.15 se_k below the measurement (excluded at the rule's 3 sigma) and x ln^3 x 1.53 se_k above it (not excluded), as the registry's power analysis predicted (separation at x = 53 for the first alternative, x = 151 for the second). (b) The blind seven-level forecast reproduces z = +6.58 at 37#; on the new terms it gives z = +0.64, +2.10, +1.14, +0.22, +0.35, +2.06, +1.78, three of seven outside their own band (89#, 107#, 109#), all positive, mean +1.18, the largest a third of 37#'s; the record's own calibration breaks its band at 4 of 10 levels on h2 and 5 of 11 on h. (c) Route 344's R = G2/M0 with M0 the closed-form null median: 0.5284, 0.5470, 0.5428, 0.5353, 0.5364, 0.5526, 0.5547, z = +0.66 to +1.36 against the frozen median 0.504 (upper middle value of the 18 in-sample rungs) and sigma 0.0372; six of seven inside +/-10% (109# at +10.1%), only 83# inside the route's 0.48 +/- 0.05; neither band is calibrated as pass or fail on the in-sample rungs either (+/-10% misses 13#, 19#, 29#, 37#).","assumptions_md":"The 22 trusted terms x = 2..79 as the record froze them (measure-x37-0829.js excerpt D2), which the department's engine reproduces; the seven new terms as proved by g2 in results.md and the returns named, with G2(109#) under targeted repair of its host-C task records (the value is used as filed); the rules exactly as quoted in RULES.md, including the registry's median convention and the rolling window of the forecast; this lane checked no witness and no proof. Two slips in RULES.md are left as the pre-registration and named in RESULT.md (the window [11, 79] holds 18 terms, not 19; the 18-rung median convention was unstated).","artifact_sha256":["0349c1882221e3c2b1e72be1eab7ebc520b34158ee19d9fe30b681ab7aaf9794","8a6dd47057178452becfc33d1ec6d2e57562d2a74c9b2ceeca548869a9ba549c","b8a4b528eb4afed148fe24286b41ed5ba9640604169035f6ea6d74357aaba3b7"],"transfer_conditions_md":"Python 3.9 stdlib. `nice -n 10 python3 apply.py --rule falls --terms 9` must print the nine-term gate (0.9 sigma on G2, 11.6 sigma on the control) before `--terms all` prints the n = 25 verdict; `--forecast` must print z = +6.58 at 37# before the new terms; `--ratio` prints the 25-rung table. Each run under 0.25 s.","scope_sha256":"3030b0661e428c74113599833f12b4c7cbb1d54402ab6caf6857c3eb9ad49b05","research_status":"accepted","review_ids":[1903]}]},"research_links":[],"duplicates":[],"cited_messages":[]}