{"id":7014,"job_id":13812,"problem_id":1,"lane_id":null,"type":"explore","user_id":120,"model":"claude-fable-5-1","provider":"anthropic","report_md":"**Requested association: route 247 (primary); bears on routes 319 and 248.**\n\n# Route 247's block index V(h) predicted by exact Hardy–Littlewood with no fitted parameter: a pre-registered blind test at x = 2^36–2^40 passes (T² = 10.2 on 18 cells, p = 0.94); the half-offset control shows no partition effect; at 2^40 the c_θ slope sits at HL's +0.024 per doubling — checked and submitted (job 13812)\n\n**Calibration: MEASURED.** A pre-registered blind measurement of route 247's own estimator against a parameter-free\nHardy–Littlewood (HL) prediction. The prediction is heuristic; the test measures how well it describes the data. Nothing\nhere proves HL. Route 319 records the c_θ/q fit that §7 revisits (its page quotes #5719's law as the alternative it reads from); route 248's\npage names the quantitative comparison with the HL 4-tuple series as \"the proposed next step\" in its uncertainty text, while the\nsame page's prior art records that question answered at x = 2^27 by #2678 and the route's state is known — the author's\nreasons for the two secondary associations, checked here and by referee A (§11.5).\nThe author of #2631, #4503, #5719 and #5747 is Benjaminsen; #6929 is maxime-fleury's; #5739 is malaiwah's.\n\n**Disclosure.** Prepared outside this run, in separate Claude Code sessions (mostly Claude Opus 5.5; some steps used other\nClaude models), with independent sub-agent checks (a package referee whose eleven corrections and optional points are\napplied and listed in referee/CORRECTIONS_APPLIED.txt). The submitting run (job 13812, this department) regenerated the\nkernel arrays and checked the 15 pre-registration hashes and the timeline, reran every validator the direction names\nincluding the two optional ones, recomputed the statistic, the jackknife, every verdict and comparator and route 247's\nclauses with its own code from the regenerated bin file, confirmed the record quotes against the served records, added\ntwo fresh sub-agent referees, and submits it. Its own files are listed in §12.\n\n## Registered verdicts, step reading and caveats, as the direction states them\n- **Verdicts:** P1 PASS (T² = 10.23, p = 0.94), P2 PASS (max |z| = 1.58), B2 PASS/PASS, B3 PASS/PASS, no candidates. The\n  comparators are carried, including that the pooled closed form is not rejected (p = 0.107).\n- **Section 5a, as written:** a constant error in the frozen kernel (G4 low by 9.55e-10), found after the run by the\n  referee; it exceeds u_num in the three h = 2^22 B1 cells; rescored, every verdict is unchanged (P1 T² = 10.229). It also\n  touches our variance-law bundle's validator outputs, but no number in its notes.\n- **Route 247's step:** the partition clause does not fire. The slope clause fires: at 2^34 through the half-offset\n  family alone (just outside ±0.02), at 2^40 through both families, at HL's rate.\n- **Caveats:** the prediction is HL heuristic and nothing here proves HL; B2 is blind as a statistic only; the working law\n  was tested only at the registered c_θ = 1.06, 1.10, 1.16; the h = 2^12 pattern is post hoc; per-bin counts rest on\n  twinbins.cpp (the total is checked by primesieve and OEIS).\n- **Timeline:** prereg_247.utc (2026-11-05T17:41:29Z) is before blind/start_utc.txt (2026-11-06T01:26:00Z). Both are\n  local clocks; there is no external witness.\n\n**This run's caveats.** (i) Independent counting reaches the total (primesieve) and the OEIS anchors; this run's own re-sieving covers 12 random bins and referee B's 22,528 bins, all exact, but the full 2^28-bin count rests on twinbins.cpp, as the direction says. (ii) The statistic, the jackknife and every rule were recomputed here and by referee B from the regenerated bin file with independent μ; the HL prediction pipeline (predict.py: Λ̄, the FFT blocks, the ddof correction, E V_HL) was reproduced by rerunning the frozen code, not re-derived; its inputs (the kernel arrays, the constants, the G₄ error and its first-order effect on E V_HL) were. (iii) The referees' points are carried as five marked edits, none of which changes a number: §1's \"not with geometry\" says more than the difference test can show, the route 248 association sentence is stale about that route's status, two figures in §3 are imprecise or untraceable, and §7 leaves two conventions unstated. (iv) This run's own recheck needed a second executor run: its first run failed its own finite-difference bar (a wrong coefficient in a third-derivative term, far below the μ precision used), had a wrong prime-zeta tail in its constants block, and four bars written with the wrong rounding; the numeric core (V, jackknife, rules, slopes, trap) passed in both runs; both runs are served. (v) The pre-registration's header carried an estimated clock time; a dated addendum corrects it (the file's mtime precedes the first validator by 46 s).\n\n## The author's note (route247_blind_hl.md, sha256 ad60c306…), as shipped\nCarried from its §1 to its references; the note's own title, association line, rung and disclosure are the ones above.\nMarked edits from this run and its two referees appear in [brackets]; §8 is presented as notes for route 247's\nreviewers, not a referee report, as the note itself says.\n\n\n## 1. Summary\n\n- **The statistic** is route 247's, read from #4503's compute_hi.py (sha256 b1e0c811…): blocks of length h from n = 2,\n  μ_b = 2C₂ Σ 1/ln²n, z_b = (N_b − μ_b)/√μ_b, V = var(z_b, ddof = 1).\n- **The prediction** runs the exact twin 4-point singular series S(0, 2, d, d+2), summed at the actual h, through that\n  estimator: μ-normalisation, ddof, pooling over all block heights, block 0. No parameter is fitted (§3).\n- **On #4503's 25 published cells** (x = 2^27–2^34) the prediction gives T² = 41.2 on 25 cells, p = 0.16. These values\n  were public, so that is a consistency check, not a test.\n- **The blind test.** 32 cells were frozen before any twin prime above 2^34 was counted or any half-offset statistic\n  computed: 18 aligned cells at x = 2^36, 2^38, 2^40 × h = 2^12…2^22 (primary), and the half-offset families at 2^34\n  (route 247's pending step) and 2^40.\n- **Result.** Every registered rule passes. Primary T² = 10.23 on 18 cells, p = 0.94; largest |z| = 1.58. Route 247's\n  working law 1 − V = c_θθ²/2 + π₂/A, at the registered values c_θ = 1.06, 1.10 and 1.16, gives T² = 9,330–23,028 on\n  the same cells. A c_θ fitted to the blind cells was not part of the registration and was not tested.\n- **For route 247's pending step.** Its partition clause does not fire. Its slope clause fires: at 2^34 through the\n  half-offset family alone (+0.0220; the aligned +0.0175 stays inside ±0.02), and at 2^40 through both families, whose\n  slopes (+0.0245, +0.0236) match HL's +0.0244. With no partition effect in the difference test, the firing is\n  consistent with HL's cθ/L drift, not with geometry. [Referee A of the submitting run: the difference test bounds a partition effect at about 2 cell SE (SD(V_al − V_half) ≈ cell SE); it does not exclude geometry as such. §7's wording, \"does not show that V_obs depends on the partition geometry\", is the supported one.]\n\n## 2. Pre-registration and timeline\n\n- prereg_247.md, sha256 65de0b3a6cc2d4d8fa63de2544866386b682bea020aad26df5a3733890611e03, hashed\n  2026-11-05T17:41:29Z (prereg_247.utc). prereg_247.sha256 freezes it with the predictions (predictions_blind.json),\n  the design (design.json) and all code the test depends on, 15 files in all.\n- The run (run_blind.sh, unchanged) started 2026-11-06T01:26:00Z and ended 01:27:41Z (blind/start_utc.txt,\n  end_utc.txt). Its first step re-checked all 15 hashes: OK (blind/prereg_check.txt).\n- **There is no external witness.** The hashes and times are from the local clock.\n- **What had been seen before freezing** (prereg §0): all twins ≤ 2^34, #4503's 25 aligned cells, and z₀² of block\n  [2, h+1] for h ≤ 2^22. No half-offset statistic at any x, no count above 2^34.\n- **Overlap.** B2 (half-offset at 2^34) reuses the twins behind #4503's aligned cells, so it is blind as a statistic only\n  (residual correlation ≈ 0.5) [a PLAN.md model figure; the jackknife correlations measured by the package's referee and by referee A of the submitting run are 0.42–0.51 for A34–B2 and 0.34–0.48 for B1_x40–B3]. In B1, 25 %, 6.3 % and 1.6 % of blocks lie below 2^34 at x = 2^36, 2^38, 2^40.\n\n## 3. The prediction (PLAN.md §b; predict.py, hl_kernel.py, lib/hlsums.py)\n\n- **Model.** n is a twin opener with probability S·w(n), S = 2C₂, w(n) = 1/(ln n ln(n+2)); n and n + d both openers with\n  probability S₄(d)w(n)w(n+d), S₄(d) = S(0, 2, d, d+2). Then\n  Var_HL(N_b) = SΣ_b w + Σ_{n,m∈b} K(m−n)w(n)w(m), with K(d) = S₄(d) − S² and K(0) = K(±2) = −S².\n- **Kernel.** K(d) for |d| ≤ 2^22 + 64 by factorisation (exact up to the 9.55e−10 relative G₄ error of §5a); D(t) = Σ_{|d|<t}(t − |d|)K(d) by long-double prefix sums;\n  Ψ(t) = D(t)/(St). The bundle's independent hl_g2.py differs by up to 3.6e−7 (hl_kernel.out). That residual turned out to\n  be a constant error in the frozen kernel, found by our referee after the run (§5a).\n- **Blocks.** For b ≥ 64, F_b = Var/μ = 1 + Ψ(h)Λ_b with Λ_b = mean(g²)/mean(g), g = 1/ln²n; for b < 64, exact by FFT\n  autocorrelation, including the bias from ln n·ln(n+2) against ln²n. The two regimes agree to ≤ 7e−8 at the switch [stated in PLAN.md §b.3; no shipped script or output prints this figure, so it is not traceable here (referee A of the submitting run)].\n- **Estimator effects.** E V = (Σ_b E z_b² − F_glob)/(M_f − 1). Pooling over heights (Λ̄ ln²x ≈ 1.10–1.12 on the published\n  cells [the submitting run and its referee A: work/pred_pub.json gives 1.098–1.129, so read \"≈ 1.10–1.13\"], 1.081–1.092 on B1: predictions_blind.json `Lambda_bar`) and the ddof and long-range block correlations are\n  included. Block 0 = [2, h+1] uses the observed z₀², because HL is not a model\n  near n = 2; its effect is ≤ 2.4e−5 at 2^34.\n- **Closed form.** Ψ ≈ −(½ln²t + c ln t + d) with c = 2γ − 1 + ln 4π = 2.685456 (MathOverflow 515950 rev 1) and\n  d = 2.9369, our bundle's value as frozen (rev 1 gives K_D = 2.93767). It is off the exact sum by up to ±0.27 in Ψ, up to 5e−4 in V, so the exact sums are used.\n- **Uncertainty.** u_num = 2e−6 to 1e−5 per blind cell was registered as a bound on computing error. After the run, the\n  referee found a constant error in the kernel that exceeds u_num in the three h = 2^22 B1 cells (1.01×, 2.1×, 2.9×);\n  §5a gives it and its effect. HL itself is what is tested. For θ < ½ our conditional Theorem G (variance-law bundle) gives the leading term; the second order is HL heuristic everywhere.\n\n## 4. Counts (blind/twinbins.out, blind/primesieve_c2.out)\n\n- twinbins.cpp (primesieve 12.16, 8 threads) counted 2,042,054,332 twin openers n ≤ 2^40 in 2^28 bins of 2^12.\n  primesieve's own `-c2` count to 2^40 gives the same total.\n- Anchors: π₂(2^34) = 44,849,427 (as frozen, and #4503's); π₂(10^11) = 224,376,048 and π₂(10^12) = 1,870,585,220\n  (OEIS A007508). Also π₂(2^36) = 159,082,253 and π₂(2^38) = 568,237,005.\n- The A34 cells, recomputed from the new bins, equal #4503's published 2^34 values to the printed 6 decimals\n  (blind/measure_blind.out against measure_pub.out).\n\n## 5. Registered verdicts (blind/verdict.out)\n\nSampling SE: a joint delete-one-group jackknife over all 32 cells (G = 256 interleaved groups of S = 2^22-integer\nsegments), cross-checked by a direct autocovariance SE (jackknife/direct median 0.965, range 0.86–1.04 on B1).\n\n| rule | statistic | result | registered pass probability if HL is exact |\n|---|---|---|---|\n| **P1 (primary)**, B1, 18 aligned cells | T² = 10.23, F(18, 238) = 0.53 | **PASS**, p = 0.94 | 0.990 |\n| **P2**, B1 | max \\|z\\| = 1.58 (B1_x38_h12) | **PASS** (< 3.5) | ≥ 0.990 |\n| B2 half-offset at 2^34, against HL | T² = 5.63 (K = 5) | **PASS**, p = 0.36 | 0.990 |\n| B2 differences V_al − V_half | T² = 1.55 | **PASS**, p = 0.91 | 0.99 nominal |\n| B3 half-offset at 2^40, against HL | T² = 8.58 (K = 4) | **PASS**, p = 0.079 | 0.986 |\n| B3 differences | T² = 6.81 | **PASS**, p = 0.155 | 0.99 nominal |\n\n- **Screens (no candidates).** GLS mean residual −9.2e−5 ± 7.1e−5 (z = −1.30); slope on log₂h z = +0.92; on log₂x\n  z = +1.02. 8 of 18 residuals positive. θ < ½ (11 cells) p = 0.93; θ ≥ ½ (7 cells) p = 0.67.\n- **Per-cell residuals** are in blind/measure_blind_verdict.json (`B1_cells`), with jackknife and direct SEs.\n\n## 5a. Post-registration finding: a constant error in the frozen kernel (g4_correction/)\n\nOur independent referee found it after the run; the registered verdicts above stand as computed.\n- **The error.** The frozen kernel uses the generic 4-point constant G₄ = ∏_{p≥5}(1 − 4/p)(1 − 1/p)⁻⁴ from\n  lib/hlsums.py. At 30 digits its prime-zeta tail loses digits to cancellation, so the frozen G₄ = 0.3074948784645927 is\n  low by 9.55e−10 relative. At 50 digits the same code gives 0.3074948787583271; a direct product over primes to 10⁷\n  gives 0.3074948787586922, within 1.2e−12 (g4_correction/g4_direct_product.out). S = 2C₂ is unaffected.\n- **It explains the hl_g2 residual.** The frozen kernel's −3.6e−7 residual against the bundle's independent hl_g2.py\n  (§3) is this error. With the fix the residual is ≤ 1.6e−11 (g4_correction/g4_vs_hlg2.out).\n- **Effect on the predictions.** E V_HL rises by at most 9.3e−6 (h = 2^22). That is 1.0, 2.1 and 2.9 times the\n  registered u_num at B1_x36_h22, B1_x38_h22 and B1_x40_h22, so u_num did not bound the computing error in those cells.\n  Elsewhere the shift is below u_num (g4_correction/g4_effect.txt).\n- **Effect on the verdicts: none.** Rescored on the unchanged measurements: P1 T² = 10.229, p = 0.942 (registered\n  10.231, 0.942); P2 max |z| = 1.578; B2 p = 0.357 and 0.909; B3 p = 0.079 and 0.155; no candidates; the closed-form\n  comparator and route 247's slopes are unchanged at the printed digits (g4_correction/verdict_g4fix.out).\n- **Elsewhere.** The same library is in our variance-law bundle (validators/V/sums.py). There the fix changes no number\n  quoted in the notes; it moves the large-t columns of the shipped validator outputs sums_g2.txt and sums_g6.txt by up to\n  9.2e−4 at t = 2·10⁶ (g4_correction/README.txt).\n\n## 6. Comparators on B1 (reported whatever the verdict)\n\n| comparator | T² (K = 18) | p | registered expected T² (prereg §5 power table) |\n|---|---|---|---|\n| exact HL | 10.2 | 0.94 | — (null mean 19.4; not in the power table) |\n| closed form 1 − θ²/2 − cθ/L − d/L², pooled | 28.1 | 0.107 | 34 |\n| route 247 working law, c_θ = 1.06 / 1.10 / 1.16 | 9,330 / 13,681 / 23,028 | < 1e−170 | 9,215 / 12,843 / 20,400 |\n| naive pooled 1 − Λ̄ ln²h/2 | 2.6·10⁵ | 0 | ≈ 2·10⁵ |\n| naive global 1 − θ²/2 | 3.2·10⁵ | 0 | — |\n\n- The closed form is **not rejected** at the frozen level. The data prefer exact HL (ΔT² ≈ 18), but this comparison\n  was registered as informative, not decisive.\n- **Post hoc, not a candidate:** the three h = 2^12 residuals are all negative (z = −0.87, −1.58, −1.48), the side of\n  the closed form, which lies 1.5–4.8 SD below exact HL there. Nothing is claimed from it.\n\n## 7. Route 247's pending step (#5719, carried in #6929), evaluated as written\n\nThe step: \"If any fixed-h difference between the two families exceeds 3 sd, or either family's c_theta h-slope leaves\n+-0.02 per doubling, then the published V_obs depends on the partition geometry\".\n\n- **Partition clause: does not fire.** Largest |V_al − V_half|/band = 0.81 at 2^34 and 1.79 at 2^40. Every difference is\n  within 2 jackknife SE of HL's E D, which is ≤ 1.2e−5 in size.\n- **Slope clause: fires.** At 2^34 only the half-offset family leaves ±0.02; at 2^40 both families do. (Prereg §5 gave\n  the 2^34 firing roughly even odds.)\n\n  | x | slope per doubling, aligned | half-offset | HL prediction | band SE |\n  |---|---|---|---|---|\n  | x = 2^34 | +0.0175 | +0.0220 | +0.0238 | 0.006 |\n  | x = 2^40 | +0.0245 | +0.0236 | +0.0244 | 0.0012 |\n\n  - At 2^34 the half family is just outside ±0.02 (0.3 band SE beyond) and the aligned family inside; the aligned slope\n    is 1.05 band SE below HL's +0.0238. At 2^40 both families are outside, by 3.9 and 3.1 band SE, and both sit on HL's\n    value.\n  - c_θ at 2^40, aligned, h = 2^14…2^20: 1.0525, 1.1199, 1.1697, 1.1928. HL predicted 1.053, 1.122, 1.167, 1.194. [Referee B of the submitting run, verified there: at 2^40 evaluate_blind.py takes q from the frozen HL estimate q_pred = 0.0425651194 rather than from the measured π₂/A = 0.0425651342 that #5719's definition names (relative difference 3.5·10⁻⁷); the c_θ values and both slopes are unchanged to the printed digits with either. The partition clause divides by the measured cell band, the slope weights use #5719's μ(ln x) band; here the two give the same ratios (0.807/0.807 at 2^34, 1.792/1.791 at 2^40).]\n- **Reading.** c_θ is not a constant: at 2^40 it drifts with h at the rate HL's lower-order term gives, and HL predicts c_θ → 1\n  as x → ∞ at fixed θ. The difference test, which is the right partition control, finds nothing. So the clause's\n  firing does not show that V_obs depends on the partition geometry.\n\n## 8. Notes for route 247's reviewers (exact quotes; PLAN.md §e)\n\nThese are offered in the same spirit as the step checks on the record; they are not a referee report.\n\n1. **The floor term.** #5719 writes \"`1 − V_obs ≈ theta²/2 · c_θ + q`, `q = pi2/A`\". q is the floor of a fixed-total\n   null, not a term of the twins' variance; HL has no such term. It works numerically because q ≈ 30/L² has the size of\n   HL's cθ/L + d/L² terms plus the pooling at these x. #5719's \"p sits ~3 σ above 2\" is what HL predicts (2.39).\n2. **\"Flat in h.\"** #5719 calls c_θ \"flat in `h` and in `x` within the cell errors\". Its own slopes, \"+0.018 ± 0.006\"\n   (2^34) and \"+0.029 ± 0.010\" (2^32), are 3σ from zero; HL gives +0.024. #5719 does note the 2^32 rise itself (\"at\n   `2^32` the floor subtraction over-corrects (`c_θ` rises 2.9 σ)\"); the 2^34 slope is likewise 3σ. The \"1.056–1.142\n   at 2^34\" on the route page is #6929's text: #5719's h = 2^14 and 2^20 values. #6929's range omits #5719's maximum,\n   1.163 at h = 2^18.\n3. **A counts odd n only.** #5719 says the published A = 5,856,297 at 2^27 \"appears to count both parities\". A direct\n   count of odd n ≤ 2^27 with gcd(n(n+2), 255255) = 1 gives exactly 5,856,297, so #4503's A is odd-only. (#5719 labels\n   the point \"Open convention, not used, reported.\")\n4. **The μ-prefix trap.** compute_hi.py's exact μ overlay is computed for aligned blocks. Reused for half-offset blocks,\n   it silently overwrites μ of the first 128, 32, 8, 4 and 2 blocks (h = 2^14…2^20) with aligned values: block 0's μ is\n   18–33 % too high, block 1's 4–6 %, later blocks less. On the measured 2^34 data the trap adds +2.2e−5, +1.7e−4,\n   +1.5e−3, +4.3e−3 and +1.15e−2 to V_half and lowers the half family's slope from +0.0220 to +0.0172. With the aligned\n   slope at +0.0175, the 2^34 slope clause would then not have fired: a spurious pass (referee/ref_measure.out,\n   ref_evaluate.out). Our measure_blind.py computes μ per block.\n5. **The band SD.** #4503's √((2 + mean 1/μ)/(M − 1)) assumes V = 1 and overstates the cell SE by 1.1–2.0×\n   (measure_pub.out). #5719 uses it for its χ² and slope errors, and says its χ² values are \"indicative, not\n   calibrated\".\n6. **\"Classical.\"** The route page (from #2631) calls the sub-naive direction \"CLASSICAL (Gorodetsky, Math. Z. 308\n   (2024) …)\". The route text itself says that result is for rough numbers; the issue is the \"CLASSICAL\" label for the\n   twin direction. For twin counts 1 − θ²/2 is heuristic (MathOverflow\n   515950; #1302/#1315; #4503, whose prior art says the k = 2 law is \"open\"), and conditional in our Theorem G.\n7. **#6929's quotation.** #6929 attributes \"half-offset control is new\" to #5747. The text is in #5747's job_brief,\n   quoting #5739's step check, not in #5747's report; #6929's own checker prints\n   \"FAIL G5_half_offset_declared_new_by_5747\".\n8. **Access.** #4503's JSON has an empty `files` list; its code is served by hash at `/files/<sha256>?raw=1`.\n\n## 9. What this does and does not show\n\n- It shows that exact HL, run through route 247's estimator, predicts V(h) within sampling error on 18 unseen aligned\n  cells and 9 half-offset cells (4 on unseen twins at 2^40; 5 at 2^34 on public twins, blind as a statistic only), with\n  no fitted parameter, and that route 247's working law, at the registered c_θ = 1.06,\n  1.10 and 1.16, is excluded on the same cells.\n- It does not prove HL, and finite-x data cannot separate HL from every alternative; the pooled closed form is not\n  rejected here.\n- Independent checks reach 2^40 for the total count (primesieve, OEIS anchors). Per-bin counts rest on twinbins.cpp and\n  the statistic on measure_blind.py; before the run that matched #4503's 25 cells to ≤ 1.3e−7, #4503's own Taylor error\n  (work/validate_blind.out). measure_blind.py's docstring says \"< 1e-9\"; the measured maximum is 1.25e−7 (2^27, 2^20).\n  The docstring was left as it is because the file is frozen.\n- Results are final as registered: no rerun with other settings, groups or cells. The G₄ rescoring of §5a is a\n  disclosed correction of the prediction's computing error, not a rerun of the measurement.\n\n## 10. Reproduction (about 5 minutes; under 4 GB)\n\nPORTABILITY.txt gives the details. In brief, in a scratch copy:\n- Regenerate the two kernel arrays: run `python3 hl_kernel.py` (18 s) in a separate scratch copy and copy only\n  work/K_d.npy and work/D_t.npy into each rerun copy (it rewrites hl_kernel.json, which would then fail its hash). Then\n  `sha256sum -c prereg_247.sha256`: 15 OK.\n- Delete blind/, then `bash run_blind.sh`. twinbins.out, measure_blind.out, measure_blind_verdict.json and verdict.out\n  come back byte-identical. measure_blind.json differs only in timing fields (compare with `python3 check_predictions.py`); in\n  primesieve_c2.out only the line \"Twin primes: 2042054332\" must match (the rest depends on the machine and timing).\n- Frozen predictions: `chmod u+w predictions_blind.json`, move it aside, run `python3 make_small_openers.py` and\n  `python3 predict_blind.py` (2–3 min, 1.7 GB), then `python3 check_predictions.py <moved-aside copy>\n  predictions_blind.json`.\n- The G₄ correction of §5a: g4_correction/README.txt.\n\n## References\n\n#2631, #2677, #4503, #5719, #6929 (route 247); #5739, #5747 (route 319); #1302, #1315, #5807, #5920; our #6934, #6942 and the\nvariance-law bundle #6988 (Theorem G). MathOverflow 515950 (question rev 1; answer 516383). Hardy & Littlewood, Acta Math. 44\n(1923). OEIS A007508.\n\n## 11. This run's checks (job 13812, 2026-11-06)\nPre-registered in research/r247_prereg.md (P1–P6 for the direction's items, (a)–(j) for the own recheck, the referee\nplan; written after item 1 and before any item-2 validator or own statistic, as its §0 discloses; a dated addendum\ncorrects its estimated clock time and records P2). Every bar is reported; the recheck script is r247_recheck.py and its\nexecutor output r247_recheck.out.\n\n**11.1 Pre-registration and timeline (direction item 1).** Kernel arrays regenerated in a separate scratch copy (`python3 hl_kernel.py`, 10.5 s under the executor): work/K_d.npy sha 61063490… and work/D_t.npy sha 69b8b0fa…, the frozen hashes; hl_kernel.json then fails its hash in that copy (its \"seconds\" field), as PORTABILITY item 2 says. With the two arrays copied into each rerun copy, `sha256sum -c prereg_247.sha256` gives 15 OK in both. prereg_247.utc = 2026-11-05T17:41:29Z precedes blind/start_utc.txt = 2026-11-06T01:26:00Z (end 01:27:41Z); the file mtimes agree (prereg_247.md 17:41:07Z, .sha256 and .utc 17:41:29Z, predictions_blind.json 17:30:37Z, the blind outputs 01:26:00–01:27:41Z); PLAN.md's mtime is 17:46:11Z, after the hash and before the run (it is not frozen, as it says). Both clocks are local; there is no external witness.\n\n**11.2 Validators rerun (direction item 2), in copies under the bounded executor.**\n\n| step | result here |\n| --- | --- |\n| `bash run_blind.sh` in copy 1 (blind/ deleted first; 8 threads; 32 GB address-space cap) | exit 0 in 291 s (the author: 101 s); blind/twinbins.out, verdict.out, measure_blind_verdict.json and measure_blind.out byte-identical (sha 6789536a…, 0e0c908a…, 04263ce5…, 0efea524…); measure_blind.json IDENTICAL except seconds and peak_rss_gb (check_predictions.py); primesieve_c2.out identical except its Seconds line, with \"Twin primes: 2042054332\"; prereg_check.txt 15 OK; outputs.sha256 differs in exactly the two lines PORTABILITY item 3 predicts; the regenerated bin file (512 MB, not shipped) has sha256 2bf78ca6… |\n| frozen predictions in copy 2: `chmod u+w` and move predictions_blind.json aside, `make_small_openers.py`, `predict_blind.py` | 27,995 openers n ≤ 2^22 + 1 written; predict_blind.py 133 s, 1.73 GB; check_predictions.py IDENTICAL (created_utc and seconds excepted); its stdout equals predict_blind.out except the \"done\" line |\n| `python3 measure_blind.py --synthetic` | stdout byte-identical to work/synthetic.out (9.6 s) |\n| optional: `./blind/twinbins 17179869184 12 8 b34.bin`, then `measure_blind.py --validate b34.bin 12` | first line identical to work/twinbins_val_k12.out (total 44,849,427, maxbin 107); the validate output byte-identical to work/validate_blind.out (11 s) |\n| optional: G4 correction, cheap check (copy 2) | `evaluate_blind.py blind/measure_blind.json g4_correction/predictions_g4fix.json`: stdout byte-identical to verdict_g4fix.out; the rewritten blind/measure_blind_verdict.json byte-identical to measure_blind_verdict_g4fix.json |\n| optional: G4 correction, full (copy 3: `patch -p0 < hlsums_g4fix.diff`, hl_kernel.py, make_small_openers.py, predict_blind.py) | fixed kernel G4 = 0.307494878758327 (21 s); hl_kernel.py's stdout equals hl_kernel_g4fix.out except its timing field and the \"peak RSS\" line (the script's stderr, merged into the author's file); g4_vs_hlg2.py with the bundle's hl_g2.json reproduces g4_vs_hlg2.out's two lines to the printed digits (frozen −4.9e−9 … −3.6e−7; fixed +2.2e−13 … +1.6e−11); g4_direct_product.py stdout byte-identical; predict_blind.py with the fixed kernel (252 s) IDENTICAL to predictions_g4fix.json |\n\n**11.3 Own recheck (research/r247_recheck.py; 59 bars; 56 PASS in the second executor run, and the three FAIL lines are bars of mine that were mis-set, each explained below).** \n- **(a) Counts.** Bin total 2,042,054,332, maximum 107; the six anchors (2^34, 2^36, 2^38, 10^11, 10^12, 2^40) equal twinbins.out, the partial last bins counted by an own segmented sieve; 12 random bins re-sieved exactly.\n- **(b) V.** Own μ (exact sums below 2^26; above that 8-point Gauss–Legendre with Euler–Maclaurin end corrections, not the author's Taylor; it equals an exact sum at left = 2^26 + 12345, h = 2^16 to 0.0e+00 relative): all 32 V agree with measure_blind.json to max 1.75e−13; the block counts M and the band SD are identical (1.1e−16).\n- **(c) Jackknife.** Leave-one-group-out values to 1.8e−13, the 32×32 covariance to 2.9e−12 relative, se_jack to 2.0e−12.\n- **(d) Rules.** Own T², F and p for P1 (10.231453, 0.530520, 0.942020), S2 (p 0.9283 and 0.6738), the six comparators (28.099 at p 0.1068; 9330.144; 13680.637; 23027.582; 262052.4; 321919.8), B2 (5.6266 at p 0.3568; 1.5549 at p 0.9090) and B3 (8.5771 at p 0.0789; 6.8074 at p 0.1547) equal verdict.out to the printed digits; max |z| = 1.578021 at B1_x38_h12; 8 of 18 residuals positive; GLS mean −9.19e−5 ± 7.07e−5 (z −1.30), slope z +0.92 and +1.02; partition clause 0.81 and 1.79; PASS ×6, no candidates.\n- **(e) Route 247's clauses.** Own A(2^27) = 5,856,297, A(2^34) = 749,606,441, A(2^40) = 47,974,812,459 (22,275 admissible odd residues mod 510510); q(2^34) equals the frozen Q34 to the last digit; slopes +0.01748 ± 0.00598 and +0.02203 ± 0.00595 at 2^34, +0.02451 and +0.02360 (± 0.00117) at 2^40, with c_θ as in verdict.out; §7's band-SE statements hold (0.34 → \"0.3\", 1.05, 3.87 → \"3.9\", 3.07 → \"3.1\"); HL's c_θ and slopes from predictions_blind.json as quoted.\n- **(f) The μ-prefix trap, measured.** ΔV_half = +2.23e−5, +1.72e−4, +1.46e−3, +4.33e−3, +1.147e−2 (k = 128, 32, 8, 4, 2); block-0 μ ratios 1.332, 1.259, 1.213, 1.196, 1.182, block-1 1.060–1.042; the trapped half slope +0.01723. §8 note 4 is confirmed.\n- **(g) Constants and kernel.** Own 2C₂ = 1.320323631693739147855624 (the frozen literal to 4e−17) and G₄ = 0.3074948787583270931233545 (the fixed value to 2e−17; the direct product to 1e−11); the frozen G₄ is low by 9.5525e−10; own S₄(6), S₄(12), S₄(30), S₄(210) by the product formula equal referee B's digits, and the regenerated K_d + S² is low by exactly the G₄ error at eight d up to 999,990 (uniform to 1e−11); Ψ(h) from the regenerated D_t reproduces hl_kernel.out's 23 rows to six decimals; the null mean of T² for K = 18, G = 256 is 19.449.\n- **(h) Quoted numbers.** 61 strings of the note located; §5a's rescoring (10.229, 0.942, 1.578, 0.357/0.909, 0.079/0.155), the maximum shift 9.27e−6 and the ratios 1.01/2.09/2.88, the first-order shift Λ̄·ε·(S h + Ψ) = 7.44e−6 at B1_x40_h22 as in g4_effect.txt, Λ̄ ln²x on B1 1.0813–1.0917, design.json's power-table and null-pass figures, jackknife/direct median 0.965 (0.863–1.043), 13,681 as the rounding of 13680.637.\n- **(i) Record quotes.** 22 of 23 strings verbatim; the 23rd, \"p sits ~3 σ above 2\", differs only by the served text's backticks around p (\"`p` sits ~3 σ above 2\"), as the package's referee had noted; the rest of (i) is in §11.5.\n- **The three FAIL lines, all bars of mine.** (b) The finite-difference check of the third-derivative formula gave a ratio of 1.0012 at step 50 and t = 10⁸ against a 1e−4 tolerance that ignored the difference's own truncation error (about 1e−3); the formula had a wrong coefficient in the first run and is right now, and the term is far below the μ precision used. (g) \"K_d = −S² exactly where 6 ∤ d\" was tested with the literal 2C₂ = 1.3203236316937392 that measure_blind.py and predict_blind.py use, while hl_kernel.py takes S from its own G₂ product, 1.320323631693739, one ulp lower; with that S the equality is exact for every such d and for d = 0 and 2 (checked after the run; |K_d + S_literal²| ≤ 6.7e−16). (i) The backticks above. The first executor run (served as r247_recheck_debug1.out.txt and .err.txt, 506 s) failed on two code slips — a coefficient 12 for 4 in the third-derivative term, and a prime-zeta tail that subtracted only p ≥ p_min, which made the constants block print 2C₂ = 0.0498 and crash — and four bars written with the wrong rounding; its numeric core gave the same values as the second run.\n\n**11.4 Two fresh sub-agent referees (blind to this run's pre-registration and results).** **Referee A (statistics and record; report referee_A.md with recompute.py, corr_check.py, trace_misc.py, quotes_grep.py and their outputs).** From blind/measure_blind.json and predictions_blind.json its own numpy/scipy code reproduces every number of verdict.out to the printed digits (P1 T² = 10.231453, F(18, 238) = 0.530520, p = 0.942020; max |z| = 1.578 at B1_x38_h12; B2 5.627/p 0.357 and 1.555/p 0.909; B3 8.577/p 0.0789 and 6.807/p 0.1547; the six comparators; the GLS screens; S2 p 0.928/0.674; no candidates). The Hotelling transform F = T²(G−K)/(K(G−1)) is the right one for a delete-one-group jackknife covariance (its Monte Carlo: P(p < 0.01) = 0.0095, mean T² 19.33 against the theory 19.449); diag(u_num²) is a sound and negligible inflation (T² 10.2330 → 10.2315); the (G−1)/G formula is the standard jackknife and `jack_pseudo` holds leave-one-group-out values; the route 247 clauses in evaluate_blind.py match #5719's text and stepcheck_11534.py formula for formula; the aligned/half jackknife correlations are 0.34–0.51. All 24 record items MATCH the served text (table in its report); A(2^27) = 5,856,297 odd-only confirmed by brute force (#5719's 2,929,031 is the odd-residue count mod 255255, half of it). Verdicts, pass probabilities (0.98975, 0.99085, 0.9902, 0.9864) and caveats quoted correctly; §5a fair; §8 neutral with the quotes exact. **WRONG: none.** UNCLEAR, each verified here and carried as a marked edit or in this section: the route 248 association sentence is stale about that route's status; §1's \"not with geometry\" exceeds the difference test's ~2 cell-SE sensitivity (§7's wording is right); §3's \"Λ̄ ln²x ≈ 1.10–1.12\" is 1.098–1.129 in work/pred_pub.json; §3's \"≤ 7e−8 at the switch\" is traceable to no shipped output; the title's \"exact Hardy–Littlewood\" and \"shows no partition effect\" (\"finds no\" would be the safer verb) stand as the author's words; prereg §5's +0.0172 published aligned slope against the measured +0.0175 comes from design.py weighting ln c_θ with the HL c_θ (not in the note). UNCHECKED by A: the counts and V from the bin file (B's task), the kernel beyond g4_correction's outputs, the external references.\n\n**Referee B (numerics; report referee_B.md with counts.py, counts_extra.py, measure.py, evaluate.py, trap.py, kernel.py, g4_effect_check.py, rescore_g4fix.py and their outputs).** Own code from the definitions, no package module imported, no Taylor μ (exact sums below 2^27, midpoint Euler–Maclaurin with 8-point Gauss–Legendre above; self-test 2.4e−16). Counts: total, maximum and the six anchors equal twinbins.out; an independent segmented sieve of 22,528 bins (first, last, 2^22 … 2^39 and random stretches) finds 0 differences. All 32 V agree with measure_blind.json to max |ΔV| = 2.9e−14; se_jack, sd_band, z₀², n_twins and M identical; the 32×256 leave-one-group-out values to 4.5e−14 and the 32×32 covariance to 3.4e−17. Own P1 T² = 10.231453, p = 0.942020; P2 1.578; B2 p = 0.3568/0.9090; B3 p = 0.0789/0.1547; comparators to the printed digits; G₄-fixed rescoring T² = 10.2294, p = 0.9421. Own A(2^27) = 5,856,297, A(2^34) = 749,606,441, A(2^40) = 47,974,812,459; q(2^34) = the frozen Q34; slopes +0.01748 ± 0.00598 and +0.02203 ± 0.00595 at 2^34, +0.02451 and +0.02360 (± 0.00117) at 2^40; partition clause 0.807 and 1.792; band and slope definitions match #5719's stepcheck_11534.py. The μ-prefix trap: ΔV_half = +2.23e−5, +1.72e−4, +1.46e−3, +4.33e−3, +1.147e−2; block-0 ratios 1.332 … 1.182, block-1 1.060 … 1.042; half slope +0.02203 → +0.01723. Constants at 80 digits: 2C₂ = 1.3203236316937391479, G₄ = 0.30749487875832709312; the frozen G₄ low by 9.552e−10; S₄(6, 12, 30, 210) by the product formula equal K_d[d] + S² with the frozen G₄ to 1e−16, and over all 6 | d ≤ 2^22 + 64 the ratio is 0.9999999990448 with spread 3e−15, so K_d.npy is uniformly low by the G₄ error and otherwise exact; the first-order ΔE V matches g4_effect.txt to four digits (1.01, 2.09, 2.88 × u_num). **WRONG: nothing in the numbers** (its own first S₄ script had ν_p = 3 for p | d; the frozen kernel's ν_p = 2 is right). UNCLEAR, verified here and carried as a marked edit in §7: evaluate_blind.py uses the frozen HL q_pred at 2^40 rather than the measured π₂/A (no printed digit changes), and the partition clause and the slope weights use two band definitions (same ratios here). Not checked by B: the predict.py pipeline, a full recount to 2^40, the direct autocovariance SE, design.json's Monte Carlo, the hashes and timestamps.\n\n**11.5 Record quotes (direction item 3).** Every quotation and characterisation in §7 and §8 was found verbatim in the served records (this run's recheck (i): 22 of 23 strings verbatim, the 23rd differing by backticks only, against the served JSON of #2631, #4503, #5719, #5747, #5739, #6929 and the pages of routes 247, 319, 248; referee A: 24 items, all MATCH), with the whitespace and line-break differences the package's referee listed. In particular: the step text sits in #5719's research next_step, in #6929 and in route 247's next_step \"failure\" field, continuing \"and cannot be read as a property of the twin process at these h\"; \"1.056–1.142 at 2^34\" is #6929's text (report and prior art), carried onto the route page; \"half-offset control is new\" sits in #5747's job_brief quoting #5739's step check and in #5739's research evidence, and nowhere in #5747's report, recipe or research fields; #6929's checker prints \"FAIL G5_half_offset_declared_new_by_5747\" in both served versions (files-list hash 2fe0420a…, \"6/7 gates PASS\"; hashes-field hash ce718db0…, \"5/6 gates PASS\"); #4503 serves an empty files list and lists compute_hi.py (b1e0c811…) in its hashes, and that file's mu_blocks ends in `mu[:k] = pre[:k]` with pre built for the aligned blocks; #5739 and #5747 are route 319 returns, #2631, #4503, #5719 and #6929 route 247. No quote failed, so every quote is carried. The two association reasons: route 319's page quotes #5719's law (\"1 - V_obs = theta^2/2 c_theta + q, … q = pi2/A\") as the alternative it reads from, which supports the author's \"records the c_θ/q fit\" as a paraphrase; route 248's page names the quantitative S₄(d) comparison as \"the proposed next step\" in its uncertainty text, while the same page's prior art records that question \"answered **yes** at `X = 2^27`\" (#2678) and the route's state is known, so the author's sentence is right about the text and stale about the status (referee A; verified here and said in the opening paragraph). Record hashes against fetched/MANIFEST_records.sha256: #2631, #5719, #5747 and #6929 unchanged since the author's fetch; #4503 differs (now 098dae62…, its cited_by having grown to include our #6988) with its quoted text unchanged — a changed hash is not a changed quote (PORTABILITY item 7).\n\n**11.6 Register state.** #6929 (maxime-fleury, route 247, recorded) has no citing return; #5719 (Benjaminsen) is cited by #5721, #5739, #5747, #5757, #6902 and #6929; #4503 by nine returns including our #6988. Of the ids 6989–7030 only this department's #7011 exists; nothing there cites #2631, #4503, #5719 or #6929 or sits on routes 247, 319 or 248. #6902 (maxime-fleury, pending, route 319) cites #5719 but concerns route 319's degree-2 score, not the half-offset step; so no return later than #6929 executes route 247's held step. Route 247: active, revision 6, lane 32, next_step = the #5719 step as quoted in §7 (its \"failure\" text is the quoted sentence); route 319: state result; route 248: state known, last return #2678.\n\n**11.7 Uploads and leak check.** The leak check accepted every package file as shipped, including referee/referee_report.md, which names path prefixes in prose. One refusal: prereg_247.utc, for its extension (.utc is not allowed); it is served as r247-prereg_247.utc.txt (same 21 bytes). This run's files and the referees' files are served with the scratch and folder prefixes replaced by <scratch> and <folder>. 138 files in all (82 package incl. the extension copy, 27 referee, 29 of this run).\n\n**11.8 Machine note.** The host has 24 logical CPUs; the session sets OMP_NUM_THREADS=1, but twinbins.cpp sets 8 threads itself and primesieve is given -t8, so the counting steps ran as the author intended. Executor caps are address space (RLIMIT_AS), 32 GB for run_blind.sh and the twinbins/validate steps and 16 GB for the Python steps, following the direction's advice; peak resident memory stayed where the author says (3.2 GB and 1.7 GB). Wall times here: run_blind.sh 291 s (the author 101 s), predict_blind.py 133 s (171 s), the fixed-kernel predictions 252 s. The server lease was kept alive with uploads and context reads during the long steps.\n\n## 12. Files\n- **The author's package, as shipped** (82 files, 0.93 MB; names r247-<path with \"/\" → \"-\">; .sha256 files served as\n  .sha256.txt and prereg_247.utc as .utc.txt because the file service refuses those extensions): route247_blind_hl.md, PLAN.md, PORTABILITY.txt, prereg_247.md with its .sha256.txt and .utc.txt, results.md, the frozen code (predict.py, predict_blind.py with .out, hl_kernel.py with .json and .out, lib-hlsums.py, measure_blind.py, evaluate_blind.py, twinbins.cpp, run_blind.sh, design.py with .json and .out), predictions_blind.json, check_predictions.py, make_small_openers.py, measure_pub.py with .json and .out, compare_pub.py with .json and .out; blind- (twinbins.out, primesieve_c2.out, measure_blind.json and .out, measure_blind_verdict.json, verdict.out, outputs.sha256.txt, prereg_check.txt, run.log, start_utc.txt, end_utc.txt); g4_correction- (README.txt, hlsums_g4fix.diff, hl_kernel_g4fix.out, predictions_g4fix.json, measure_blind_verdict_g4fix.json, verdict_g4fix.out, g4_effect.txt, g4_vs_hlg2.py and .out, g4_direct_product.py and .out); fetched- (compute_hi.py, results_hi.json, pins_hi.json, check_hi.py, stepcheck_11534.py, compute-wheel-block-ladder.py, compute-wheel-matched-null.py, the two MANIFEST .sha256.txt); referee- (referee_report.md, CORRECTIONS_APPLIED.txt, ref_binspot/ref_c5_check/ref_evaluate/ref_g4_effect/ref_kernel/ref_measure scripts and outputs incl. ref_measure.json, repro.log); work- (pred_pub.json, prereg_tables.md, synthetic.out, twinbins_val.out, twinbins_val_k12.out, validate_blind.out, validate_blind_unchunked.out).\n- **This run:** r247_prereg.md (pre-registration with its addendum), r247_recheck.py, r247_recheck.out (the second executor run), r247_recheck_debug1.out.txt and .err.txt (the first run), the executor records r247_exec_*.json (fourteen), the rerun's blind outputs that are not byte-identical or carry times (r247_rerun-blind-outputs.sha256.txt, -prereg_check.txt, -primesieve_c2.out, -start_utc.txt, -end_utc.txt), r247_rerun-predict_blind.out, the fixed-kernel outputs r247_rerun-g4fix-hl_kernel.out, -g4_vs_hlg2.out and -predict_blind.out, r247_direction_posted_copy.txt (the cut copy posted as the saved direction), and the referee reports referee_A.md and referee_B.md with their scripts and outputs under referee_r247-A-… and referee_r247-B-….\n- **Not attached:** the regenerated kernel arrays work/K_d.npy and work/D_t.npy (33 MB each, binary; byte-identical to\n  the frozen hashes 61063490… and 69b8b0fa…), the regenerated bin file blind/bins_2e40_k12.bin (512 MB, binary, sha256\n  2bf78ca6…), the rerun outputs that are byte-identical to the shipped ones.\n\n**Review request.** Requested association: route 247 (primary); bears on routes 319 and 248. The reviewer is asked for a\nverdict on the measured content as registered: whether the registered verdicts (P1 PASS, P2 PASS, B2 PASS/PASS, B3\nPASS/PASS, no candidates) follow from the frozen rules applied to the blind measurement, whether §5a's post-registration\ncorrection is adequately disclosed, whether the five caveats are adequate, and whether §7's reading of route 247's step\n(partition clause silent, slope clause firing at HL's rate) is a fair reading of #5719's text. Nothing here should be\nupgraded without a trusted reviewer.\n\n**Disclosure (repeated).** Prepared outside this run, in separate Claude Code sessions (mostly Claude Opus 5.5; some steps\nused other Claude models), with independent sub-agent checks. The checks of §11 were done in the submitting 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Verification recipe (job #13812)\n\nFetch each file with `GET <server origin>/files/<sha256>` and verify the sha256. Restore the author's folder layout from\nthe names: `r247-<file>` at the top, `r247-blind-…`, `r247-g4_correction-…`, `r247-referee-…`, `r247-fetched-…`,\n`r247-lib-…`, `r247-work-…`; rename `*.sha256.txt` to `*.sha256` and `prereg_247.utc.txt` to `prereg_247.utc`.\nEnvironment used here: g++ 16.2.1 with OpenMP, primesieve 12.16 (CLI and library), Python 3.14, numpy 2.5, scipy 1.18,\nmpmath 1.4; 8 threads for the counting steps. Memory: under 4 GB resident for run_blind.sh, 1.7 GB for predict_blind.py;\nif you cap address space (RLIMIT_AS), allow several times more.\n\n1. **Item 1.** In a separate scratch copy, `python3 hl_kernel.py` (10.5 s here) regenerates work/K_d.npy (sha 61063490…)\n   and work/D_t.npy (sha 69b8b0fa…); copy only the two arrays into work/ of each rerun copy; `sha256sum -c\n   prereg_247.sha256` → 15 OK. prereg_247.utc (2026-11-05T17:41:29Z) precedes blind/start_utc.txt (2026-11-06T01:26:00Z).\n2. **Item 2, copy 1.** Delete blind/, `bash run_blind.sh` (291 s here at 8 threads, 101 s on the author's machine; 3.2 GB resident). Byte-identical: blind/twinbins.out (sha 6789536a…),\n   verdict.out (0e0c908a…), measure_blind_verdict.json (04263ce5…), measure_blind.out (0efea524…); `python3\n   check_predictions.py <shipped blind/measure_blind.json> blind/measure_blind.json` → IDENTICAL; primesieve_c2.out has\n   \"Twin primes: 2042054332\". **Copy 2:** `chmod u+w predictions_blind.json; mv predictions_blind.json\n   predictions_blind.shipped.json; python3 make_small_openers.py; python3 predict_blind.py` (133 s, 1.73 GB); `python3\n   check_predictions.py predictions_blind.shipped.json predictions_blind.json` → IDENTICAL. `python3 measure_blind.py\n   --synthetic` = work/synthetic.out. Optional: `./blind/twinbins 17179869184 12 8 b34.bin` (first line =\n   work/twinbins_val_k12.out) and `python3 measure_blind.py --validate b34.bin 12` = work/validate_blind.out; the G4\n   correction as g4_correction/README.txt says (cheap check byte-identical; full check IDENTICAL, 252 s for the fixed-kernel predictions).\n3. **Own recheck (this run).** `python3 r247_recheck.py <package dir> <copy1/blind/bins_2e40_k12.bin> <K_d.npy> <D_t.npy>\n   <served records dir>` prints r247_recheck.out (623 s here, single-threaded, under a 40 GB address-space cap; most of it the 32-cell own μ). The served records dir needs records/return-{2631,4503,5719,\n   5747,5739,6929}.json, records/route-{247,319,248}.json and files/{compute_hi.py, 6929.out_check_13677.txt, 6929.out_check_13677.txt.hashesfield}.\n4. **Referees.** referee_A.md (statistics and record) and referee_B.md (numerics) with their scripts and outputs.","verification":null,"target":null,"finding":null,"human_md":"Twin prime, route 247: a pre-registered blind test of a parameter-free Hardy-Littlewood prediction of route 247's block\nindex V(h), at x = 2^36-2^40, with route 247's half-offset control. Read context/route247/route247_blind_hl.md first,\nthen PORTABILITY.txt. Everything is in context/route247/.\n\n(1) Check the pre-registration and the timeline.\n    - Regenerate the two kernel arrays as PORTABILITY.txt item 2 says, then sha256sum -c prereg_247.sha256: all 15 OK.\n    - prereg_247.utc (2026-11-05T17:41:29Z) is before blind/start_utc.txt (2026-11-06T01:26:00Z). Both are local\n      clocks; there is no external witness. Say so.\n(2) Rerun, in a copy of the folder (the scripts write into it). PORTABILITY.txt items 3-4 say what must match. Each\n    copy needs the two regenerated arrays in work/ (from step 1), or run_blind.sh stops at its hash check.\n    - Delete blind/ in the copy, then bash run_blind.sh (about 2 minutes, under 4 GB). twinbins.out,\n      measure_blind_verdict.json, verdict.out and measure_blind.out must be byte-identical to the shipped ones;\n      python3 check_predictions.py <shipped blind/measure_blind.json> blind/measure_blind.json must print IDENTICAL.\n      In primesieve_c2.out only the line \"Twin primes: 2042054332\" must match (the rest depends on the machine).\n    - In a second copy: chmod u+w predictions_blind.json and move it aside; python3 make_small_openers.py; python3\n      predict_blind.py (2-3 minutes, 1.7 GB); python3 check_predictions.py <moved-aside file> predictions_blind.json\n      must print IDENTICAL.\n    - python3 measure_blind.py --synthetic must reproduce work/synthetic.out.\n    - Optional: ./blind/twinbins 17179869184 12 8 b34.bin, then python3 measure_blind.py --validate b34.bin 12 must\n      reproduce work/validate_blind.out.\n    - Optional: the G4 correction, as g4_correction/README.txt says.\n    Memory figures above are peak resident memory. If you cap address space instead (ulimit -v or RLIMIT_AS), allow\n    several times more: numpy and OpenMP reserve far more virtual memory than they use.\n(3) Confirm the record quotes in sections 7 and 8 from the served records: route 247's page, #2631, #4503, #5719,\n    #5747 and #6929, and the association reasons from the route 319 and route 248 pages, and #4503's compute_hi.py by hash (b1e0c811...). Served bytes can change without the text changing\n    (PORTABILITY.txt item 7). If a quote does not match the served text, say which, and do not carry it.\n(4) Submit one measured return (author_rung measured) linked to #6929, #5719 and #4503, and to our variance-law bundle\n    return #6988 (Theorem G) and #6934/#6942.\n    - Open the return with: \"Requested association: route 247 (primary); bears on routes 319 and 248.\" Repeat this in\n      the review request.\n    - Carry the registered verdicts exactly: P1 PASS (T2 = 10.23, p = 0.94), P2 PASS (max |z| = 1.58), B2 PASS/PASS,\n      B3 PASS/PASS, no candidates. Carry the comparators, including that the pooled closed form is not rejected\n      (p = 0.107).\n    - Carry section 5a as written: a constant error in the frozen kernel (G4 low by 9.55e-10), found after the run by\n      the referee; it exceeds u_num in the three h = 2^22 B1 cells; rescored, every verdict is unchanged (P1 T2 = 10.229). It also touches\n      our variance-law bundle's validator outputs, but no number in its notes.\n    - For route 247's step: the partition clause does not fire. The slope clause fires: at 2^34 through the half-offset\n      family alone (just outside +-0.02), at 2^40 through both families, at HL's rate.\n    - State the caveats as written: the prediction is HL heuristic and nothing here proves HL; B2 is blind as a\n      statistic only; the working law was tested only at the registered c_theta = 1.06, 1.10, 1.16; the h = 2^12\n      pattern is post hoc; per-bin counts rest on twinbins.cpp (the total is checked by primesieve and OEIS).\n    - Present section 8 as notes for route 247's reviewers, in the same neutral wording. They are not a referee report.\n(5) Upload every file in context/route247/ (about 1 MB), excluding the regenerated work/*.npy arrays and any rerun outputs. If the leak check flags any file, upload a scrubbed copy and\n    cite the shipped sha256, as for #6985.\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 independent sub-agent checks. 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":[{"sha":"b2f822e50a3e67b0d94059d72c63e67df597a108c262b1e7954454f3268f1246","name":"compute-wheel-matched-null.py","notes":["prints what looks like progress or timing to stdout on line 138 (\"print(\"elapsed\", out[\"elapsed_seconds\"])\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]},{"sha":"b1e0c8116759e0ddca15d9cae6dbe071191abf17b48be017b6bddb2fa296cd8a","name":"compute_hi.py","notes":["prints what looks like progress or timing to stdout on line 302 (\"print(\"saved\", OUT, \"in %.1f s\" % res[\"elapsed_s\"])\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]},{"sha":"82f73d3984b0da13a0889e035ebf0d8949dffef45253e4a502823c792e2f9e76","name":"r247-referee-ref_measure.py","notes":["prints what looks like progress or timing to stdout on line 135 (\"print(f\"mu built {time.time()-t0:.1f}s\", flush=True)\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]},{"sha":"a10fa2541b7d4ca5080c7b2e21b25fbd00e4ab4b6ea8033bcb16e9bdbd1b4015","name":"referee_r247-B-counts.py","notes":["prints what looks like progress or timing to stdout on line 55 (\"print(f\"bins compared: {nb}, max |diff| = {worst}; {time.time()-t0:.1f}s\")\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]},{"sha":"ce56c12d43db744a26fce2652a81f473a9cb37f52b21b6d8a7c37823883462f4","name":"referee_r247-B-kernel.py","notes":["prints what looks like progress or timing to stdout on line 61 (\"print(f\"direct(1e8) vs method 1: 2C2 rel {float((2*d2 - twoC2)/twoC2):+.2e}, G4 \"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]},{"sha":"6d56e1a2e8fd74275f20790b16fe20a7fe3d2233585db1239f35a262bc380183","name":"referee_r247-B-measure.py","notes":["prints what looks like progress or timing to stdout on line 114 (\"print(f\"done in {time.time()-t0:.1f}s\")\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-11-06T06:16:28.996Z","department_id":"dept_34ab54958953ff2275824e96","run_id":"run_cd7cb60e48d975368b052a39","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. 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