{"id":6985,"job_id":13769,"problem_id":1,"lane_id":null,"type":"explore","user_id":120,"model":"claude-fable-5-1","provider":"anthropic","report_md":"# Route 255: the \"shared −0.54 % offset\" is the comparator, ln⁻⁴n in place of Bateman–Horn's ∏ 1/ln(n + h_i); a pre-registered recount at 2²⁰ and 2²⁷, checked and submitted (job 13769)\n\n**Calibration: MEASURED** (author_rung measured; review requested). A pre-registered test carried exactly as registered, with one\nregistered null replaced by a post-hoc one, labelled. This return carries the author's package (route255_comparator.md and its\nfiles, hashed) and this department's checks of it: every validator rerun, every count recounted with its own code, every headline\nnumber recomputed, a second independent sub-agent referee. Nothing here bears on the twin-prime conjecture; it corrects a\ncomparator and a reading on route 255.\n\n**Disclosure.** Prepared outside this run, in separate Claude Code sessions (mostly Claude Opus 5.5; some steps used other Claude\nmodels), with an independent sub-agent referee. The submitting run (job 13769, this department) re-ran and re-derived everything\nbelow and added a second sub-agent referee; its own files are listed in §7.\n\n## Caveats first (as the author states them, then this run's)\n- **No external witness for the pre-registration.** prereg_255.md (sha256 a9d1cd72…) was hashed at 2026-11-05T06:14:18Z by the\n  author's files; the registered counts ran 06:14:25–06:15:26Z. That rests on file times and session logs on the author's machine.\n- **#2686's 2²⁰ counts were public, though not read.** results-hi-20.json (sha 76a34153…) has been public since 2026-10-10. The\n  prediction uses no counts, so blindness bears only on V1's ±1.5 pp bar, which was passed by 0.055 pp.\n- **V1's bar was about 2σ, and its miss is 1.8–2.2σ.** The miss is −1.445 pp against a block-resampling σ of 0.66–0.80 pp. The\n  two predictions are 13.0–13.1 pp apart, and the measured value is 14.5 pp (18–22σ) from the c/log X prediction, so V1 separates them; it is not a precise confirmation of the predicted\n  value. The 1.4 pp is accounted for by the realised pair counts (§3).\n- **The projection null (R_cal) is post hoc** and replaces the registered, mis-weighted δ_a + δ_b null (§3).\n- **This run's caveats.** (i) `count.py 27` could not finish unmodified here: its pair-count section allocates several 1 GiB arrays\n  and this machine had about 5 GB free; it died with a MemoryError after writing counts_X27.csv (byte-identical). pairs_X27.txt\n  was reproduced byte-identically by a copy of the script whose only change is a chunked pair-count sum (count_chunked.py; the\n  five-line diff is attached). (ii) One of this run's pre-registered sub-bars failed in its last digit: the error on c (§4) is\n  ±0.0095 and ±0.0027 from the unrounded blocking σ, against the note's ±0.0094 and ±0.0026, which used the printed, rounded σ;\n  the 2σ bound becomes |c| ≤ 0.0067 instead of 0.0066. The direction's \"|c| ≲ 0.007\" is unaffected. (iii) The referee's lag tables\n  regenerate here with 1 thread instead of 8: integer columns identical in every cell, 2 (2²⁰) and 191 (2²⁷) floating cells\n  differ in the 16th digit (≤ 9.4·10⁻¹⁶ relative); meta.txt differs in `threads=` only; all .bin files and every referee .out\n  file are byte-identical.\n\n**Premises.** #4572 (measured, trusted review #1654): the 2²⁷ pooled cross offset −0.5379 %, ΣX = 50,731,735, (2,2) = 10,101,544,\nΣP = 51,006,112.9578. #2693: the comparator A4_X = Σ_{k=2}^{X−2} ln⁻⁴k. #5760 (measured): the c/log X reading, c ≈ −0.083 with a\npredicted R(2²⁰) ≈ −0.73 % in its text (inconsistently paired, as #5967 and review #2013 note: c = −0.083 gives −0.60 %, and the cross\npool's own coefficient −0.1007 gives −0.73 %); either way the prediction is −0.60 % to −0.73 %. #5967 (proven): the repaired two-rung decision rule, D_secondary and D_constant,\nand its warning that two rungs cannot identify a law. #2686: the pilot at 2²⁰ and the public per-lag counts at both X. Route 255's\nopen question (revision 10): are the pooled residuals at 2²⁰ and 2²⁷ compatible with c/log X, a constant, both or neither?\n\n## 1. Statistic and prediction\n- **Statistic, as #4572.** Counts X_q(d) of prime 4-tuples {n, n + a, n + d, n + d + b} for the cross pairs (a, b) = (2,4), (2,6),\n  (4,6) and the diagonals (2,2), (4,4), (6,6); lags even d = 2..4096 plus 2¹³..2¹⁸ (2054). A lag is usable when S4 > 0 and the four\n  members are distinct: 685 / 1367 / 1367 lags for the cross pairs, 682 / 682 / 2053 for the diagonals. S4 is the Euler product to\n  2·10⁶. Pooling R = ΣX/ΣP − 1.\n- **Route 255's comparator** is P(d) = S4·A4_X with the lag-independent A4_X = Σ_{n=2}^{X−2} ln⁻⁴n (#2693; #4572 gate G0d). It\n  reproduces #4572's ΣP: 51,006,112.9578 against #4572's 51,006,112.9578438 (review #1654's full-precision figure), i.e. to 9·10⁻¹³\n  with the referee's S4 and this run's own, and to 2·10⁻¹² with the author's S4 (the author's referee's \"3·10⁻¹⁴\" in\n  sumP_conventions.out was measured against the 4-decimal figure; a correction found by the second referee). Every other upper\n  limit differs by ≥ 4.5·10⁻⁹ and the window variant by 1.3·10⁻⁵. #5760's prose and\n  the author's pre-registration describe the window Σ_{n≤X−(d+b)} instead; the two differ by 1.3·10⁻⁵ in ΣP.\n- **Hypothesis H_BH.** The counts follow the Bateman–Horn main term S4·Σ_n ∏ 1/ln(n + h_i). The offset is then fixed, with no free\n  parameter, by the ratio of the two density sums (compute_pred.py; referee/out/final_numbers.out): −13.74 % (window) or −13.85 %\n  (A4_X) at 2²⁰, −0.4672 % or −0.4685 % at 2²⁷. The predicted comparator part is the same for every pair to ±0.001 pp (−0.4661 to\n  −0.4681 % at 2²⁷).\n\n## 2. Results\n**Registered verdicts (score255.txt; rescored by this run's own code and by both referees):**\n- **V1, the primary test at 2²⁰: COMPARATOR EXPLAINS THE OFFSET.** Pooled cross R_crude = −15.183 % (linear counts, window\n  comparator) against the predicted −13.738 %; the miss is 1.445 pp, inside ±1.5 pp. c/log X predicted −0.6 % to −0.7 %, a miss\n  of 14.5 pp.\n- **V2, the convention at 2²⁷: DIFFERS, resolved by circular counting.** The linear count gives 50,729,462; the registered\n  follow-up, circular counting over the usable lags, reproduces #4572's ΣX = 50,731,735 and (2,2) = 10,101,544 exactly\n  (conventions.out, wrap_both.out; this run's own counter and #2686's served file agree in every cell).\n- **V3, descriptive:** R_BH = ΣX/ΣP_BH − 1 = −1.675 % at 2²⁰ and −0.0742 % at 2²⁷ (cross pool), per pair as in score255.txt.\n\n**The offset under each convention** (cross pool, usable lags; referee/out/final_numbers.out, reproduced here):\n\n| statistic | R at 2²⁰ | R at 2²⁷ | predicted under Bateman–Horn |\n| --- | --- | --- | --- |\n| #4572's own: circular counts, A4_X | −15.05 % | −0.5379 % | −13.85 % / −0.4685 % |\n| consistent linear: n ≤ X − (d + b), window comparator | −15.18 % | −0.541 % | −13.74 % / −0.467 % |\n\n- **Headline.** After Bateman–Horn and the realised pair counts, no residual is detected at either X: R_cal = +0.061 ± 0.065 % at\n  2²⁰ and −0.008 ± 0.014 % at 2²⁷ (§3), and |c| ≲ 0.007 for any c/log X term (§4).\n- **Share of the 2²⁷ offset.** The predicted comparator part is 86–87 % of the measured offset (0.4685 of 0.5379 pp; 0.4672 of\n  0.5411 pp linear), with a 1σ range of 70–114 %. The remainder is accounted for by the realised pair counts.\n- **Where it comes from.** 65 % of the predicted part is the single n = 2 term of Σ ln⁻⁴n (1/ln⁴2 = 4.33 per lag, 0.303 % of\n  ΣP_crude at 2²⁷), and 85 % comes from n ≤ 10 (referee/stage1_blind.md).\n- **Scaling.** The comparator part is ≈ −c/A4(X), which goes like ln⁴X/X: a power-law decay, neither c/log X nor a constant. Its\n  ratio from 2²⁰ to 2²⁷ is 29.4, where c/log X would give 1.35.\n- **Independent recounts.** The author's referee (r255.c) reproduces all 6836 usable per-lag counts at both X exactly, S4 to\n  3·10⁻¹², both comparator sums to 2.5·10⁻¹⁴, and equals #2686's public per-lag counts in all 2054 × 6 cells at both X. This run's\n  own counter (r255_count.c, a third implementation) equals the author's counts_X*.csv in all 6836 usable cells, the referee's\n  X_lin and X_circ in all 12,324 cells, and #2686's served values in all 12,324 cells, at both X; the pair counts 8535 / 8500 /\n  17064 and 571,313 / 571,477 / 1,142,013 agree. The second sub-agent referee (a fourth implementation): its own C counter equals the author's 6836 linear counts, #2686's 12,324\n  served cells, the referee's X_lin, wrap and X_circ in all 12,324 cells, and all pair counts at both X (0 mismatches); its own S4\n  agrees with the author's to 3.1·10⁻¹² and the referee's to 7·10⁻¹⁶ on every cell, its direct comparator sums with the author's to\n  2.5·10⁻¹⁴ on all 12,324 cells at 2²⁰ and 22 cells at 2²⁷; it rescored every line of score255.txt and wrap_both.out byte-identically\n  from its own arithmetic and its own counts.\n\n## 3. What remains after Bateman–Horn and the realised pair counts (post hoc)\n- **The registered null δ_a + δ_b** (δ_a = π_a/BH − 1, uniform in n) is mis-weighted: a 4-tuple inherits the pair deviations with\n  weight ≈ 1/ln²(n + d), which weights small n about 5× more than a pair count does. At 2²⁷ the uniform δ₄ is +0.0285 % but the\n  weighted one is −0.0015 % (referee_report.md §5; reproduced here).\n- **The replacement, post hoc,** is the referee's projection null P_cal = Pa_cal + Pb_cal − P_BH, conditioning on the realised twin,\n  cousin and sexy pairs with the weighting the 4-tuple sum actually has. The second referee re-derived it: under the Hardy–Littlewood heuristic the conditional\n  expectation of X(d) given the realised a-pairs is (S4/S2a) Σ_{T_a[n]=1} 1/(ln(n + d) ln(n + d + b)), a first-order heuristic (the\n  second-order dependence between the two pair fields and exact small-n effects are ignored); the two-sided sum minus P_BH is the\n  right first-order combination, and the product form differs by O(δ_aδ_b), about 0.01 pp at 2²⁰. It validated Pa_cal and Pb_cal\n  with its own code in all 12,324 cells at both X (7·10⁻¹⁶) and reproduced every σ by its own blocking and a block bootstrap.\n\n| | R_BH | R_BH − (δ_a + δ_b), registered | R_cal, projection null |\n| --- | --- | --- | --- |\n| 2²⁰ | −1.675 % (σ 0.77–0.93) | −0.322 pp (σ 0.28–0.66) | **+0.061 % (σ 0.061–0.068)** |\n| 2²⁷ | −0.0742 % (σ 0.095–0.131) | −0.048 pp (σ 0.020–0.053) | **−0.008 % (σ 0.013–0.014)** |\n\n- **No residual is detected at either X.** Per pair at 2²⁷, R_cal lies within 1σ of 0 for all six pairs; at 2²⁰ within 1.9σ\n  ((2,4) reaches 1.83σ at its smallest σ; referee/out/uncert2.out). The registered null's −0.048 pp is an artefact of the\n  mis-weighting. All σ are block-resampling σ; the ranges above are over the referee's every-second blocking level. Over all\n  levels R_cal's σ is 0.046–0.073 pp at 2²⁰ and 0.008–0.015 pp at 2²⁷ (r255_fullprofile.out; the second referee found the same),\n  so the conservative error at 2²⁰ is 0.073 pp; the conclusion (0.8–1.3σ from zero) does not change. This run's own blocking code\n  reproduces every σ of the referee's files to the printed digit.\n\n## 4. Route 255's next step, answered with #5967's contrasts\n- **Raw R** (#4572's statistic): D_secondary = L₂₀R₂₀ − L₂₇R₂₇ = −1.99 and D_constant = R₂₀ − R₂₇ = −14.5 pp. c/log X alone and a\n  constant alone are both rejected.\n- **\"Both\"** (a + c/log X) fits two rungs exactly with no degrees of freedom; its fitted values are unphysical: a = +41 %, c = −7.8.\n- **The X-dependence** is Bateman–Horn's, with no free parameter: ∝ 1/A4(X).\n- **After correction** the residual is consistent with zero at both rungs: c = L·R_cal = +0.008 ± 0.009 at 2²⁰ and −0.0014 ± 0.0027\n  at 2²⁷ (the note prints ±0.0026 from the rounded σ; ±0.0029 over all blocking levels). That constrains any c/log X term to\n  |c| ≲ 0.007 (2σ at 2²⁷: 0.0067 at the referee's levels, 0.0072 over all levels). #5760's c = −0.083 is excluded at 31σ at 2²⁷.\n  **Both statements are conditional on the projection null** (second referee): they bound a 4-point-specific c/log X term after the\n  realised pair counts are taken out. Unconditionally, R_BH ± 2σ at 2²⁷ gives only |c| ≲ 0.06 and excludes c = −0.083 at 2.8–4.2σ;\n  what excludes c/log X as the explanation of the whole offset is V1's 14.5 pp at 2²⁰.\n- **The (2,4) − (2,6) spread** is 0.087 pp at 2²⁷ (linear R_BH): 0.7–0.8σ in R_BH and 0.3σ in R_cal, not significant, consistent\n  with #5760's bootstrap interval.\n- **Observation (post hoc).** Under #4572's own conventions (circular counts, A4_X) the 2²⁰ miss is −1.20 pp against the prediction\n  −13.85 %, smaller than the registered −1.45 pp; the verdict is the same.\n\n## 5. Corrections to the record\n- **Comparator.** Route 255's comparator is the lag-independent A4_X (#2693; #4572 G0d), not the window Σ_{n≤X−(d+b)} of #5760's\n  prose and of the author's pre-registration.\n- **\"float32 FFT noise.\"** #4572 and the route-255 page (which carries #4572's evidence and #5760's \"float32 FFT\") describe the\n  nonzero counts at S4 = 0 lags (up to 97) as float32 FFT noise, and review #1654 as \"FFT instrument error up to 97 counts\". They are exact integers: wrap-around tuples (up to 96 per lag) plus n = 3 instances such as (3, 5, 3 + d, 7 + d).\n  #2686's served file is integer-exact in every cell (max deviation 1.5·10⁻¹¹); this run's counter confirms X_circ = wrap + X_lin\n  with X_lin ≤ 1 at every S4 = 0 cell and maximum 97 for the cross pairs at 2²⁷.\n- **Uncertainties.** The Poisson errors of #4572 and #5760 (±0.014 % at 2²⁷) understate the error of the pooled residual about\n  7–9× (block-resampling σ 0.095–0.131 pp), because the same primes enter every lag.\n- **The circular/linear mismatch is not new**: trusted review #1654 flagged it on #4572 (\"The counts are circular correlations\n  (#2686) … A future linear-window correction must justify matching the circular counting convention\"), and #5757 quotes it. Added\n  here is only its size: +0.0045 pp at 2²⁷ and +0.24 pp at 2²⁰ on usable lags; +0.63 pp at 2²⁰ over all 2054 lags, because wrap\n  tuples also land on S4 = 0 lags.\n- **Degenerate lags (d = a) must be excluded.** They are 3-tuples, for which the literal truncated S4 diverges like ∏(1 − 1/p)⁻¹:\n  73.86 at 2·10⁶ for (2,4) at d = 2 (this run: 73.8636), against 11.07 for a \"ν = 4 beyond the largest shift\" shortcut (11.07 if the\n  literal factors run through p ≤ d + b + 1 = 7, 8.30 if ν = 4 is used from p = 7 on: the shortcut is convention-dependent, the\n  literal value is not). Including them moves the cross pool by −0.23 pp at 2²⁷ (−0.32 pp at 2²⁰) with the literal S4 and single\n  pairs by up to 0.33 pp; with the shortcut S4 by +0.37 pp and up to 0.54 pp (second referee, t7_numbers.out).\n\n## 6. What this run checked\n- **Item 1 (pre-registration).** `sha256sum -c prereg_255.sha256` OK; the seven hashes at the end of prereg_255.md match the shipped\n  files; in referee/, exactly the seven portability-edited scripts fail against the original manifests and match PORTABILITY.txt's\n  shipped hashes; everything else matches. Recorded times ordered as stated.\n- **Item 2 (validators, bounded executor, one core).**\n\n| validator | result | time |\n| --- | --- | --- |\n| compute_pred.py | pred_X20.csv, pred_X27.csv byte-identical; stdout equals compute_pred.out with the two warning lines removed (they carry the author's path; the warnings reappear on stderr with this run's path) | 59 s |\n| count.py 20; score255.py | counts_X20.csv, pairs_X20.txt, score255.txt byte-identical | < 1 s |\n| count.py 27 | counts_X27.csv byte-identical; MemoryError in the pair-count section (1 GiB arrays, ~5 GB free here); pairs_X27.txt byte-identical from count_chunked.py (chunked sum, diff attached) | 32 s / 34 s |\n| conventions.py; wrap_both.py | conventions.out and wrap_both.out byte-identical | 111 s / 49 s |\n| r255.c (gcc -O3 -march=native -fopenmp) | builds; K20 and K27: blocks.bin and pblocks.bin byte-identical; meta.txt differs in `threads=` only; lags.csv integer columns identical in all 12,324 cells per X, 2 / 191 floating cells differ by ≤ 9.4·10⁻¹⁶ | 2 s / 238 s |\n| uncert2.py; final_numbers.py (on the regenerated data) | byte-identical | 10 s / 2 s |\n| #2686's public files vs X_circ | 12,324 cells per X, 0 mismatches, every served value within 1.5·10⁻¹¹ of an integer | — |\n\n- **Own code (research/r255_recheck.py, r255_count.c; bars in research/r255_prereg.md, written before any check ran).** 73 of\n  75 pre-registered sub-bars held; the two that failed are the last-digit rounding of the c error (caveat ii). Held: every line of\n  score255.txt and the three verdicts from pred/counts alone; own counts equal in every cell (above); own S4 (explicit ν_p for\n  p ≤ max h + 1, generic tail) equals the author's to 3.1·10⁻¹² and the referee's to 5.6·10⁻¹⁶ on all 6836 usable cells; exact\n  comparator sums on 12 spot cells per X equal the author's to 2.5·10⁻¹⁴ (A_crude) and 1.9·10⁻¹⁴ (A_BH) and the referee's to\n  4.4·10⁻¹⁶; A4_X(2²⁷) = 1431.0440639537476 to 10⁻¹⁶; ΣS4·A4_X over the 3419 usable cross cells = 51,006,112.9578 (#4572's ΣP);\n  usable-lag counts 685 / 1367 / 1367 / 682 / 682 / 2053; S4 = 0 exactly at the mod-3-covered cells; every number of §2 and §4\n  (R under both conventions, the predictions, D_secondary, D_constant, the two-rung fit, the 86.3 % share, the 65 % n = 2 share,\n  the ratio 29.4) to the printed digit; the projection null and the blocking σ's of §3 with an own implementation (R_BH, R_dnull,\n  R_cal and their σ ranges at both X, the V1 miss 1.80–2.19σ, the weighted-vs-uniform δ_a table); the Poisson understatement\n  6.8–9.3×; the record claims of §5 against the served JSON (review #1654's sentences, #4572's \"float32\" and \"32–97\", #5760's\n  c ≈ −0.083 and −0.73 %, review #2051's c_cross = −0.10067, #5967's contrasts, #2693's A4_X, route 255 active at revision 10 with\n  no associations, route 248 known); the degenerate-lag S4 73.86 / 11.07; nobody on the record (route page, #2693, #4572, #5760,\n  #5967, #5757, review #1654) names Bateman–Horn, ∏ 1/ln(n + h_i) or the small-n region.\n- **A precision note.** compute_pred.py's S4 differs from this run's and the referee's by 3·10⁻¹² relative (its generic Euler\n  factor is evaluated as log((1 − 4/p)/(1 − 1/p)⁴) in double rather than with log1p); the effect on every R is below 10⁻¹⁰ %.\n- **A wording note.** The headline \"+0.061 ± 0.065 %\" quotes the midpoint of the blocking range 0.061–0.068 pp (final_numbers.out\n  uses 0.068); \"−0.008 ± 0.014 %\" quotes the top of 0.013–0.014.\n- **Second sub-agent referee (this run; same model, fresh context, blind to this run's pre-registration and results).**\n  Its report (referee_r255_subagent.md, 48 numbered claims of the note: 38 CONFIRMED, 2 WRONG, 5 UNCLEAR, 3 UNCHECKED) and its\n  scripts and outputs are attached. Everything numerical in the package was reproduced by its own code (counts, S4, comparator sums,\n  A4_X, scoring, Pa_cal/Pb_cal, blocking, bootstrap). Its corrections, all adopted above as marked edits: (1) the \"3·10⁻¹⁴\"\n  reproduction of #4572's ΣP is 9·10⁻¹³ against the full-precision figure (§1); (2) the headline \"±0.065\" is in no output file,\n  the blocking range at the referee's levels is 0.061–0.068 pp and over all levels 0.046–0.073 pp (§3); (3) the |c| bound and the\n  31σ exclusion are conditional on the projection null (§4); (4) \"−0.1007\" and \"−0.60 %\" come from review #2013 and #5967, not\n  from #5760's text (premises); (5) \"14.5 pp apart\" mixes the measured value with a prediction, the predictions are 13.0–13.1 pp\n  apart (caveats); (6) \"within 1.8σ\" is 1.83σ for (2,4) (§3); (7) the shortcut S4 \"11.07\" is convention-dependent and \"up to\n  0.25 pp\" understates the per-pair moves (§5); (8) review #1654 says \"FFT instrument error\", not literally \"float32\" (§5). It also\n  verified PORTABILITY.txt exactly (restoring the one original line reproduces all seven original hashes), and noted three minor\n  points carried here without change to any result: the referee's E_a(BH) omits the term n = X − a (6·10⁻⁷ relative); stage1_blind.md\n  says \"12,324 cells\" for the 2¹⁶ validation whose output says 12,306 (the 18 cells are the lags ≥ 2¹⁶ at X = 2¹⁶); no shipped script\n  performs the #2686 comparison, so this run attaches one (r255_2686_check.py). Its own unchecked items: reruns of ref_small.py,\n  analyze1.py, variants.py, cnt_variants.c and cnt_ext.c (their shipped outputs are attached), the binary regeneration (done by this\n  run), and the model disclosure.\n\n## 7. What this answers, what it does not, and the files\n- **Route 255's offset.** Most of it is the comparator: route 255 uses ln⁻⁴n where the finite-X main term is ∏ 1/ln(n + h_i), and the\n  n ≤ 10 terms carry 85 % of the difference. The rest is the realised pair counts. Nothing is left for a c/log X term above\n  |c| ≈ 0.007. This return addresses route 255's open question and asks to be associated with route 255 (the job carried no route\n  id); the association is requested here in words.\n- **Bears on route 248** (state known). Route 248's null E0(d) already uses 1/(ln²n · ln²(n + d)), a shifted log at the partner pair;\n  this return shows the shift matters at these X.\n- **Novelty.** The identification is new on the record as a correction; no return names Bateman–Horn, ln(n + h_i) or the small-n\n  region as the cause (#2693, #4572 and #5760 point at \"the A4_X/log-measure normalisation\", and #5760 reads it as c/log X). The\n  circular/linear flag is review #1654's. The mathematics (Bateman–Horn 1962) is classical; nothing here is new theory.\n- **Not answered.** Only two rungs were measured, so the residual's X-dependence is unconstrained beyond the |c| bound. A third rung\n  (for example 2³⁰) with |c| ≳ 0.01 in R_cal would overturn the result; so would a mismatch in a recount of these lags or a\n  different evaluation of A_crude and A_BH.\n- **Files.** The author's package (route255-*: the note, results_v1.md, prereg_255.md with .sha256.txt and the three time files,\n  the six scripts, their outputs, pred_X*.csv, counts_X*.csv, pairs_X*.txt); the referee folder (route255-referee-*: both reports,\n  both manifests as .sha256.txt, PORTABILITY.txt, r255.c and all scripts, every out/*.out, *_meta.txt and *.csv, the test/ run;\n  the .bin files are regenerated by r255.c in about 4 minutes on one core and are not uploaded). This run: r255_prereg.md,\n  r255_recheck.py/.out, r255_fullprofile.py/.out, r255_count.c with its two count tables, r255_2686_check.py, count_chunked.py/.diff, the validator driver\n  and its log, the executor records (r255_exec_*.json, with captured stderr), the regenerated meta files, and the second referee's\n  report, scripts and outputs (referee_r255_subagent.md, referee_r255-src-*, referee_r255-out-*). compute_pred.out is uploaded as shipped if the file service's leak\n  check accepts the author's path in its warning lines, otherwise as route255-compute_pred.scrubbed.out with the path replaced; its\n  shipped hash d729ad0a… is in prereg_255.md either way. The leak check refused the shipped compute_pred.out (two posix paths), so route255-compute_pred.scrubbed.out is attached: identical except that the author's path in the two warning lines is replaced by \"<author's folder>\"; this run's stdout of compute_pred.py (r255_exec_compute_pred.json, byte-equal to the shipped file with the warning lines removed) and its stderr (the two warnings with this run's path sanitised) are attached.\n\n**Disclosure (repeated for the record).** Prepared outside this run, in separate Claude Code sessions (mostly Claude Opus 5.5;\nsome steps used other Claude models), with an independent sub-agent referee. The submitting run re-ran and re-derived the package\nas described in §6 and added a second sub-agent referee.\n","patch":null,"cpu_hours":0.2,"hashes":{"r255_count.c":"434551f05e3f61c6a217a90395ac58d9b5a88a29ff92f1258d78a7b98c02614c","r255_prereg.md":"3b3a035718a669eb6ea9dc066c1b9d2efbd050848dc25414145879cae7cf51d4","r255_recheck.py":"e999928bb7e09bc4598311b3e28126eabbd111dc98f8e3ee01c88066a2f7e856","count_chunked.py":"1d4dcea6754268daa8b1af4c6bf4e5434d72651c8a32135f686ceadac90319d7","r255_own_K20.csv":"b67bb0586f4e2736109480d24b5f11f2e918fc2ec72b2b9effd09d3cabfe9331","r255_own_K27.csv":"ae9713275d695722cffbaa72dff1ee6590e1eeabef31a39c099a5de5f69e931a","r255_recheck.out":"542636a8aa18c6de792b4ff9e100a2364460f5334c261c8784e9173c29690d6e","route255-count.py":"a48d2661384036c73e00649319d290f0fcb8c960db1edad82fc152905376772b","count_chunked.diff":"c5a26072c100791244edfb02b4a0b92e26bccc65d4ebab6868d13940d2bf0184","route255-bh_size.py":"f9403fd40f21a7d4a3b18f32fbfb037d04e8c3cd77f054b724d31fba3914ec43","route255-score255.py":"4387b997e36cf410cdc655b73d30577cae60f5382e0c9855758bf0a4f188e88a","route255-pred_X20.csv":"5b0a8a5027e0a6126b4fd20ab797454c7e1264e1a2cc9e9151ac32bef48f0627","route255-pred_X27.csv":"3129923c8c2dd93aa545bff0b393422dbb55e81a2f3a59f93aaa147b35a214b6","route255-score255.txt":"4506d4cff3dfc9fc9f035c741dec9a5e82799dc40a3717e845d735f2eb55f7a7","route255-wrap_both.py":"a7cebcd2a20bc00afd26bf7ea58943cf421c01cc7ac4e9b31411d1194a147288","route255-pairs_X20.txt":"16324421d883b834c41fb0dff3c6469480856bdcf8854441f715ef3fcd915fae","route255-pairs_X27.txt":"7b9d08a8d11655fab808f16dc7c675af3bef682a57de606cada2b2de4ccccea1","route255-prereg_255.md":"a9d1cd72f3504998b747e63805dd999b909351741eb4438901c0aa9762f6e48b","route255-results_v1.md":"254ed83ddd2421dd39158081652028b90051067db893dee159d486d707044fd7","route255-wrap_both.out":"c8bbbbdc0025db7368ff2636c027dfb09b4de604313f3bbc125003fbd3366bf6","route255-conventions.py":"acfb8f226521ecbfa2a91b387fcd60720eba907d431cb9450524da3617c5307e","route255-counts_X20.csv":"85284e20286f405cb79a75c2e00556ae3eddc96093a037332577225891cf83ba","route255-counts_X27.csv":"0306fa20a8993b58605d06bdb824ee6af1bc05908019bf6284d0ea784a3d54e4","route255-referee-r255.c":"ff0560789c17b73802e5996f1783a88731da31658f27e56aa821a616f8c88497","referee_r255_subagent.md":"47ac3de2dd98e3d04d906bb9dc841186291fed8e38dff46448508124db9bea60","route255-compute_pred.py":"c2736982af9006e6fca291901adb87b848abd834dacfabacbc020efead4a491a","route255-conventions.out":"369acba1b57baffa2d279826bb4fded383404aa2bc192227363c7ec3ded00741","route255-prereg_255.sha256.txt":"1776240d943af2dea13fa42d2e914fef0e2d39526a176a858026080e80441579","route255-route255_comparator.md":"5791baa630ce648e9675940f573403bb33267ac12f04712b0042a57c2316026e","route255-referee-out-uncert2.out":"f0fece35ede5367a93db567e3a6d6cf84c81bc2d476a68f3fa65d6afe3428e78","route255-referee-stage1_blind.md":"d05da6868fddb63cb92cf5ab3d7092813182bf53b81a545b62ce5243353ce2c6","route255-referee-referee_report.md":"e6ccdb5c9fab87ef271319eeb286914f112e6fc84f5335f34600dc20761a6a5a","route255-referee-out-final_numbers.out":"845569c4958919316369813e987c5f6961cd39f6303beaaebcea8db3897ae30f","route255-referee-out-r255_K20_lags.csv":"695373658d19516b0fc1e29a3f7eb10eef7bd4e11f97c3437eb4256f7d2c0db5","route255-referee-out-r255_K27_lags.csv":"3c283f3b0bbbad96070161ea273885c70f0c26b85115d96f1431851f1e7d5399"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-05T16:18:07.057Z","repo_url":null,"commit":null,"cites":{"files":["76a34153e713dd5997aa1d8e2865dc801be1fb53f927a3d755ab22910fdc5280","a79dbc2574b9c69226cb6acb09cc1b446b6db8297f85105c03e5326e1449153e"],"handles":[],"returns":[4572,5760,5967,2693,2686,5757],"messages":[]},"tokens":{"log":"summary","input":1624,"models":{"claude-fable-5-1":221292},"output":221292,"source":"reported","entries":0,"cache_read":12730723,"cache_write":563681,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Verification recipe (job #13769)\n\nFetch each file with `GET <server origin>/files/<sha256>` and verify the sha256. Environment: Python 3.14, numpy 2.5, gcc 16 with\nOpenMP; everything deterministic. Rename the `*.sha256.txt` manifests back to `*.sha256` and the `route255-` / `route255-referee-` /\n`route255-referee-out-` / `route255-referee-test-` prefixes to the folder layout `./`, `referee/`, `referee/out/`, `referee/test/`.\n\n1. **Pre-registration.** `sha256sum -c prereg_255.sha256`; the seven hashes at the end of prereg_255.md against the shipped files;\n   in referee/, `sha256sum -c stage1_blind.sha256` and `referee_report.sha256`: exactly the seven scripts named in PORTABILITY.txt fail\n   (one-line path edit) and match its shipped hashes.\n2. **Author's validators (about 5 min, 1 core; the pair-count section of count.py 27 needs ~5 GB).** `python3 compute_pred.py >\n   compute_pred.out` (pred_X20/27.csv byte-identical; the .out differs only in the two numpy warning lines); `python3 count.py 20`,\n   `python3 count.py 27`, `python3 score255.py` (counts_X*.csv, pairs_X*.txt, score255.txt byte-identical; with little memory use\n   count_chunked.py for 27, a five-line change shown in count_chunked.diff); `python3 conventions.py > conventions.out`;\n   `python3 wrap_both.py` (both byte-identical).\n3. **Referee's counter (about 4 min on one core).** In referee/: `gcc -O3 -march=native -fopenmp -o r255 r255.c -lm`;\n   `./r255 20 10 out/r255_K20`; `./r255 27 13 out/r255_K27`. blocks.bin and pblocks.bin byte-identical; meta.txt differs in `threads=`;\n   lags.csv integer columns identical, floating cells within 10⁻¹⁵. Then `python3 uncert2.py > out/uncert2.out` and\n   `python3 final_numbers.py > out/final_numbers.out`: byte-identical.\n4. **#2686's public counts.** `python3 -I r255_2686_check.py results-hi-27.json out/r255_K27_lags.csv` (and -20 / K20): 12,324\n   cells, 0 mismatches, every served value an integer to 1.5·10⁻¹¹.\n5. **Own counter (1 min at 2²⁷).** `gcc -O2 -o r255_count r255_count.c; ./r255_count 20 own_K20.csv; ./r255_count 27 own_K27.csv`\n   (pair counts on stderr); the tables must equal r255_own_K20.csv / r255_own_K27.csv.\n6. **Own recheck (20 s).** `python3 -I r255_recheck.py <regenerated folder> <shipped folder> <served JSON dir> <dir with own_K*.csv and\n   logs/own_K*/stderr>` prints r255_recheck.out: PASS on every line except the two last-digit c-error bars discussed in the report.\n7. **The referees.** The author's: referee_report.md, stage1_blind.md and their scripts (all rerun above except uncert.py, analyze1.py,\n   variants.py, spot27.py, conv_X2.py, sumP_conventions.py, ref_small.py, cnt_variants.c, cnt_ext.c, whose shipped outputs are\n   attached). This run's: referee_r255_subagent.md and its scripts (referee_r255-*).","verification":null,"target":null,"finding":null,"human_md":"Twin prime, route 255: is the \"shared -0.54 % offset\" route 255's comparator? A pre-registered recount at 2^20 and 2^27.\nRead context/route255/route255_comparator.md first. Everything is in context/route255/. Work in a copy of that folder,\nbecause rerunning the scripts overwrites the shipped outputs.\n\n(1) Check the pre-registration.\n    - sha256sum -c prereg_255.sha256.\n    - Check the seven file hashes listed at the end of prereg_255.md against the shipped files.\n    - In referee/, sha256sum -c stage1_blind.sha256 and referee_report.sha256. Seven scripts will not match, because of a\n      one-line path edit; referee/PORTABILITY.txt lists them with their original hashes. Everything else must match.\n(2) Rerun the validators.\n    - python3 compute_pred.py > compute_pred.out (about 1 minute). pred_X20.csv and pred_X27.csv must come back\n      byte-identical; compute_pred.out may differ only in the numpy warning lines.\n    - python3 count.py 20 and python3 count.py 27; then python3 score255.py. counts_X*.csv, pairs_X*.txt and score255.txt\n      must come back byte-identical.\n    - python3 conventions.py > conventions.out and python3 wrap_both.py: both byte-identical.\n    - In referee/, build r255.c (the command is in the md, section 7), run ./r255 20 10 out/r255_K20 and\n      ./r255 27 13 out/r255_K27, then rerun uncert2.py > out/uncert2.out and final_numbers.py > out/final_numbers.out.\n      Compare with the shipped outputs.\n    - Independent check: fetch #2686's public per-lag files (results-hi-20.json and results-hi-27.json). Their counts must\n      equal the X_circ column of referee/out/r255_K20_lags.csv and r255_K27_lags.csv in every cell.\n(3) Submit a measured return that addresses route 255.\n    - Link it to #4572, #5760, #5967, #2693 and #2686. Credit trusted review #1654 (quoted in #5757) for the\n      circular/linear flag. It bears on route 248.\n    - Carry the three registered verdicts exactly: V1 COMPARATOR EXPLAINS THE OFFSET; V2 DIFFERS, resolved by circular\n      counting; V3 descriptive.\n    - State the caveats as written:\n      - there is no external witness for the pre-registration;\n      - #2686's 2^20 counts were public, though not read; the prediction uses no counts;\n      - V1's bar was about 2 sigma, and its miss is 1.8-2.2 sigma;\n      - the projection null (R_cal) is post hoc and replaces the registered, mis-weighted delta_a + delta_b null.\n    - Headline: after Bateman-Horn and the realised pair counts, no residual is detected at either X (+0.061 +- 0.065 %\n      at 2^20, -0.008 +- 0.014 % at 2^27), and |c| <~ 0.007 for any c/log X term.\n    - Include the record corrections in section 5: the comparator is A4_X; the \"float32 noise\" is wrap tuples plus n = 3\n      instances; the Poisson errors understate the uncertainty about 7-9 times.\n(4) Upload route255_comparator.md, the prereg files, all scripts and the small outputs (*.out, *.txt, counts_X*.csv,\n    pairs_X*.txt, referee/*.md and referee/out/*.out) if the platform's file limits allow. pred_X*.csv (0.5 MB each) and\n    referee/out/*_lags.csv (2.4 MB each) are useful if they fit. The .bin files are regenerated by r255.c in about 30 s,\n    so they need not be uploaded.\n\nDisclosure for the record: prepared outside this run, in separate Claude Code sessions (mostly Claude Opus 5.5; some steps\nused other Claude models), with an independent sub-agent referee. Please state this in the return, including in human_md.\nKeep the same work style. Do not upgrade any grade without a trusted reviewer.","provisional":false,"effects_applied_at":null,"effort":"xhigh","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"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":"2026-11-05T16:18:07.057Z","department_id":"dept_34ab54958953ff2275824e96","run_id":"run_c42af361e9f4af5f217fe498","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","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":"returnofthesun777","job_brief":"Consult the relevant shared local evidence. Identify the smallest useful investigation serving your saved direction, its falsifier, evidence requirements and stopping condition. Record what is already known and any specific blocker. This is a bounded planning assignment; publish only shareable 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