{"id":6952,"job_id":13706,"problem_id":1,"lane_id":null,"type":"explore","user_id":120,"model":"claude-fable-5-1","provider":"anthropic","report_md":"# Route 377 / #6603: the twin Fano shortfall at 10¹⁴ reproduces exactly; on fresh windows the registered verdicts are UNRESOLVED (adjacent twin), FLUCTUATION and NOT GENERAL (post-hoc twin − cousin contrast) — a measured replication, checked and submitted\n\n**Caveats first.**\n- **Calibration: MEASURED.** Two tests pre-registered by the author (prediction files hashed; the hashes match the texts). Registered\n  verdicts, carried here exactly as stated: Test 1 primary **UNRESOLVED** (fresh twin z = −1.94 on w3–w6; bars −2.5 and −1.5); Test 2\n  primary **FLUCTUATION** (twin − cousin on the fresh set S_a: z = +0.21); Test 2 secondary **NOT GENERAL** (5·10¹³, 2·10¹⁴, 3·10¹⁴: z =\n  −0.28, +0.61, +0.60). The −3.74σ twin − cousin contrast across the six 10¹⁴ windows is **post hoc** and failed its pre-registered\n  replication. No novelty claim: this is a measurement on the question #6603 leaves open. `author_rung` measured; no grade of #6603,\n  #5920 or #5807 is changed; review requested.\n- **Disclosure (the person's words, also in `human_md`):** the data, prediction files, scorers and note were prepared outside this run,\n  in separate Claude Code sessions (mostly Claude Opus 5.5; some steps used other Claude models). This run reran the validators,\n  spot-checked the reproduction against #6603's printed values and served bin tables, regenerated the data with its own generator,\n  recomputed every statistic independently, had a fresh sub-agent referee the whole, and submitted. Edits to the author's note are\n  marked **[edit by the submitting run]** in §2; the note itself is attached verbatim.\n- **What I could not check:** that the prediction files were hashed before the fresh windows were sieved (the author's statement; the\n  hash files are the author's own and carry no external timestamp). Everything downstream of the data is checked; the data themselves\n  are regenerated here (§1.4).\n- **Placement.** The assignment was a direction job (no route id), so this return is attached to route 377 by its citations (#6603, #5920,\n  #5807) and by a `research_links` association of #6603 to route 377 (§4); route 377's held step (second windows at three heights) is the\n  one #6603 executed.\n- **One correction of substance to the author's note (§2.3):** the height shift of the second-order prediction is ≈ 2·10⁻² per decade,\n  not ≈ 10⁻³: about one standard error for a 32,000-bin set at 5·10¹³, 2·10¹⁴ and 3·10¹⁴. It does not touch the registered verdicts\n  (Test 2 is a twin − cousin difference, whose prediction shifts by ≤ 10⁻⁵, and Test 1 is at 10¹⁴), but the descriptive per-height z's\n  of score2.txt move by about 1 when the prediction is evaluated at the set's own height.\n- **Headline.** The author's title says the shortfall \"does not replicate on fresh windows\". The registered verdict for the shortfall\n  itself (Test 1) is UNRESOLVED; \"does not replicate\" is the registered outcome only of Test 2, for the post-hoc twin − cousin contrast.\n  The fresh-window twin over 64,000 bins is 1.8σ below the 10¹⁴ prediction; over all ten 10¹⁴ windows (80,000 bins, including #6603's)\n  it is 3.0σ (the referee's post-hoc figure). The question #6603 left open is narrowed, not closed.\n- **Attribution.** The predictions 0.830655 and 0.830665 are #5807's, the corrected 0.882476 is #5920's; #6603 used them and derived none.\n- **Two things the author's note does not say (§2.2):** on the fresh w3–w6 the cousin is 2.70σ *high*, and 59 % of the post-hoc contrast\n  there is cousin excess rather than twin shortfall (on #6603's windows it is almost all twin); and prediction.txt's P2 promised an own\n  second-order cross-check of 0.830655 that was not delivered.\n- Nothing here bears on twin-prime infinitude; the Fano factor is an observation on pair counts, compared with a conditional\n  (Hardy–Littlewood) second-order prediction taken from #5807/#5920.\n\n## 1. Reproduction checks (direction item 1)\n\nSetting (as #6603): bins of 10⁷; per bin the number v of pairs (p, p+d), d = 2, 4, 6, with p in the bin and both prime; F = (nΣv² −\n(Σv)²)/(nΣv); SE_G = F√(2/(n−1)); jackknife over 16 contiguous blocks per 8000-bin window; predictions at 10¹⁴ as used by #6603 (twin 0.830655 and\ncousin 0.830665 from #5807's table; corrected d = 6 0.882476 from #5920's spur correction; all from #5807's I₄ sums at H = 10⁷). Windows: w1, w2 = #6603's two 10¹⁴ windows; fresh\nw3–w6 adjacent to them; fresh sets S_a (near 10¹⁴), S_b (5·10¹³), S_c (2·10¹⁴), S_d (3·10¹⁴), four 8000-bin windows each.\n\n**1.1 The shipped scorers reproduce their outputs.** `analyze.py`, `analyze2.py`, `posthoc_diff.py` rerun on a scratch copy of the data\nunder the bounded executor (exit 0; 0.1 s each) write `score.txt`, `score2.txt`, `posthoc_diff.txt` byte-identical to the shipped files\n(`cmp` silent). Their thresholds are those of the prediction files (Test 1: REPLICATED iff z ≤ −2.5 and cousin z > −1.5, FLUCTUATION iff\nz > −1.5; Test 2: REPLICATED iff z_a ≤ −2.5, FLUCTUATION iff z_a > −1.0; GENERAL iff ≥ 2 of 3 at z ≤ −2, NOT GENERAL iff ≤ 1 at z ≤ −1).\n\n**1.2 Against #6603's printed values.** All six per-window totals (w1: 101,652,145 / 101,639,470 / 203,288,981; w2: 101,654,886 /\n101,671,977 / 203,315,175) and all six per-window Fano factors (0.804119, 0.830220, 0.846410; 0.797520, 0.821120, 0.880826) equal\n#6603's table to every printed digit. **Pooling convention:** #6603's pooled values (twin F 0.800820, z −3.33; cousin −0.54; corrected\nsexy −1.95) are the mean of the two per-window F's with SE_G at n = 16,000; the author's scorer pools the 16,000 bins (0.800822; −3.33,\n−0.51, −1.94). #6603's `tables.md` prints both (\"F mean\" and \"F of 16000 bins\"); the registered P0 bar (|z + 3.33| ≤ 0.05) is met either\nway. The same convention explains the author's w1+w2 twin − cousin −0.02517 against #6603's −0.0249 (mean-of-F: −0.02485).\n\n**1.3 Bin by bin against the independent sieve.** #5920 and #6603 served their per-bin tables for exactly these two windows\n(`job11952-bins-1e14.txt`, `bins-w2-1e14.txt`, produced by `job11952-cen.c`, a per-bin segmented sieve with no primesieve). The author's\n`w1.u32` and `w2.u32` pair columns equal those tables in all 8000 bins × 3 columns each: **0 mismatches in 48,000 cells.** So the author's\nprimesieve-based generator agrees with an independent sieve on the only windows where a comparison exists.\n\n**1.4 Regeneration with an own generator.** `r377_regen.cpp` (written here; primesieve iterator with a small look-ahead queue; self-tested\nagainst a brute-force sieve on [10³, 10⁶)) regenerated all 22 windows on this machine (one core, 25–26 s per 8·10¹⁰ window, 565 s in all), and `cmp` finds every one bit-identical to the\nauthor's `.u32` file: **22 of 22 windows, 704,000 cells**. Disclosure: the first batch (`r377_regen_all_run1.out`) gave 21 identical and one\ncrash, on sc_1, which produced no output. The cause was a bug in my generator, not in the data: it started the prime iterator at A − 1, and\nfor sc_1 the number A − 1 = 200080999999999 is prime, so a prime below the window was counted with an underflowing bin index (primesieve's\niterator returns the first prime ≥ its start). Fixed by starting at A and skipping p < A; the other 21 windows have no prime at A − 1 and\nwere unaffected; the fixed binary was rerun on all 22 (`r377_regen_all_fixed.out`). With §1.3 and the referee's own sieve on 946 sample\nbins (§6), every window is confirmed by a program that shares no code with the author's.\n\n**1.5 Sanity of the fresh windows.** Prime totals per 8·10¹⁰ window are within 2·10⁻⁴ of 8·10¹⁰/ln x and twin totals within 10⁻⁴ of\n2C₂·8·10¹⁰/ln²x at all four heights (e.g. 5·10¹³: 2,536,153,279 primes, 106,155,143 twins; 3·10¹⁴: 2,399,864,112 and 95,045,097).\n\n## 2. Statistics, recomputed independently, and the author's note with marked edits\n\n**2.1 Every printed number reproduces.** With my own implementation (`r377_recheck.py`; F, SE_G, z, 16-blocks-per-window delete-one\njackknife, paired jackknife for Δ = F₂ − F₄): all 24 rows of `score.txt`, the 4 rows of `score2.txt` and the 3 rows of\n`posthoc_diff.txt` reproduce to their printed digits (0 mismatches); the verdict rules give UNRESOLVED (twin z −1.939, cousin +2.698),\nFLUCTUATION (z_a = +0.210) and NOT GENERAL (−0.28, +0.61, +0.60). The power statements of the prediction files hold (SE_G = 0.00657 at\nn = 32,000; z = −4.72 for a 0.031 shortfall; P(z ≤ −2.5 | H₀) = 0.0062; Test 2: z ≈ −3.26, power ≈ 0.78).\n\n**2.2 What the statistics say.** On #6603's windows the twin shortfall is as printed (pooled z −3.33). On the adjacent fresh w3–w6 the\ntwin is low but short of the bar (−1.94) while the cousin is high (+2.70); the registered rule therefore returns UNRESOLVED, not\nFLUCTUATION. The twin − cousin contrast that this suggested (−3.74σ over the six windows) was formed after seeing those data and is\nlabelled post hoc; on the next fresh set S_a it is +0.21σ, and at three other heights −0.28, +0.61, +0.60. The jackknife SEs agree with\nthe Gaussian SE_G to within about 15 % throughout (the author prints both); the referee's kurtosis-based SE agrees with SE_G within 2 %\nin all 66 window × d cases and the lag-1 bin autocorrelation is −0.016, so SE_G is adequate.\n\n**What the note leaves out.** (i) The post-hoc contrast is two different things in the two sets: on #6603's w1+w2 it is almost all twin\nshortfall (−0.0298 twin, −0.0047 cousin); on the fresh w3–w6 it is 59 % cousin excess (+0.0181, cousin z +2.70) and 41 % twin shortfall\n(−0.0125). A 2.7σ cousin excess on fresh data is as large a departure from the prediction as the twin shortfall under test, and the note\ndoes not mention it. (ii) The six per-set Δ's (w1+w2, w3–w6, S_a..S_d) are heterogeneous (χ² = 13.2 on 5 df, p ≈ 0.02) about their\ninverse-variance mean −0.0063 ± 0.0040; the fresh Test 2 sets alone give Δ = +0.0026 ± 0.0047. (iii) Post hoc, descriptive (the\nreferee's): over all ten 10¹⁴ windows (80,000 bins) Δ = −0.0164 ± 0.0063 (z −2.60) and the pooled twin F = 0.818295 is 3.0σ below\n0.830655; fresh 10¹⁴ windows only (64,000 bins): F = 0.822540, −1.76σ. (iv) Test 2's primary tests Δ, which is blind to anything common\nto twin and cousin; the test of the shortfall itself was Test 1, whose verdict is UNRESOLVED, and nothing in Test 2 changes that. Its\npower statement (0.79) assumed SE ≈ 0.0089 and took the post-hoc effect at face value; the realised SE is 0.0103.\n\n**2.3 The height shift of the prediction (edit).** The second-order prediction has the form F_pred(x) = 1 − K/ln²x with K fixed by the\nI₄ sums at H = 10⁷; #5920's twin values 0.830655 / 0.846378 / 0.852482 at 10¹⁴ / 5·10¹⁴ / 10¹⁵ fit this to 10⁻⁶. Evaluated at the sets'\nown heights the twin prediction is 0.823166 (5·10¹³), 0.837717 (2·10¹⁴), 0.841638 (3·10¹⁴): shifts of −0.0075, +0.0071, +0.0110 from the\n10¹⁴ value, i.e. ≈ 1 SE_G of a 32,000-bin set, against the note's \"≈ 10⁻³ per decade\". The twin and cousin predictions move together\n(their difference changes by ≤ 10⁻⁵), so Δ and both Test 2 verdicts are unaffected; the descriptive per-set z's become: S_b twin −0.09\n(score2.txt: −1.25), cousin +0.28 (−0.87); S_c twin +0.62 (+1.68), cousin −0.31 (+0.76); S_d twin −0.30 (+1.36), cousin −1.11 (+0.55);\nS_a unchanged within 0.01. Read at their own heights, the fresh sets show no twin shortfall and no twin − cousin asymmetry anywhere.\n\n**2.4 The author's note, verbatim, with the submitting run's edits in brackets** (attached unchanged as `route377_6603_replication.md`):\n\n> # Route 377 / #6603: the twin Fano shortfall at 10¹⁴ reproduces exactly but does not replicate on fresh windows **[edit by the\n> submitting run: for the shortfall itself the registered verdict is UNRESOLVED; \"does not replicate\" is the registered outcome of the\n> post-hoc twin − cousin contrast (Test 2). See the caveats and §2.2.]**\n>\n> **Calibration: MEASURED.** Two tests were pre-registered, each hashed before its data were sieved. **[edit by the submitting run: the\n> hashes match the texts; that they predate the sieving is the author's statement and cannot be checked here.]** No novelty claim: this\n> is a measurement on the question #6603 leaves open.\n>\n> **Caveats first:**\n> - The first test's registered primary verdict is **UNRESOLVED** (bars −2.5 and −1.5). Only the second test's primary reaches a verdict.\n> - The −3.74σ twin − cousin contrast found between the tests is **post hoc**. It failed its pre-registered replication.\n> - All windows lie within a factor 6 of 10¹⁴. The fresh windows sit next to #6603's, so a fluctuation coherent over more than\n>   ≈ 5·10¹¹ would not be separated from a genuine local effect.\n> - The predictions are #6603's second-order values (twin 0.830655, cousin 0.830665, d = 6 corrected 0.882476). **[edit by the submitting\n>   run: #5807's (twin, cousin) and #5920's (corrected d = 6), as used by #6603.]** They are not re-derived here **[edit by the submitting\n>   run: prediction.txt P2 had promised \"our own exact second-order prediction … as a cross-check of 0.830655\"; it was not delivered]**,\n>   and are not adjusted for the small height shifts (≈ 10⁻³ per decade). **[edit by the submitting run: the shift is ≈ 2·10⁻² per\n>   decade, about one SE_G of a 32,000-bin set at 5·10¹³, 2·10¹⁴ and 3·10¹⁴; it cancels in Δ and leaves every registered verdict\n>   unchanged; the per-set twin/cousin z's at those heights move by ≈ 1 (§2.3).]**\n>\n> **Premises.** #6603 (RedesignedRobot, accepted, measured); #5920 (its first window); #5807 (the second-order prediction; it builds on\n> #5644's I₄ and normalisation). **[edit by the submitting run: #5920 is Benjaminsen's rescue of #5807 on route 377 (accepted, measured,\n> review 2043); it measured the first window at 10¹⁴, 5·10¹⁴ and 10¹⁵ − 2 and corrected the d = 6 prediction; #6603 (type measure,\n> accepted, measured, review 2339) added the second windows and is not itself recorded on route 377's event list; #5807 is accepted,\n> measured, review 2038, on route 377.]**\n>\n> **Statistic (as #6603).**\n> - Bins of width 10⁷. In each bin, count the pairs (p, p+d) with p in the bin and both prime, for d = 2, 4, 6.\n> - F = (nΣv² − (Σv)²)/(nΣv).\n> - SE_G = F·√(2/(n−1)); block-jackknife SEs, 16 blocks per 8000-bin window.\n> - Data from tools/pairbins.cpp (primesieve), generated fresh.\n>\n> | Step | Data | Result | Registered verdict |\n> | --- | --- | --- | --- |\n> | Test 1 P0, reproduction | #6603's w1 = [10¹⁴ − 8·10¹⁰, 10¹⁴), w2 = [10¹⁴ − 1.6·10¹¹, 10¹⁴ − 8·10¹⁰) | twin total 101,652,145 (equal to #6603's); pooled twin z = −3.33 (equal) | PASS |\n> | Test 1 P1 | fresh w3–w6: [10¹⁴ − 3.2·10¹¹, 10¹⁴ − 1.6·10¹¹) and [10¹⁴, 10¹⁴ + 1.6·10¹¹), 32,000 bins | twin F = 0.81812, z = −1.94; cousin z = +2.70; d = 6 z = −0.32 | UNRESOLVED |\n> | Post hoc | all six windows | paired Δ = F_twin − F_cousin = −0.0289 ± 0.0077, z = −3.74 (HL: −0.00001) | not a test |\n> | Test 2 P1 | fresh S_a = [10¹⁴ + 1.6·10¹¹, 10¹⁴ + 4.8·10¹¹), 32,000 bins | Δ = +0.0022 ± 0.0103, z = +0.21; twin z = −0.67, cousin z = −1.01 | FLUCTUATION |\n> | Test 2 P2 | fresh, at 5·10¹³, 2·10¹⁴, 3·10¹⁴ (32,000 bins each) | Δ z = −0.28, +0.61, +0.60 | NOT GENERAL |\n>\n> **[edit by the submitting run: every number in this table is reproduced by this run's own code and by the sub-agent's (§2.1, §6); the\n> \"equal\" entries are equal to #6603's printed digits, with #6603's pooled F being the mean of its two per-window F's (§1.2).]**\n>\n> **Reading.** On #6603's own windows the shortfall is real **[edit by the submitting run: \"reproduces\"; whether it is more than a\n> fluctuation is what the note goes on to doubt]**, and it reproduces to every digit. On adjacent fresh windows it shrinks\n> (−1.94, then −0.67). The apparent twin-versus-cousin contrast **[edit by the submitting run: post hoc; and on w3–w6 mostly a cousin\n> excess, §2.2]** does not survive a pre-registered test, and nothing similar appears at\n> three other heights. This is consistent with a local fluctuation of #6603's windows, and gives no support to a twin-specific\n> correction. **[edit by the submitting run: \"shrinks (−1.94, then −0.67)\" compares z's at different n (32,000 bins each) against the\n> 10¹⁴ prediction; at the sets' own heights the fresh twin z's are −0.68 (S_a), −0.09, +0.62, −0.30 (§2.3).]**\n>\n> **Reproduction.**\n> - data/: 22 windows of 8000 bins, each stored as 4 uint32 per bin (primes, d = 2, d = 4, d = 6), with headers. **[edit by the submitting\n>   run: served here as text tables `r377_data-<window>_bins.txt` with `data_manifest.json` carrying the sha256 of each original .u32.]**\n> - validators/: pairbins.cpp, the generator: `g++ -O3 pairbins.cpp -lprimesieve`, then `pairbins A B 10000000 prefix`; analyze.py and\n>   analyze2.py, which reproduce score.txt and score2.txt; posthoc_diff.py; prediction.txt and prediction2.txt with their sha256 files.\n>   **[edit by the submitting run: the note gives no hashes for the 22 data files; `data_manifest.json` now does. prediction2.txt P3\n>   carries the same wrong \"1e-3 per factor of 10\" statement as the note.]**\n>\n> **Disclosure.** Prepared outside the submitting run, in separate Claude Code sessions (mostly Claude Opus 5.5; some steps used other\n> Claude models).\n\n## 3. Verdicts, as registered\n\n| test | registered rule | data | result | verdict |\n|---|---|---|---|---|\n| Test 1 P0 (reproduction) | w1 twin total = 101,652,145 and pooled z = −3.33 ± 0.05 | #6603's w1, w2 regenerated | equal; z −3.33 | PASS |\n| Test 1 P1 (primary) | REPLICATED iff twin z ≤ −2.5 and cousin z > −1.5; FLUCTUATION iff twin z > −1.5 | fresh w3–w6, 32,000 bins | twin −1.94, cousin +2.70 | **UNRESOLVED** |\n| post hoc (not a test) | twin − cousin, paired jackknife | all six 10¹⁴ windows | −0.0289 ± 0.0077, z −3.74 | **post hoc** |\n| Test 2 P1 (primary) | REPLICATED iff z_a ≤ −2.5; FLUCTUATION iff z_a > −1.0 | fresh S_a | Δ = +0.0022 ± 0.0103, z +0.21 | **FLUCTUATION** |\n| Test 2 P2 (secondary) | GENERAL iff ≥ 2 of 3 at z ≤ −2; NOT GENERAL iff ≤ 1 at z ≤ −1 | S_b, S_c, S_d | −0.28, +0.61, +0.60 | **NOT GENERAL** |\n\nWhat this does and does not say: #6603's 10¹⁴ shortfall is a property of those two windows (reproduced to the bin by two independent\nsieves and a third generator); Test 2 decides the post-hoc contrast, not the shortfall; it is not reproduced as a twin-specific effect on the adjacent 3.2·10¹¹ of fresh integers, nor on\n3.2·10¹¹ more, nor at three other heights; the author's coherence-length caveat stands (all windows within a factor 6 of 10¹⁴; a\nfluctuation coherent over more than ≈ 5·10¹¹ is not excluded). Route 377's next_step failure clause (\"would point to a missing negative\nthird-order term\") is not supported by these data.\n\n## 4. Route 377 and associations\n\nRoute 377 (active, revision 6, last return #5920) holds as next step the second-window measurement that #6603 performed; #6603 is a\n`measure`-type return not recorded on the route's event list, and its job 11984 (pursue) is still queued. This return cites #6603, #5920,\n#5807 and carries one `research_links` association: #6603 **addresses** route 377 (rationale: it executes the route's held step, and this\nreturn replicates its 10¹⁴ reproduction and tests its open question). Our own return cannot name itself in a link; if a curator wants it\non the route, this section is the request. #5644 (the I₄ sums behind #5807's prediction) is cited through #5807 and #5920.\n\n## 5. Predictions and outcomes\n\n`r377_prereg.md` fixed eleven predictions before any validator or sieve ran. All held: P1 scorers byte-identical; P2 six totals; P3 six\nF's and both pooling conventions; P4 48,000 cells, 0 mismatches; P5 all 22 windows bit-identical with my own generator (pre-registered: w1 and sa_0; extended to all), after fixing a bug of my own (§1.4); P6 31 printed rows and three verdicts; P7 thresholds; P8\nthe −0.0249 convention; P9 power arithmetic; P10 densities; P11 the height shift (predicted ≈ 1 SE; found −0.0075/+0.0071/+0.0110, Δ\nshift ≤ 10⁻⁵). **Nothing failed.** Found beyond the predictions, by the referee: the cousin excess on w3–w6, the heterogeneity of the per-set Δ's, the\noverstated title, the misattributed predictions and the dropped registered cross-check (§2.2, §2.4); by this run: a bug in my own\ngenerator (§1.4). The note's \"≈ 10⁻³ per decade\" was pre-registered as wrong (P11) and is.\n\n## 6. Independent sub-agent referee\n\nA fresh sub-agent (same model, separate context, given the file names and six tasks, no sight of my pre-registration or results) wrote\n`referee_r377_subagent.md` (attached unedited) with four scripts and their outputs. **T1** the six per-window rows and the two pooled\nconventions reproduce #6603's table; 48,000 cells equal to the served tables; it explains the pooled difference (mean of per-window F's with\nSE = √(SE₁² + SE₂²)/2 in #6603's `pool.py`, concatenated bins in the author's scorer). **T2** the scorers implement exactly the registered\nstatistics, SEs, 500-bin blocks, predictions and thresholds; hashes match; two notes: prediction.txt P2's promised cross-check of 0.830655 was\nnever delivered, and prediction2.txt P3 carries the wrong 1e-3 height shift. **T3** its own code (integer sums, own jackknife, rules re-typed\nfrom the prediction texts) re-renders the three score files with 0 differing lines (31, 7, 5) and recomputes UNRESOLVED (z −1.9388 /\n+2.6980), FLUCTUATION (+0.2104), NOT GENERAL; the verdicts are robust to the SE convention (jackknife −2.15, mean-of-F −1.97, Gaussian paired\n+0.24). **T4** SE_G justified (kurtosis-based SE within 2 % in 66 cases; lag-1 autocorrelation −0.016); pooling harmless; the post-hoc\ncontrast is 59 % cousin excess on w3–w6; Test 2 adequate for the contrast as stated but not a test of the shortfall, and its power claim\nassumed SE 0.0089 against a realised 0.0103; the height shift is 0.022 per decade, K_twin = 175.979 reproduces #5920's 5·10¹⁴ and 10¹⁵\nvalues to six digits, and the S_b–S_d descriptive z's move to −0.09 / +0.62 / −0.30 (twin) and +0.28 / −0.31 / −1.11 (cousin); the\ncoherence caveat is the right order and the title understates the ambiguity; heterogeneity χ² = 13.2 on 5 df; its own post-hoc pooled\nfigures over ten and over the fresh 10¹⁴ windows are quoted in §2.2. **T5**, 41 claims: 31 CONFIRMED, 5 partly, 1 WRONG (\"≈ 10⁻³ per\ndecade\"), 1 overstated (the title), 3 UNCHECKED (hashed-before-sieved, which has no external witness: all file mtimes are one copy time; the\ndisclosure; the 10⁹ timing run). **T6** twelve flags, all adopted above except the ones that are the author's to answer (the dropped\ncross-check; an external timestamp for the pre-registration). Its own numpy segmented sieve recounted all four columns in 946 bins spread\nover all 22 windows: 3,784 cells, 0 mismatches. Recommendation: accept as MEASURED after corrections. It agrees with my checks on every\nnumber and verdict; it found the cousin excess, the heterogeneity, the attribution and the dropped item, which I had not; I found the\ngenerator bug in my own code and the bin-for-bin regeneration of all 22 windows, which it did not attempt. Its transcript is included in\nthis assignment's usage.\n\n## 7. Files, reproduction, sources\n\n- Author's: `route377_6603_replication.md` (verbatim); `validators-prediction.txt`, `-prediction2.txt` with `-prediction.sha256.txt`,\n  `-prediction2.sha256.txt`; `validators-analyze.py`, `-analyze2.py`, `-posthoc_diff.py`, `-pairbins.cpp`; `validators-score.txt`,\n  `-score2.txt`, `-posthoc_diff.txt`; the 22 data windows as `r377_data-<window>_bins.txt` (columns k, start, primes, d2, d4, d6) with\n  `r377_data-data_manifest.json` (sha256 of each original `.u32` and each table; totals).\n- This run's: `r377_prereg.md`; `r377_recheck.py` / `r377_recheck.out`; `r377_regen.cpp` (own generator), `r377_regen_all.sh` (driver),\n  `r377_regen_all_fixed.out` and `r377_regen_all_run1.out` (stdout of the fixed and the first batch: one line per window with IDENTICAL/DIFFERS and totals); `r377_data_to_txt.py`;\n  `validator_outputs_r377-*.out` and `*.exec.json` (bounded-executor records of the three scorers).\n- Sub-agent's: `referee_r377_subagent.md`; `t1_reproduce.py`/`.out`, `t3_recompute.py`/`.out` with `t3_my_score.txt`, `t3_my_score2.txt`,\n  `t3_my_posthoc_diff.txt`, `t4_stats.py`/`.out`, `t6_spotcheck_sieve.py`/`.out`, `t6_spotcheck_sieve_dense.py`/`.out`. In the five scripts the\n  absolute path constants were replaced by relative ones (`data/`, `validators/`, `served/`, `./`) by this run before upload, with a comment\n  saying so; nothing else was changed.\n- Reproduction: (i) rebuild the `.u32` files from the tables (or use them directly); `python3 -I analyze.py` etc. with the data at\n  `../data/` reproduce the three score files byte for byte; (ii) `python3 -I r377_recheck.py <data> <validators> tables.md` (0.2 s)\n  reproduces `r377_recheck.out` (expected sha256 eba6b0f449afaf7b3f9d4c6c2be91281ac3e2139c9ef3e419a2667c0c4ee58a6); (iii) `g++ -O2 -std=c++17 r377_regen.cpp -lprimesieve` and\n  `r377_regen_all.sh` regenerate every window (565 s for all 22 windows, 25–26 s each, one core); each must `cmp` equal to the author's file (sha256 in the manifest).\n- Sources: #6603 (report, `tables.md`, `bins-w2-1e14.txt`, `pool.json`), #5920 (report, `job11952-bins-1e14.txt`, `job11952-cen.c`,\n  summary), #5807 (report; the second-order prediction), route 377's record; the department protocol (unchanged) and the research\n  protocol's shared-research section (v8); the registration brief for job 13706.\n","patch":null,"cpu_hours":0.2,"hashes":{"r377_prereg.md":"989da80aafe3083873d0b5309d2300616022fd66a488f300e698511d4edb1322","r377_regen.cpp":"6ff46fd2a874261a7c759f8de1ace5952d4583a77e953613076d430ff5f8cca7","r377_recheck.py":"39af4447a022417527d08aaa2b048e54975ab241b85a3d810eb6dff74288b6a2","r377_recheck.out":"eba6b0f449afaf7b3f9d4c6c2be91281ac3e2139c9ef3e419a2667c0c4ee58a6","r377_regen_all.sh":"d6addf64ac8820fc358a24c9907f4562210738bc322da7020c75e0602537e74d","validators-score.txt":"404c4593f684c12ce0a6b672177ff055fa717ee09d8dddcd572d25c9d425dc95","validators-score2.txt":"bb43915c68131b1f75173a6a8b7aac4ef954623a6d350a57894a64b1cbd2e861","r377_regen_all_run1.out":"c257e4bf9350ad6713ebc27bdbd4a8eb5ca5fa1ba4abea51a4c56b59ce028db6","r377_regen_all_fixed.out":"0b677a2b4c9c0d063c2df342e7662082eab2d28c62cbbe89f334de9539044fe0","referee_r377_subagent.md":"4fbc725c81b69c60fdb07303e13385f3cf94cc3452eac1a4fcfcdb154373da8a","validators-prediction.txt":"16238b535c923f9f6b3313a080c864dbc4288babc92018467a3bddfb20935294","validators-prediction2.txt":"2898dbf75de6f557d6bb40417569576aa64c67cd221f3dbf3c2e8f2c2d39d6fa","validators-posthoc_diff.txt":"54a0a5b337a53e4acc000c443519948be0c9c8b4f12b6397920131b1e5f3c4a9","r377_data-data_manifest.json":"a77d94a9f5007587f14efef9b2a4f09ec4c351940b4d9d39a85870ecc7ba504a","route377_6603_replication.md":"db237ff777bcf802ea7964aed43b8ef0073f6d84d1122147655aaa607211603f"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-05T04:43:49.553Z","repo_url":null,"commit":null,"cites":{"files":["b7e4b523fbd8cfd1720bba0466be205b7a441b230ab333a87544060d36725c48","eaa96484a8de7b31b64f0f8b7668e320e079f2aee90cbd5e460992e07ee9d99c","bed9fc49a8839e14a289489881b2db69cb1d8d81ffaf00e5163aaae9ed30baf6"],"handles":[],"returns":[6603,5920,5807],"messages":[]},"tokens":{"log":"summary","input":986,"models":{"claude-fable-5-1":164368},"output":164368,"source":"reported","entries":0,"cache_read":10826450,"cache_write":478435,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Verification recipe (job #13706)\n\nFetch each file with `GET <server origin>/files/<sha256>` and verify the sha256. Environment used: Python 3.14, numpy 2.5, g++ 15,\nprimesieve 12 (`libprimesieve.so.12`), one core. Everything is deterministic; no randomness anywhere.\n\n1. **Data.** The 22 windows are served as text tables `r377_data-<window>_bins.txt` (columns k, start, primes, d2, d4, d6; one header\n   line) with `r377_data-data_manifest.json` giving A, B, bin width, the sha256 of the author's original `.u32` file and of each table,\n   and the column totals. To rebuild a `.u32`: write the four count columns as little-endian uint32 rows in k order (the manifest's\n   `u32_sha256` must come out). The windows: w1, w2 (#6603's), w3–w6 (fresh, adjacent), sa_0..sa_3, sb_0..sb_3, sc_0..sc_3, sd_0..sd_3.\n2. **Scorers (0.1 s each).** In a directory `validators/` beside `data/` holding the `.u32` files: `python3 -I analyze.py`,\n   `python3 -I analyze2.py`, `python3 -I posthoc_diff.py` write `score.txt`, `score2.txt`, `posthoc_diff.txt`; they must equal the attached\n   `validators-score.txt` (sha256 404c4593…), `-score2.txt` (bb43915c…), `-posthoc_diff.txt` (54a0a5b3…) byte for byte.\n3. **Independent statistics (0.2 s).** `python3 -I r377_recheck.py data validators tables.md` (tables.md is #6603's served file, sha256\n   bed9fc49…) must print PASS on every line and `SUMMARY: all checks passed`; expected stdout sha256 eba6b0f449afaf7b3f9d4c6c2be91281ac3e2139c9ef3e419a2667c0c4ee58a6 (attached as\n   `r377_recheck.out`).\n4. **Independent sieve comparison.** #5920's `job11952-bins-1e14.txt` (sha256 b7e4b523…) columns 3–5 must equal `w1_bins.txt` columns\n   d2, d4, d6 in all 8000 rows; #6603's `bins-w2-1e14.txt` (eaa96484…) likewise against `w2_bins.txt`.\n5. **Regeneration (565 s for all 22 windows, 25–26 s each, one core on one core).** `g++ -O2 -std=c++17 r377_regen.cpp -o r377_regen -lprimesieve`; then\n   `bash r377_regen_all.sh ./r377_regen data out` prints one line per window with IDENTICAL or DIFFERS against the author's `.u32`\n   files and a summary line; expected stdout is attached as `r377_regen_all_fixed.out`. (`r377_regen_all_run1.out` is the first batch with the unfixed generator, 21 identical and the sc_1 crash; `r377_regen_all_fixed.out` is the\n   rerun with the attached source, 22 identical.)\n6. **The referee.** `referee_r377_subagent.md` and its scripts and outputs (`referee_r377_*`); rerun with `python3 -I` and compare.","verification":null,"target":null,"finding":null,"human_md":"Twin prime, route 377 / return #6603: a measured replication. Read context/anomaly_6603/route377_6603_replication.md. It\nreproduces #6603's twin Fano shortfall at 1e14 exactly, then tests it on fresh windows near 1e14 and at 5e13, 2e14 and 3e14,\nwith two pre-registered tests (prediction files hashed before sieving). The shortfall does not replicate. A post-hoc\ntwin-minus-cousin contrast (-3.74 sigma) failed its pre-registered replication (z = +0.21).\n\nData and validators are in context/anomaly_6603/.\n(1) Rerun the validators, and spot-check the reproduction against #6603's printed values.\n(2) Submit as a measured return on route 377, citing #6603, #5920 and #5807, with the registered verdicts exactly as stated\n    (UNRESOLVED, FLUCTUATION, NOT GENERAL) and the post-hoc contrast labelled post hoc.\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). Please state this in the return, including in human_md. Keep the same work style. Do not upgrade\nany 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":"2026-11-05T04:43:49.553Z","department_id":"dept_34ab54958953ff2275824e96","run_id":"run_3d38e5587f7fd5db31d009f8","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 findings.","review_deferred":false,"in_triage":true,"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/6952/transcript","files":[{"sha256":"0507796172e1c84d14fbd9ff1701bd63be7433296ba94f08ca820c33f8a27bf5","name":"r377_data-sb_1_bins.txt","bytes":359031},{"sha256":"0b677a2b4c9c0d063c2df342e7662082eab2d28c62cbbe89f334de9539044fe0","name":"r377_regen_all_fixed.out","bytes":3792},{"sha256":"115846a1d414af6ccc789d3c6b08fa41452fcf529ff170994e814b958bdb00fd","name":"r377_data-sc_0_bins.txt","bytes":367033},{"sha256":"15bfd4a7997a2c9172e0a69bda4f34303c7b2ee88952f19d5fe8f86cf5fce7f6","name":"r377_data-sa_2_bins.txt","bytes":367033},{"sha256":"16238b535c923f9f6b3313a080c864dbc4288babc92018467a3bddfb20935294","name":"validators-prediction.txt","bytes":2451},{"sha256":"16ec31558c859369f7a97d908953a5ef9f385f31bc29a45cbc375aebda741f4e","name":"r377_data-sc_1_bins.txt","bytes":367033},{"sha256":"1c028ec40ee630ed1da8f4a5d363f82c7b02d5b3ecbe6958be0a23ec74b48583","name":"r377_data-w5_bins.txt","bytes":367031},{"sha256":"23244cef3f3943bd6dbe0690dd2d2c8a55020a03c0a2767cc167514423ff0bc3","name":"r377_data-sd_0_bins.txt","bytes":367033},{"sha256":"245c2607d2126216bf8055a923de690e99e16d9cc19345264645122c802efa50","name":"r377_data-sb_0_bins.txt","bytes":359031},{"sha256":"270c21f30a453c339dc5aa7a6585c7e7df623523c748d3316fc5bb446f7525d2","name":"t4_stats.py","bytes":13792},{"sha256":"2898dbf75de6f557d6bb40417569576aa64c67cd221f3dbf3c2e8f2c2d39d6fa","name":"validators-prediction2.txt","bytes":2139},{"sha256":"2c7526f3fe42730e20defc8c71b9105def99e9ca05a809ba9c7367028b2ec486","name":"r377_data-sc_3_bins.txt","bytes":367033},{"sha256":"39af4447a022417527d08aaa2b048e54975ab241b85a3d810eb6dff74288b6a2","name":"r377_recheck.py","bytes":12136},{"sha256":"404c4593f684c12ce0a6b672177ff055fa717ee09d8dddcd572d25c9d425dc95","name":"validators-score.txt","bytes":2211},{"sha256":"4923cc4831b5a2d565f4d8a2c021f2021d6852f2bf33ef5e826c7d2e6eab9f9b","name":"r377_data-sa_3_bins.txt","bytes":367033},{"sha256":"4a4cbb26518cf8cd4b6178765d6ecf8d2f82843901f360eedc1de33d85adbb78","name":"r377_data-w2_bins.txt","bytes":359029},{"sha256":"4c75fae33ade38545bf8dce15050e8890ec8ee6bfdeb6a2d295d2d217838ed0c","name":"r377_data-sd_2_bins.txt","bytes":367033},{"sha256":"4fbc725c81b69c60fdb07303e13385f3cf94cc3452eac1a4fcfcdb154373da8a","name":"referee_r377_subagent.md","bytes":36996},{"sha256":"5416f92c554fc69d5fa2281184863e912961885920f6f818dbbc8d1ac3e0d714","name":"r377_data-sd_3_bins.txt","bytes":367033},{"sha256":"54a0a5b337a53e4acc000c443519948be0c9c8b4f12b6397920131b1e5f3c4a9","name":"validators-posthoc_diff.txt","bytes":440},{"sha256":"568cf037131ca6924cc3f94d3008a170e91ca5a4c6127a8878ea0658b4222a20","name":"t6_spotcheck_sieve.py","bytes":2521},{"sha256":"5c739e1e496b5ae607db882536ef4093dcf81f410a4508a7cb894061f1360054","name":"validator_outputs_r377-posthoc_diff.exec.json","bytes":792},{"sha256":"60e65ced3c8b5b41a263cf407cab3bfc80e4943b292715a8ddd6a4756fd15a81","name":"r377_data-w4_bins.txt","bytes":359029},{"sha256":"629da0c0b12177c7d32c164df2aabb054586368247c7c07db8b11734bfa67f02","name":"t3_recompute.out","bytes":5096},{"sha256":"6ce210e31016db972e1102b317482b7a648850bddd667366d69b2fce2b1a11e5","name":"t1_reproduce.out","bytes":3845},{"sha256":"6ff46fd2a874261a7c759f8de1ace5952d4583a77e953613076d430ff5f8cca7","name":"r377_regen.cpp","bytes":3112},{"sha256":"7605790c07d9713221788d2c271cd1f3c044e3266b72f87fceba8f620ae32e28","name":"t3_recompute.py","bytes":8699},{"sha256":"7a937655e33f6438e933f0670678b5f3f6afb87309f34c2b1ca7662f08bceac2","name":"r377_data-sd_1_bins.txt","bytes":367033},{"sha256":"812a4b375764447de70f5b7120d69cea5b478b32c80fbcc610f4365b5a4c6273","name":"r377_data-sb_2_bins.txt","bytes":359031},{"sha256":"8fe60b28900b4224025cea24a7b8bf00cd453260af220027dc91a553e06cc329","name":"validators-analyze.py","bytes":2339},{"sha256":"989da80aafe3083873d0b5309d2300616022fd66a488f300e698511d4edb1322","name":"r377_prereg.md","bytes":6458},{"sha256":"99ac73db1db780ae13c4f49fdae801945caaaaa122f90d20dfb1595c363c68f4","name":"r377_data-sa_1_bins.txt","bytes":367033},{"sha256":"9f2e697e2bbf0b2b537c0f821379c804c30b3a8cb508af5cbddfd35d7fd199e1","name":"validator_outputs_r377-regen_all_run1.exec.json","bytes":886},{"sha256":"a246fd6cd1a57a57b9cbfef591583ae46cba9e5c213c6d90b64ce7efab3383b5","name":"validator_outputs_r377-analyze2.exec.json","bytes":788},{"sha256":"a77d94a9f5007587f14efef9b2a4f09ec4c351940b4d9d39a85870ecc7ba504a","name":"r377_data-data_manifest.json","bytes":9419},{"sha256":"ad434b4e6354331869b2bb7b86e2650a1d1df777404b21be41d549a2c278078c","name":"validators-posthoc_diff.py","bytes":1363},{"sha256":"b31d1dcc2cfce87ce5a7288661f39124ddf4776c30333b04b919c87407f9a709","name":"r377_data_to_txt.py","bytes":1791},{"sha256":"b6dfac596749453df4a1f9ec968bf9e4e5f1ffa122cd85cf9883f61f26132028","name":"r377_data-w1_bins.txt","bytes":359030},{"sha256":"b8c4f5fba36f452626c459edc140109a1be3d47419703213e2604bb9b3df6695","name":"t1_reproduce.py","bytes":7255},{"sha256":"bb43915c68131b1f75173a6a8b7aac4ef954623a6d350a57894a64b1cbd2e861","name":"validators-score2.txt","bytes":675},{"sha256":"bc5b03946a3d8417f3a01bcb9d887c19ecbd8b49800587c849c0599708eac361","name":"r377_data-w3_bins.txt","bytes":359029},{"sha256":"bdc10937a080f1ecfafcd8aa9a6f3f6fcdcc7d8bf6b8b714ff11ece9030deb8f","name":"t4_stats.out","bytes":10996},{"sha256":"bed5905d9f72df7c360ee5f506304e9065e9d83292cbae7d0f8e8c7095dec215","name":"validators-analyze2.py","bytes":1791},{"sha256":"c2218fab7cf97ced94b933acf0d989092d9d44c2e42fc5b7e7f9f0dc94b2e8d6","name":"t6_spotcheck_sieve_dense.py","bytes":2597},{"sha256":"c257e4bf9350ad6713ebc27bdbd4a8eb5ca5fa1ba4abea51a4c56b59ce028db6","name":"r377_regen_all.out","bytes":3683},{"sha256":"cb22bf4d00dc7bf910824822ac9f9f0c2b5804550c37709953826bee4d3f23cd","name":"t6_spotcheck_sieve_dense.out","bytes":95203},{"sha256":"cd7f87f25db9caadb6e6114e0063a535174ab97bf10858426b76160bde7bd8f3","name":"validators-prediction2.sha256.txt","bytes":82},{"sha256":"d6addf64ac8820fc358a24c9907f4562210738bc322da7020c75e0602537e74d","name":"r377_regen_all.sh","bytes":1041},{"sha256":"d6fc7c8f967e59f3c4f4ac4a977642d52f605562217aaa0fa66f83035116b933","name":"validator_outputs_r377-analyze.exec.json","bytes":788},{"sha256":"d79ed2dd9022a863902a9ddc9ed45ea17fbbb68fa469bc1eceb83474255ef65e","name":"validators-prediction.sha256.txt","bytes":81},{"sha256":"d8df3a68f872039ae39f568dfbe7d9d1be59895580c917a3fcc1c532fb64a889","name":"r377_data-sc_2_bins.txt","bytes":367033},{"sha256":"d93933de52744aee68658a8028f883e6750d2b2280789991e00c402d75c47df1","name":"validator_outputs_r377-regen_all_fixed.exec.json","bytes":889},{"sha256":"db237ff777bcf802ea7964aed43b8ef0073f6d84d1122147655aaa607211603f","name":"route377_6603_replication.md","bytes":3373},{"sha256":"df2ddd6383cbcf677ce6329294f1417a9538fd4ea88dc974713587e11657391b","name":"r377_data-sb_3_bins.txt","bytes":359031},{"sha256":"e651f4c03a364237dd23d4452102cde453cc04c30cc0cf599bb02960b1fd29b9","name":"r377_data-sa_0_bins.txt","bytes":367033},{"sha256":"eba6b0f449afaf7b3f9d4c6c2be91281ac3e2139c9ef3e419a2667c0c4ee58a6","name":"r377_recheck.out","bytes":3929},{"sha256":"f213cd0497efa54424f0d873cde24eb8f44c40dac079e92e9c858c58dd3c85e2","name":"validators-pairbins.cpp","bytes":1746},{"sha256":"f30155ead03bbbf9fd61269b2b34252eb661e40c4a64e5dbac8388d5578d306e","name":"t6_spotcheck_sieve.out","bytes":7289},{"sha256":"f6520554c35c5367b1efab1de1e4bfda64f7af087fd5bbbec4af19debbbf388a","name":"r377_data-w6_bins.txt","bytes":367031}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"cc4f184c42dc9e8806b804262ed654cdcbbe8382474851ba45d63d4943b6d512","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}