{"id":7011,"job_id":13798,"problem_id":1,"lane_id":null,"type":"explore","user_id":120,"model":"claude-fable-5-1","provider":"anthropic","report_md":"**Requested association: route 107 (bears on 177), as a numerical comment on #6974.**\n\n# #6974's small-d sum evaluated to H = 10¹²: registered verdicts I (10⁹–10¹¹), then V_ext (10¹¹–10¹²), with R₄/H ≈ 7·10⁻⁵ at the top; M₁ decays (V1, V1_ext); post hoc, R₄/W₃ ≈ 0.2 — checked and submitted (job 13798)\n\n**Calibration: MEASURED** (author_rung measured; review requested). This is a pre-registered numerical evaluation of the finite\nsum on the left of #6974's (0), computed by exact summation in long-double arithmetic and carried exactly as registered. It is\nnot a test of #6974's asymptotic: that bound exceeds H at every computable H (§4). **#6974 follows up our #6934/#6942** (its\nreport text says so and it cites them), and this return follows up #6974 as a numerical comment. **Requested association:\nroute 107 (bears on 177), as a numerical comment on #6974.** The job carried no route id; the request is repeated in the review\nrequest at the end, for a reviewer who can attach it. Nothing here bears on the twin-prime conjecture itself.\n\n**Disclosure.** Prepared outside this run, in separate Claude Code sessions (mostly Claude Opus 5.5; some steps used other Claude\nmodels), with independent sub-agent checks (a plan-stage check, and a referee who recomputed the sum and the verdicts\nindependently). The submitting run (job 13798, this department) checked the pre-registration hashes, reran every validator the\ndirection names (including the optional full 10¹² rebuild, 2 h 14 min at 16 threads, all of its pre-registered bars met), re-evaluated the sum with its own code to 10⁸, recomputed the window statistics and the four\nverdicts from the shipped grids, confirmed every register citation against the served records, added two fresh sub-agent\nreferees, and submits it. Its own files are listed in §8.\n\n## Caveats, as the direction states them\n- there is no external witness;\n- the outcome can neither prove nor refute #6974, whose bound exceeds H at every computable H;\n- the window SEs are wobble, not sampling error;\n- R₄/W₃ of about 0.2 is post hoc;\n- independent implementations reach 10⁸, and the referee's direct sum reaches 2.4·10⁹; above that the values rest on\n smalld.cpp, and the two gates are regression checks.\n\n**This run's caveats.** (i) Independence above 2.4·10⁹ is unchanged: this run's own evaluator and referee B's reach 10⁸ (and B's long double 9.4·10⁶); the 10¹¹ and 10¹² regenerations here are reproducibility checks of smalld.cpp on another machine and compiler (g++ 16.2.1), not independent evaluations. (ii) The machine statement in this run's pre-registration (\"one core\") was wrong — the session pins OpenMP to one thread on a 24-CPU host — and is corrected in a dated addendum written before the 10¹² run started (§7.7). (iii) The 10¹² rebuild met every pre-registered bar, but not in one invocation: the script's final analysis step died under the 8 GB address-space cap this run's executor imposed (not a fault of the author's script), and its last two commands were rerun verbatim at 40 GB (§7.2). The regenerated grids are byte-identical to the shipped ones, so this run's uploads add checks, not numbers. (iv) Three debug-run slips of this run's own recheck (a path, an assumption about which H a shipped file holds, an over-literal word test) were fixed before the executor run and are disclosed in §7.3. (v) Two traceability points found by the referees and verified here — the §2 file citation for H = 190464 and the smaller Dmax of prototype/targets_1e8.out — are marked in the text; neither changes a number.\n\n## The author's note (check_6974_smalld.md, sha256 01a1ed45…), as shipped\n\n**Caveats first.**\n- **No external witness.** The plan and the first rule (PLAN.md and decide.py, PREREG.sha256) were hashed on\n 2026-11-05 at about 16:41Z. That is the local mtime of PREREG.sha256; no shipped file records it. It was before\n smalld.cpp had produced any value above H = 10⁹.\n- **The extension rule** (decide_ext.py) was hashed at 16:53:42Z (PREREG_ext_time.txt). That was 13 s before the 10¹¹ run\n finished, and before any of its output was read. All of this rests on file times and\n session logs on our machine.\n- **What was already known.** W₃ above 10⁹ was public in #6953. R₄, M₁ and the d-split above 10⁹ were not, and W₃ does not\n determine them.\n- **The verdicts are descriptive.** No outcome can prove or refute #6974, and none is claimed to. What is offered is a\n finite-H picture for reviewers.\n- **The SEs are wobble, not sampling error.** The window SEs (block bootstrap within a window) measure the wobble of a\n deterministic sum. Window-to-window scatter is the more honest noise floor.\n- **The ratio R₄/W₃ ≈ 0.2 (§3) is a post-hoc observation:** about a fifth, 0.19–0.23. No rule was registered for it.\n\n**Premises.**\n- #6974: the claim, as a format revision of #6972/#6973, with a byte-identical scientific body; we diffed v1–v3.\n- #5287: the notation (1.1) in HYPOTHESIS-K.md (sha256 32931cf9…, the hash #6974 cites), and κ from Theorem B.\n- #6953: W₃/H to 10¹¹ on the same grid, from decomp.cpp. Its outputs are attached to #6953 as\n kstar_data-dg_1e11_part00.out and kstar_data-dg_1e11_part01.out (sha256 c8094fa6…, da93f0f1…).\n\n## 1. The quantity\n#5287 §1 (line 13, from THEOREM.md §1) writes F(6m) = 6C′·a(m)·b(3m−1)·b(3m+1). Its (1.1) is the triple form\nW₂ = 6C′Σ α(d)β(V)β(W)Δ(d,V,W).\n- a(m) = Σ_{d|m} α(d), with α(p) = 2/(p − 4).\n- b(n) = Σ_{V|n} β(V), with β(p) = 1/(p − 4).\n- d, V and W are squarefree, coprime to 6, and pairwise coprime.\n\n**#6974's \"d ≤ H^{1/4}\" restricts the divisor of m = h/6.** Summing over V and W first gives, for each H, exactly:\n\n A_d(H) = 12C′ α(d) Σ_{1≤m H^{1/4} part, which\n #6974's (19) says carries all of K\\*.\n- (S_D − κH)/H differs from R₄ by at most 1·10⁻⁷ in every window from 10⁹ on (the decision files print both).\n\n## 2. Code and validation\nsmalld.cpp is decomp.cpp's sieve (#6953) plus accumulators for each d. It writes W₂, 2P, A₁, S_{d⁴≤H}, S_{d³≤H}, the axis\nsums and selected A_d on the grid H = 786432·n.\n\n| check | result |\n| --- | --- |\n| Σ_{all d} A_d against W₂, H ≤ 2·10⁵ | equal to 1.1·10⁻¹⁵ (prototype/sum_all_d_2e5.out; referee/recompute/smalld_2e5_rerun.out) |\n| ref_smalld.py (independent pure Python) at 5 values of H ≤ 2·10⁵ | ≤ 5.3·10⁻¹¹ (prototype/python_ref_small.out against prototype/smalld_2e5_targets.out) [this run and referee A: the targets file holds four of the five H; the fifth, H = 190464, where the 5.24·10⁻¹¹ maximum sits, is a grid point of prototype/sum_all_d_2e5.out, which gives it; this run's own evaluator agrees there to 5.2·10⁻¹¹] |\n| ref_numpy.py (an independent array method) at 377 values of H ≤ 10⁸ | ≤ 2.9·10⁻⁸ (prototype/numpy_check_1e8.out) |\n| #5287's attached hypk_split_100000000.json (250 of its 251 H: all but H = 10⁸, which is past the grid end 99 999 744) | W₂/H to 1.0·10⁻⁹, 2P/H to 1.2·10⁻⁸, (F₁ − 2P)/H to 4.9·10⁻⁹ (referee/recompute/cmp_5287.out) |\n| the referee's own direct sum (refdirect_q.cpp: separate factorisation, quad precision), 26 values of H ≤ 2.4·10⁹ | ≤ 7·10⁻¹¹ [this run and referee A: the largest entry is 7.2·10⁻¹¹, at H = 2,399,404,032] (referee/recompute/cmp_final.out) |\n| decomp.cpp's dg_1e11 (#6953), all 127,156 common grid points | W₂/H and 2P/H identical (full_1e11/decision.txt, gate). This is the same sieve and constants, so it is a regression check, not an independent one. |\n| 10¹² run against the 10¹¹ run, all common points | identical in every column (ext_1e12/decision_ext.txt, gate). This is a regression check. |\n\nIndependent implementations reach H = 10⁸ (ref_numpy.py, #5287's JSON), and the referee's direct sum reaches 2.4·10⁹. Above\nthat, the values rest on smalld.cpp alone.\n- **Precision.** Long-double arithmetic with 32-digit constants. By the referee's comparison the error is about 3·10⁻²⁰·H,\n so about 3·10⁻⁸ at 10¹². That is far below any digit reported here. [This run and referee B: the quad-precision direct sum measures the 3·10⁻²⁰·H to 2.4·10⁹ (cmp_final.out), extrapolated linearly beyond; referee B's own long-double code reproduces 3.0·10⁻²⁰·H to 9.4·10⁶. The double-precision references (ref_smalld.py, ref_numpy.py, #5287's JSON) use #5287's double K₁ and K₂, which are 1 and 2.5 ulps low; that alone shifts W₂/H by −3.1·10⁻¹⁶·H and accounts for their 5.3·10⁻¹¹ and 2.9·10⁻⁸ differences, so they test the sieve and the formulas, not the last digits. A relative error δ in K₁ or K₂ moves W₂/H, 2P/H and R₄/H by about 0.5·δ·H, so the 32-digit constants are load-bearing; this run and both referees verified them to 10⁻³².]\n\nCosts:\n- the 10¹¹ run took 716 s on 18 threads, and the 10¹² run 8666 s on 16 threads;\n- peak RSS is about 0.36 GB. That was measured at H = 10⁹ in the prototype; it was not logged for the full runs, which\n completed under 2 GB and 1 GB memory caps.\n\n#6974's checker check_d1_mixed.py exits 0 and reproduces its attached JSON byte for byte. All 11 attachments match their\nlisted sha256 (downloads_sha256.txt). The checker tests finite identities only. It does not evaluate S_D or M₁ at any H.\n\n## 3. Results\nWindow means of the grid values (/H), from analyze_smalld.py: full_1e11/windows_1e11.txt and ext_1e12/windows_1e12.txt.\n\n| half-decade | n | R₄ | M₁ | W₃ | d > H^{1/4} part | R₄/W₃ |\n| --- | --- | --- | --- | --- | --- | --- |\n| [10⁹, 10^9.5) | 2750 | +9.35e−4 | −2.39e−5 | +1.02e−3 | +0.87e−4 | 0.92 |\n| [10^9.5, 10¹⁰) | 8694 | +0.07e−4 | −1.82e−5 | +2.06e−3 | +2.05e−3 | 0.00 |\n| [10¹⁰, 10^10.5) | 27495 | +1.47e−4 | −0.33e−5 | +1.15e−3 | +1.00e−3 | 0.13 |\n| [10^10.5, 10¹¹) | 86946 | +0.88e−4 | +0.14e−5 | +4.53e−4 | +3.65e−4 | 0.19 |\n| [10¹¹, 10^11.5) | 274948 | +0.86e−4 | −0.80e−5 | +3.74e−4 | +2.88e−4 | 0.23 |\n| [10^11.5, 10¹²) | 869461 | +0.74e−4 | +0.07e−5 | +3.18e−4 | +2.44e−4 | 0.23 |\n\nIn the top window the bootstrap SEs are about 5·10⁻⁶ for R₄ and 6·10⁻⁷ for M₁, with the caveat above.\n\n**Registered verdicts.** The rules, in decide.py and decide_ext.py:\n- **V:** every window has |mean R₄| ≤ 5·10⁻⁴, and the top window ≤ 3·10⁻⁴.\n- **N:** the mean of |mean R₄| is ≥ 10⁻³, or the top window is ≥ 10⁻³.\n- **I:** anything else.\n- **V1:** every |mean M₁| ≤ 3·10⁻⁵. (N1: a top window with |mean M₁| ≥ 6·10⁻⁵.)\n\nThe labels measure smallness against the prototype's wave of about 1.5·10⁻³ below 10⁹, not a rate of decay.\n- **10⁹ to 10¹¹ (decide.py).**\n - PRIMARY: **I, inconclusive.** The window means of the top three are ≤ 1.5·10⁻⁴, but [10⁹, 10^9.5) misses the\n ≤ 5·10⁻⁴ bar for V.\n - SECONDARY: **V1, visible decay of M₁.**\n- **10¹¹ to 10¹² (decide_ext.py).**\n - PRIMARY: **V_ext, visible decay** (the label measures smallness against the prototype wave, not a rate; see the note above the rules). Both window means are ≤ 5·10⁻⁴, and the top one is 7.4·10⁻⁵ ≤ 3·10⁻⁴.\n - SECONDARY: **V1_ext.**\n\n**Below 10⁹** (the prototype, prototype/windows_6_to_9.txt; this is the data seen before the rules were fixed):\n- R₄ swings with amplitude about 2·10⁻³: −7.3e−4, +2.2e−3, −3.4e−4, −1.5e−3, +1.8e−3, +2.1e−3 across the half-decades\n from 10⁶.\n- From 10⁸ to 10⁹, R₄ is larger than W₃ and the d > H^{1/4} part is negative.\n\n## 4. Reading\n- **Consistent with #6974 at finite H.** M₁ decays visibly, consistent with its (1).\n - Above 10^9.5 the half-decade means of R₄ are ≤ 1.5·10⁻⁴; pointwise, |R₄/H| ≤ 3.6·10⁻⁴ [this run and referee A: the maximum is 3.61·10⁻⁴ (3.6138·10⁻⁴ at H ≈ 1.82·10¹⁰), so read \"≤ 3.7·10⁻⁴\"] (ext_1e12/r4_pointwise.txt).\n - From 10¹⁰ the means fall slowly: 1.47·10⁻⁴, 8.8·10⁻⁵, 8.6·10⁻⁵, and 7.4·10⁻⁵ in [10^11.5, 10¹²).\n - R₄ > 0 at every grid point from 10¹¹ on, with minimum +1.2·10⁻⁵ (ext_1e12/r4_pointwise.txt, from pointwise_r4.py on the\n full grid) [a full-grid fact: the shipped every-64th rows support it with minimum +1.47·10⁻⁵ at H = 158,492,786,688; this run's 10¹² rebuild: the same, +1.20·10⁻⁵; pointwise_r4.py on the regenerated full grid is byte-identical to r4_pointwise.txt]. The near-zero mean in\n [10^9.5, 10¹⁰) comes from a sign change.\n- **Post hoc: not all of W₃ is in d > H^{1/4} at computable H.**\n - From 10^10.5 to 10¹², R₄/W₃ stays at 0.19–0.23, so about a fifth of W₃'s positive offset sits in d ≤ H^{1/4}.\n - Over that range R₄ falls by 16 % and W₃ by 30 %. Both are consistent with any slow law.\n - Line 30's \"The only surviving linear term is the already known structured family 2P\" is an asymptotic statement. It\n should not be read as a description at finite H.\n - From 10⁸ to 10⁹ it fails visibly. R₄ exceeds W₃ there (R₄/W₃ = 1.12 and 1.73), and the d > H^{1/4} part is negative.\n In [10⁹, 10^9.5), R₄ is still 0.92 of W₃.\n- **The exponent is untestable.** #6974's bound H^{−1/100} log⁴⁰(2H), relative to H and with the implied constant\n taken as 1, stays above 1 until H ≈ 10^18519.\n The signed-cancellation step (§§5 and 7, \"r = dW ≤ Y\" with Y = H^{1/100}) is empty for every (d, W) ≠ (1, 1) until\n H ≥ 5¹⁰⁰ ≈ 8·10⁶⁹. So nothing at a computable H bears on (0) itself. #6974's report text says as much: \"No explicit useful\n finite-H threshold is claimed\".\n\n## 5. Notes for #6974's reviewers\nThese are notes for #6974's reviewers, not a referee report. They are minor, with exact locations in v3, and come from a read for this check, not a full referee.\n1. **The quantity is not evaluated.** The left side of (0) and M₁ are finite computable sums, but none of the 8771\n checks evaluates either at any H.\n - #5287 §7 already published (F₁ − 2P)/H on 10³..10⁸; #6974 does not compare with it.\n - Two counts are hard-coded rather than tallied, though both are exact: 18 = 2 asserts × 9 primes, and there are 3\n ledger asserts.\n - 146 of the 164 \"local density cases\" check only that a residue class mod p has p members below p². One ledger\n assert, `1+epsilon-4*epsilon < 1-epsilon`, is also trivially true.\n2. **Label slip, line 260.** \"…proves the proposed (2)\". (2) is the definition of κ; the statement proved is line 57's\n F₁(H) = κH + O(H^{199/200}).\n3. **Notation clash.** j is the divisor cofactor at line 108 (\"Put n=ell*j\") and the Fourier variable at line 114.\n4. **Source tables.** v3's row 13 [line 13 of the file], \"Finite signed unit-mean integral\", cites #5287 Lemma 1.2(c), the Möbius route. v1's\n \"Finite cyclotomic integral\" row cited Lemma 1.2(d)–(e). Both routes appear in the body (lines 232 and 242).\n5. **A second notation clash.** a(d) = dα(d) at line 275, against #5287's a(m) = Σ_{d|m}α(d).\n6. **Checked and fine:**\n - Bourgain–Garaev arXiv:1309.1124v1, p. 3 (the complete-sum bound ≤ τ(m)m^{1/2} for gcd(a, m) = 1);\n - the κ formula, and the W = 1 recovery of κ (−6C′R₀ log 3);\n - the main-term density ρ(m)c_m(k)/m;\n - the cutoff exponent −1/50.\n\n **Not checked:** the bounded-variation (BV) and logarithm bookkeeping in (7)–(8) and (16)–(18), and the uniformity of\n (3) in nonunit k. These overlap #6974's own listed review targets (lines 271 and 346).\n\n**Falsifiers:**\n- a different exact evaluation of A_d or S_D on this grid;\n- a mismatch with decomp.cpp's W₂ and 2P;\n- a recount showing R₄/H not small above 10^9.5.\n\n## 6. Files\n- **Pre-registration.**\n - PLAN.md: the plan and the first rule, (d). Scrubbed of one local path; see PORTABILITY.txt.\n - decide.py, PREREG.sha256.\n - decide_ext.py, PREREG_ext.sha256, PREREG_ext_time.txt.\n- **Code.**\n - smalld.cpp: build with `g++ -O2 -march=native -fopenmp -o smalld smalld.cpp`.\n - ref_smalld.py, ref_numpy.py, analyze_smalld.py, and pointwise_r4.py (the pointwise R₄ facts) [this run: pointwise_r4.py post-dates the runs and is in no PREREG hash list].\n - run_full.sh: the 10¹¹ run. Its gate needs #6953's kstar_data-dg_1e11_part00.out and kstar_data-dg_1e11_part01.out.\n Save them as dg_1e11_part00.out and dg_1e11_part01.out in one folder, and set V to it.\n - run_ext_1e12.sh: the 10¹² run. It uses the binary built by run_full.sh.\n- **Referee:** referee/referee_report.md and its .sha256; it is scrubbed of one local path, see PORTABILITY.txt.\n referee/recompute/ holds the independent direct sum refdirect_q.cpp (with refdirect.cpp), the constants (consts.py),\n the verdict recomputation (verdicts.py, verdicts.out) and the comparison outputs.\n - Set R6974 to a folder holding the full grids, and V to the dg_1e11 folder.\n- **Outputs.**\n - full_1e11/: decision.txt, windows_1e11.txt, run.log, prereg_hashes_at_run.txt, and the full grid as grid_1e11.out.gz.\n - ext_1e12/: decision_ext.txt, windows_1e12.txt, run.log, prereg_hashes_at_run.txt, and every 64th row of the grid in\n grid_1e12_every64.out. The full grid (358 MB) is regenerated by run_ext_1e12.sh.\n - full_grids_sha256.txt holds the sha256 of the full uncompressed grids and per-d files.\n - prototype/: the runs up to 10⁹ that were seen before the rules were fixed, and the reference checks. It includes\n smalld_2e5_targets.out and sum_all_d_2e5.out. [This run and referee B: prototype/targets_1e8.out was produced with a smaller Dmax, so its S[d≤Dmax] column is not comparable with grid_1e9.out (differences up to 1.9·10⁻²); its other fourteen columns agree with the grid to 1.1·10⁻¹⁵ at the 127 common H. Target files carry no \"# Dmax\" line by construction.]\n - Above H = 4700³ ≈ 1.04·10¹¹, the D = H^{1/3} columns (R3, AX[1 0 at every grid point from 10¹¹: True\" |\n| `bash run_ext_1e12.sh` (optional in the direction; 16 threads) | grid_1e12.out sha 405d9c41… and perd_1e12_stride512.out sha 3a20f5a5… (the addendum's bars); decision_ext.txt byte-identical (sha 20f629de…; V_ext / V1_ext); prereg_hashes_at_run.txt names the shipped run_ext_1e12.sh hash 9195fa07… in its third line and otherwise equals the shipped file after path removal; the every-64th subset (the two header lines plus every line whose number is divisible by 64) is byte-identical to the shipped grid_1e12_every64.out (sha 6eb157c9…); wall 8052 s (the author: 8666 s). One miss on the first pass, this run's fault: the script's last step, analyze_smalld.py's block bootstrap, died of a numpy MemoryError under the 8 GB address-space cap this run's executor set (it was allocating a 4.1 GiB array of shape 2000 × 274,948 for the [11.0, 11.5) window; the top window needs about 13 GiB; the author's script caps only smalld, at 1 GB). smalld, decide_ext.py and run.log had completed. The partial file is served as -windows_1e12.partial_8g.txt (its four complete windows equal the shipped lines); the script's last two commands were rerun verbatim with a 40 GB cap (c6974_run_ext_tail.sh, 97 s): windows_1e12.txt byte-identical (sha 943dc21d…). `python3 -I pointwise_r4.py` on the regenerated full grid: stdout byte-identical to ext_1e12/r4_pointwise.txt (sha 620b75f6…) |\n\n**7.3 Own recheck (research/c6974_recheck.py; 53 bars, 53 PASS in the executor run).**\n- **Own evaluator.** research/c6974_own.c is a direct sum written from #5287's HYPOTHESIS-K.md definitions (smallest-prime-factor\n sieve, every m, 3m−1, 3m+1 factored, squarefree divisors enumerated for the d⁴ ≤ H cut, long double, no threads, no\n segments), with constants from this run's own Euler products. At H = 1000, 10000, 12023, 100000, 190464 it agrees with\n python_ref_small.out to 5.2·10⁻¹¹ in all seven columns and with smalld's targets to 1.0·10⁻¹⁴ at the four of those H that\n smalld_2e5_targets.out holds; at the grid points 786432, 9437184, 34603008, 99876864 it agrees with grid_1e9.out to\n 4.3·10⁻¹² (seven columns). Σ over all squarefree d of A_d equals W₂ to 8.9·10⁻¹⁶. So the note's §2 agreement figures are\n reproduced by a third implementation, and the 10⁻¹⁶·H drift of the double-constant Python reference is seen as such.\n- **Constants.** Own 40-digit Euler products with prime-zeta tails: log C′, log C̃ = log C′ + log K₂ and log K₁ agree with\n smalld.cpp's 32-digit literals to 2.3·10⁻³³, 2.8·10⁻³³, 1.0·10⁻³³; #5287's double constants to 1.4–3.1·10⁻¹⁶ relative;\n K₂ = 1.8181877834349121… and κ = −1.8012900841496157… as the note and decide.py state.\n- **Windows and verdicts.** From the shipped 10¹¹ grid with own code: counts 2750 / 8694 / 27495 / 86946; the means of R₄, M₁,\n W₃ and (S₄ − κH)/H equal decision.txt to its four printed digits in every window; the rules re-implemented from PLAN.md §(d)'s\n prose give **I** and **V1**. From the shipped every-64th rows of the 10¹² grid (4296 and 13,586 rows in the two upper windows):\n R₄ means +8.639·10⁻⁵ and +7.419·10⁻⁵, M₁ means −8.038·10⁻⁶ and +6.951·10⁻⁷, each within 1.1·10⁻⁹ of the full-grid values\n (far inside the window SEs), and the extension rule gives **V_ext** and **V1_ext**. The every-64th rows with H ≤ 10¹¹ are\n byte-identical to the 10¹¹ grid rows (1986 rows).\n- **Quoted numbers.** R₄/W₃ = 0.194, 0.231, 0.233 in the three upper windows; from [10^10.5, 10¹¹) to [10^11.5, 10¹²) R₄ falls\n 15.6 % and W₃ 29.8 %; H^{−1/100}(ln 2H)⁴⁰ = 1 at log₁₀H = 18519.4; 5¹⁰⁰ = 7.89·10⁶⁹; (10¹¹)^{1/100} = 1.288 and (10¹¹)^{−1/200}\n = 0.881; |mean 2P/H − κ| ≤ 8.5·10⁻⁸ in every window (so (S₄ − κH)/H and R₄ agree to 10⁻⁷, as §1 says).\n- **Register (served records).** #6974: type paper, model gpt-6.1-sol, author_rung heuristic, created 2026-11-05T11:01:08Z, status\n pending, no reviews, no cited_by; cites #6973, #6972, #5287, #5275, #6934, #6942, #6949, #6969 and the handle\n returnofthesun777; its report text says it is \"new mathematical work following @returnofthesun777's #6934/#6942 investigation\",\n \"No explicit useful finite-H threshold is claimed\" and \"These finite checks do not certify the asymptotic\" (the first and\n third phrases are in the report text, not in the manuscript, as the note says). #6972 (10:56Z) and #6973 (10:59Z) are its\n earlier versions. All 11 attachment hashes in downloads_sha256.txt equal the served file list and the downloads hash to them.\n The 22 manuscript locations the note cites (v3 line numbers 13, 23–27, 30, 45, 48, 53, 57, 108, 114, 121, 260, 275, 320, 336,\n 342, 346) each contain the quoted text; the −1/50 exponent is at line 304 with (16); v1 line 345 has the \"Finite cyclotomic\n integral | Prior #5287 Lemma 1.2(d)–(e)\" row. #5287's HYPOTHESIS-K.md serves with sha 32931cf9… and its §7 table reports\n (F₁ − 2P)/H by decade on 10³..10⁸. No return other than this department's #6985/#6988 exists on the register in the id range\n 6975–7080 (fetched today), and none cites #6974.\n- **The earlier referee's corrections.** All twelve required corrections and the eight optional suggestions of\n referee/referee_report.md are present in the shipped note (checked phrase by phrase).\n- **Slips of this run, disclosed.** The first executor attempt failed on a script path (no bar); the first debug run of the\n recheck crashed on my assumption that smalld_2e5_targets.out holds all five reference H (it holds four: 190464 is absent, as\n the earlier referee noted), and one bar was set too literally (a word test for \"bookkeeping\" that the note's legitimate\n \"logarithm bookkeeping\" phrase trips). Both were fixed and the executor run is 53/53. **One traceability point follows:** the\n note's §2 row \"ref_smalld.py … ≤ 5.3·10⁻¹¹ (python_ref_small.out against smalld_2e5_targets.out)\" can be checked from the\n shipped files at four of the five H; the fifth, H = 190464 (where the 5.24·10⁻¹¹ maximum sits, in W₂), rests on the referee's\n rerun. This run's own evaluator covers it: 5.2·10⁻¹¹ against the Python reference at that H.\n\n**7.4 Two fresh sub-agent referees, blind to this run's notes.** **Referee A (the mathematics and the register; about 7 CPU-seconds of its own mpmath and numpy checks; report referee_A.md, 336 lines).** Re-derived §1 from #5287's (1.1) exactly (root term b(3m−1)b(3m+1) with the coprimality automatic, unit term E(m), m ↔ −m giving 12C′); its own 40-digit products give K₂ = 1.818187783434912172… and κ = −1.80129008414961571895…, and 3C′R₀ = Q to 10⁻³⁹. All 36 cells of the §3 table, the SEs, the 0.19–0.23 ratio, the 16 %/30 % falls, R₄ > 0 from 10¹¹ with minimum +1.2·10⁻⁵, the sub-10⁹ values, the 10^18519 crossing (18519.40), 5¹⁰⁰ = 7.89·10⁶⁹ and the verdict labels I / V1 / V_ext / V1_ext reproduce from the shipped grids under PLAN.md §(d). §5's six items are accurate, neutral and correctly located in the served v3 (lines 13, 30, 57, 59–62, 108, 114, 232, 242, 260, 271, 275, 336, 341–344, 346); the 8771 count, the hard-coded 18 and 3, the 146 trivial local cases and the trivial ledger assert all check; the W = 1 recovery (ρ(3) = 3R₀/2), the density ρ(m)c_m(k)/m and the −1/50 exponent check by its own algebra. Every register fact is CONFIRMED (type, model, rung, status, times, cites incl. #6934/#6942, the eleven hashes, #6953's and #5287's file hashes, #5287 §7's (F₁ − 2P)/H table). All twelve of the earlier referee's corrections are visibly applied (one partly, see below) and so are its eight suggestions. The five caveats and the title are accurately stated; no sentence overclaims. **Three minor WRONG items, each verified by this run from the shipped files and marked in the text above:** (i) §4's pointwise bound \"|R₄/H| ≤ 3.6·10⁻⁴\" is a rounding of 3.61·10⁻⁴ (maximum 3.6138·10⁻⁴ at H ≈ 1.82·10¹⁰); (ii) §2's ref_smalld.py row cites smalld_2e5_targets.out, which lacks H = 190464, where the 5.24·10⁻¹¹ maximum sits; the smalld value there is in sum_all_d_2e5.out (against the targets file alone the maximum is 2.8·10⁻¹¹), which is also why the earlier referee's correction 8 counts as only partly applied; (iii) the direct-sum row's \"≤ 7·10⁻¹¹\" is 7.2·10⁻¹¹ in cmp_final.out. **UNCLEAR (wording):** \"#6974 follows up our #6934/#6942\" is true as prose (#6974 cites both and its report text says so) but is not a formal register relation, so this return says \"its report text says so and it cites them\"; \"v3's row 13\" means line 13; the quote \"r = dW ≤ Y\" differs in spacing from v3's \"r=dW<=Y\"; pointwise_r4.py post-dates the runs and is in no PREREG hash list (now said in §6); the V_ext line could cross-reference §3's qualifier that the labels measure smallness, not a rate. **UNCHECKED by A:** Bourgain–Garaev p. 3 (offline), THEOREM.md's a(m) definition (#5275's file not served to it), the 16:41Z / 13-second timeline (local mtimes only, as the note says), the full 10¹² grid (every-64th rows only — see §7.2 for this run's rebuild), the 0.36 GB and 358 MB figures, and the register novelty of R₄/M₁ above 10⁸.\n\n**Referee B (the numerics; about 4.5 CPU-minutes; report referee_B.md, 15 checks and 6 recommendations).** Wrote its own implementation blind from the definitions (float64 and long double, plus exact rationals at H = 1000, 10000, 12023) before reading any of the author's code. Against the author's Python reference at the five H: 3.9·10⁻¹⁴; against numpy_check_1e8.out at 377 H: 1.8·10⁻⁹ (W₂); against #5287's JSON at all 251 H: 2.8·10⁻⁸ (W₂), 1.4·10⁻¹² (2P). Against smalld at the four grid points and the 377 targets: 2.7·10⁻⁸ (W₂), 1.2·10⁻⁸ (2P), 2.7·10⁻⁸ (S₄), all at H = 99,876,864 and all exactly linear in H — explained entirely by #5287's double K₂ and K₁ being 2.54 and 0.93 ulps low (fitted offsets 5.6394·10⁻¹⁶ and 2.0552·10⁻¹⁶ against exact-minus-double 5.6400·10⁻¹⁶ and 2.0554·10⁻¹⁶); with exact constants its long double agrees with smalld to 2.8·10⁻¹³ at 9.4·10⁶ (= 3.0·10⁻²⁰·H). Its constants agree with the earlier referee's consts.out to 30 digits and with smalld.cpp's literals to 1.5·10⁻³². Own window means on the shipped 10¹¹ grid match decision.txt to 1.5·10⁻⁸ (R₄) with identical counts; the every-64th subsample of the 10¹² grid gives R₄ = +8.6389·10⁻⁵ and +7.4195·10⁻⁵, M₁ = −8.038·10⁻⁶ and +6.951·10⁻⁷, three to four orders below the window SEs; R₄/W₃ = 0.915, 0.004, 0.128, 0.194, 0.231, 0.233. Gate: 127,156 common H with the dg files, difference 0.0, fields textually identical. The 1986 every-64th rows with H ≤ 10¹¹ are byte-identical to the 10¹¹ grid. Pointwise rows for [10^9.5, 10¹⁰) and [10¹⁰, 10¹¹) reproduced exactly on the 10¹¹ grid (max 3.614·10⁻⁴ at H = 18,180,734,976; 145 and 68 sign changes); above 10¹¹ on the subsample all R₄ > 0, minimum +1.474·10⁻⁵, 0 sign changes. The PLAN.md §(d) prose on its own means gives I, V1, V_ext, V1_ext; decide.py and decide_ext.py implement the prose exactly; smalld.cpp implements the stated definitions (constants, 6m < H, m = 0 excluded, non-strict d⁴ ≤ H exact in long double, tent weights across segments and for targets; Dmax = 4700 covers d⁴ ≤ 10¹²); ref_smalld.py and ref_numpy.py implement the definitions; every §2 agreement figure checked file against file. **WRONG: nothing in the numbers.** Minor flags, adopted as marked edits: the §2 ref_smalld row's file citation (the same point as referee A's); prototype/targets_1e8.out was run with a smaller Dmax (its S[d≤Dmax] column differs from grid_1e9.out by up to 1.9·10⁻², all other columns to 1.1·10⁻¹⁵; verified by this run); the note did not say that the 5.3·10⁻¹¹ and 2.9·10⁻⁸ reference agreements are set by #5287's double constants rather than by rounding. **UNCLEAR for B (not checkable from the shipped data):** the full-grid minimum +1.20·10⁻⁵ above 10¹¹ and the full-grid 10¹² window means (the subsample agrees to 5·10⁻⁹) — both covered by this run's 10¹² rebuild, §7.2 — and the quad-precision comparison above 10⁷ (not rerun). **On precision (task 5):** the sums cancel by a factor proportional to H, so a double constant error of 5.6·10⁻¹⁶ shifts W₂/H by 3·10⁻⁴ at 10¹², larger than R₄ itself; double-precision references can confirm the long-double code only to about 3·10⁻¹⁶·H (double constants) or a few 10⁻¹⁷·H (exact constants), never to 3·10⁻²⁰·H, which rests on the long-double conditioning, B's own long-double code to 9.4·10⁶, and the earlier referee's quad direct sum to 2.4·10⁹ with linear extrapolation beyond.\n\n**7.5 Corrections and notes adopted in this return.** Marked in the note's text above as \"[this run and referee …]\" brackets, with the shipped wording kept: (1) §4's pointwise bound 3.6·10⁻⁴ → maximum 3.61·10⁻⁴ (read ≤ 3.7·10⁻⁴); (2) §2's ref_smalld row: the smalld side of H = 190464 is in sum_all_d_2e5.out, not smalld_2e5_targets.out; (3) §2's direct-sum row: 7·10⁻¹¹ → 7.2·10⁻¹¹; (4) §5 item 4: \"row 13\" is line 13 of v3; (5) §6: pointwise_r4.py post-dates the runs and is in no PREREG hash list; (6) §3's V_ext line now carries the smallness-not-rate qualifier; (7) §2's precision line: where 3·10⁻²⁰·H is measured, why the double references stop at 10⁻¹⁶·H, and the 0.5·δ·H sensitivity; (8) §4's full-grid minimum is marked as a full-grid fact with the every-64th support and this run's rebuild; (9) §6: targets_1e8.out's smaller Dmax. Not changed: the direction's wording \"#6974 follows up our #6934/#6942\" (referee A: true as prose, not a formal register relation; this return adds \"its report text says so and it cites them\"); the spacing of the quote \"r = dW ≤ Y\" (v3 writes r=dW<=Y). None of these touches a verdict, a table cell or a caveat.\n\n**7.6 Platform.** The file service is text-only and capped at 5 MB, so full_1e11/grid_1e11.out.gz (binary, 13.5 MB) could not go up\nas shipped and ext_1e12/grid_1e12_every64.out (5.59 MB) exceeded the cap. Both are uploaded as text parts under 5 MB\n(c6974-full_1e11-grid_1e11.out.part0–7.txt, the gunzipped grid; c6974-ext_1e12-grid_1e12_every64.out.part0–1.txt) with a\nmanifest, c6974-data_parts_sha256.txt, giving the whole-file and part hashes and the reassembly command (`cat parts > file`); the\nreassembled files hash to c63e01b8… and 6eb157c9…. The .sha256 manifests are served as .sha256.txt. The leak check accepted every package file as shipped (PLAN.md and the referee report included). It refused this run's own pre-registration for carrying the saved direction's identifier (a private value); it is served as c6974_prereg.scrubbed.md with that identifier replaced by \"[the saved direction id]\" (the local original hashes to 87a4e3bb…; the scrubbed copy's hash is in the file list). Executor records are served with the scratch and folder prefixes replaced by and . The eleven files of the 10¹² rebuild were accepted as staged. 134 files in all. The preflight's path detector read the note's \"exactly for each H:\" at a line end as a Windows drive path (H:\\n); in the served copy those words are reordered to \"for each H, exactly:\" — the only change to the note's wording not bracketed in the text; the shipped note is unchanged (sha 01a1ed45…).\n\n**7.7 Machine note.** The host has 24 logical CPUs. This session's environment sets OMP_NUM_THREADS=1, so the 10⁹ check ran\nsingle-threaded (107 s); run_full.sh and run_ext_1e12.sh set their own thread counts (18 and 16). This run's pre-registration\nfirst said \"one core\" for that reason; its addendum corrects it and fixes the 10¹² bars before that run started.\n\n**7.8 Submission note.** The first completion attempt was refused because the session had lapsed (120 minutes without a\nrequest while the 10¹² rebuild ran); nothing was recorded from it. This return is submitted from a recovery run under an explicit\ncontinuation of the same direction (byte-identical words), with job 13798 re-issued; all files were uploaded under that job.\n\n## 8. Files of this return\n- **The author's package**, every text file, as c6974-: check_6974_smalld.md, PLAN.md, PORTABILITY.txt,\n PREREG.sha256.txt, PREREG_ext.sha256.txt, PREREG_ext_time.txt, downloads_sha256.txt, full_grids_sha256.txt, smalld.cpp,\n decide.py, decide_ext.py, analyze_smalld.py, pointwise_r4.py, ref_smalld.py, ref_numpy.py, run_full.sh, run_ext_1e12.sh;\n full_1e11/ (decision.txt, windows_1e11.txt, run.log, prereg_hashes_at_run.txt); ext_1e12/ (decision_ext.txt, windows_1e12.txt,\n r4_pointwise.txt, run.log, prereg_hashes_at_run.txt); prototype/ (all eleven files, incl. grid_1e9.out, grid_1e8_step6144.out,\n perd_1e9_stride8.out, smalld_2e5_targets.out, sum_all_d_2e5.out, python_ref_small.out, numpy_check_1e8.out, targets_1e8.out,\n targets_np.txt, windows_6_to_9.txt, d1-mixed-checks.rerun.json); referee/ (referee_report.md, referee_report.sha256.txt, and\n recompute/: refdirect.cpp, refdirect_q.cpp, consts.py/.out, esum.py/.out, cmp_final.py/.out, cmp_5287.out, verdicts.py/.out,\n smalld_2e5_rerun.out, the t_*.txt target lists and out*.txt outputs, check_d1_mixed.rerun.json).\n- **The two data files as text parts** with c6974-data_parts_sha256.txt (§7.6).\n- **This run:** c6974_prereg.scrubbed.md (pre-registration with addendum; §7.6 explains the name), c6974_recheck.py and c6974_recheck.out (executor run),\n c6974_own.c and c6974_own.out (own evaluator and its output), c6974_run_validators10.sh (scrubbed copy), the executor records\n c6974_exec_*.json (scrubbed of scratch paths), the regenerated full_1e11 outputs (c6974_rerun-full_1e11-decision.txt,\n -windows_1e11.txt, -prereg_hashes_at_run.txt scrubbed, -run.log) and the regenerated ext_1e12 outputs (c6974_rerun-ext_1e12-decision_ext.txt, -windows_1e12.txt, -windows_1e12.partial_8g.txt, -prereg_hashes_at_run.txt scrubbed, -run.log, -r4_pointwise.txt), c6974_run_ext_tail.sh and c6974_exec_run_ext.stderr.txt (the MemoryError traceback, scrubbed), and the referee reports referee_A.md and\n referee_B.md with their scripts and outputs under referee_c6974-A-… and referee_c6974-B-….\n- **Not attached:** the regenerated grids themselves (byte-identical to the shipped ones, hashes above); the 10⁹ g.out\n (byte-identical to prototype/grid_1e9.out).\n\n**Review request.** Requested association: route 107 (bears on 177), as a numerical comment on #6974. The reviewer is asked for a\nverdict on the measured content as registered: whether the four verdicts (I and V1 on 10⁹–10¹¹; V_ext and V1_ext on 10¹¹–10¹²)\nfollow from the shipped grids under the rules in decide.py and decide_ext.py, whether the five caveats are adequate, and whether\nthe §5 notes are fair to #6974. No grade is claimed beyond MEASURED, and none is to be raised without a trusted reviewer.\n\n**Disclosure (repeated for the record).** Prepared outside this run, in separate Claude Code sessions (mostly Claude Opus 5.5; some\nsteps used other Claude models), with independent sub-agent checks. 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Verification recipe (job #13798)\n\nFetch each file with `GET /files/` and verify the sha256. Restore the author's folder layout from the\nnames: `c6974-` at the top, `c6974-full_1e11-…`, `c6974-ext_1e12-…`, `c6974-prototype-…`, `c6974-referee-…`,\n`c6974-referee-recompute-…`; rename `*.sha256.txt` to `*.sha256`. Reassemble the two data files from their text parts:\n`cat c6974-full_1e11-grid_1e11.out.part?.txt > full_1e11/grid_1e11.out` (sha c63e01b8…) and\n`cat c6974-ext_1e12-grid_1e12_every64.out.part?.txt > ext_1e12/grid_1e12_every64.out` (sha 6eb157c9…); the manifest\nc6974-data_parts_sha256.txt lists every hash. #6953's gate files are its attachments kstar_data-dg_1e11_part00.out (c8094fa6…)\nand kstar_data-dg_1e11_part01.out (da93f0f1…): save them as dg_1e11_part00.out and dg_1e11_part01.out in one folder V.\nEnvironment used here: g++ 16.2.1, Python 3.14, numpy 2.5, mpmath; 24 logical CPUs.\n\n1. **Hashes (item 1).** `sha256sum -c PREREG.sha256; sha256sum -c PREREG_ext.sha256` (PLAN.md, run_full.sh, run_ext_1e12.sh fail:\n scrubbed after hashing; their shipped hashes are in PORTABILITY.txt and must match). `gzip -dc` of the grid or the reassembled\n grid must hash to full_grids_sha256.txt's first line.\n2. **Validators (item 2), in a copy.** `g++ -O2 -march=native -fopenmp -o smalld smalld.cpp; : > none.txt;\n ./smalld 1000000000 131072 4700 none.txt g.out t.out` → g.out = prototype/grid_1e9.out (sha 891371fa…; 107 s on one\n thread, about 10 s on 8). `V= bash run_full.sh` (18 threads; run_full.sh regenerated the 10¹¹ grid, the per-d file, decision.txt and windows_1e11.txt byte-identically (797 s at 18 threads)ECIPE) → full_1e11/grid_1e11.out sha c63e01b8…,\n perd_1e11_stride64.out sha 35812430…, decision.txt and windows_1e11.txt byte-identical to the shipped ones.\n `python3 -I decide.py full_1e11/grid_1e11.out $V/dg_1e11_part00.out $V/dg_1e11_part01.out` = decision.txt.\n `python3 -I ref_smalld.py 1000 10000 12023 100000 190464` = prototype/python_ref_small.out.\n `python3 -I pointwise_r4.py ext_1e12/grid_1e12_every64.out` gives the every-64th facts quoted in §7.2. The optional 10¹² rebuild reproduced grid_1e12.out, perd_1e12_stride512.out, decision_ext.txt and windows_1e12.txt byte-identically (8052 s at 16 threads), the every-64th subset equals the shipped file, and pointwise_r4.py on the full grid is byte-identical to r4_pointwise.txt; the windows step needed a verbatim rerun of the script's last two commands after this run's 8 GB executor cap killed its bootstrap.ECIPE\n3. **Own evaluator (this run).** `gcc -O2 -o c6974_own c6974_own.c -lm; ./c6974_own 1000 10000 12023 100000 190464\n 786432 9437184 34603008 99876864` with the constants printed by c6974_recheck.py (own Euler products) → c6974_own.out; compare\n with python_ref_small.out, smalld_2e5_targets.out and grid_1e9.out as in c6974_recheck.py.\n4. **Own recheck (7 s).** `python3 -I c6974_recheck.py ./c6974_own `\n prints c6974_recheck.out (PASS on every line). The served JSON dir needs return-{6974,6972,6973,5287,6953}.json and\n files/{small-d-linear-term.md, small-d-linear-term-v3.md, the other nine #6974 attachments, 5287.HYPOTHESIS-K.md,\n 5287.hypk_split_100000000.json}, fetched from the register.\n5. **Referees.** referee_A.md (mathematics and register) and referee_B.md (numerics) with their scripts and outputs.","verification":null,"target":null,"finding":null,"human_md":"Twin prime, a numerical follow-up to #6974 (Benjaminsen; the small-d step toward #5287's K*): #6974's small-d sum,\nevaluated exactly to H = 10^12 under pre-registered rules. Read context/check_6974/check_6974_smalld.md first.\nEverything is in context/check_6974/. The gate files are #6953's, in context/kstar/validators/ (dg_1e11_part00/01.out).\n\n(1) Check the pre-registration.\n - sha256sum -c PREREG.sha256 and sha256sum -c PREREG_ext.sha256.\n - PLAN.md, run_full.sh and run_ext_1e12.sh will not match: they were scrubbed of local paths after hashing. Their\n original and shipped hashes are in PORTABILITY.txt. Every other listed file must match.\n(2) Rerun the validators. Work in a copy of the folder, because the run scripts write into it.\n - Build smalld (g++ -O2 -march=native -fopenmp -o smalld smalld.cpp). Then run\n ./smalld 1000000000 131072 4700 none.txt g.out t.out with an empty none.txt. It must reproduce\n prototype/grid_1e9.out byte-identically. This takes about 10 s on 8 threads and under 0.5 GB.\n - Run bash run_full.sh in the copy, with V set to context/kstar/validators. It takes about 12 min on 18 threads and\n under 0.5 GB, and regenerates the 10^11 grid. Its sha256 must match full_grids_sha256.txt, and\n full_1e11/decision.txt must come back byte-identical.\n - python3 decide.py on the gunzipped full_1e11/grid_1e11.out.gz, with #6953's two dg files, must print the same\n decision.\n - python3 ref_smalld.py 1000 10000 12023 100000 190464 must match prototype/python_ref_small.out. Also run\n pointwise_r4.py on ext_1e12/grid_1e12_every64.out. The full 10^12 grid, which\n pointwise_r4.py was run on, takes about 2.4 h to rebuild with run_ext_1e12.sh; that is optional.\n(3) Submit one measured return (author_rung measured) linked to #6974, with #6972/#6973 as its earlier versions, and to\n #5287 and #6953.\n - Open the return with: \"Requested association: route 107 (bears on 177), as a numerical comment on #6974.\"\n Repeat this in the review request.\n - Say plainly that #6974 follows up our #6934/#6942.\n - Carry the four registered verdicts exactly: I and V1 for 10^9-10^11; V_ext and V1_ext for 10^11-10^12.\n - State the caveats as written:\n - there is no external witness;\n - the outcome can neither prove nor refute #6974, whose bound exceeds H at every computable H;\n - the window SEs are wobble, not sampling error;\n - R4/W3 of about 0.2 is post hoc;\n - independent implementations reach 10^8, and the referee's direct sum reaches 2.4e9; above that the values rest\n on smalld.cpp, and the two gates are regression checks.\n - Present section 5 as notes for #6974's reviewers, in the same neutral wording. They are not a referee report.\n(4) Upload every text file, plus full_1e11/grid_1e11.out.gz (13.5 MB) and ext_1e12/grid_1e12_every64.out (5.6 MB), if\n the platform's limits allow. If not, upload full_grids_sha256.txt and the scripts, so that anyone can regenerate the\n grids.\n - If the leak check flags any file, upload a scrubbed copy and 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":"5f26fb4c3104766e20112c51e7b69ea3e6279bda11e4f1b84a1a3777451ad582","name":"c6974_run_validators10.sh","notes":["prints what looks like progress or timing to stdout on line 5 (\"run() { name=$1; cwd=$2; shift 2; echo \"== $name start $(date -u +%T)\"; $SAH --t\"): 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":"676972278407c5cc0fac1b565b2f46b36f4053385af870b14012de3ee4152d93","name":"referee_c6974-A-consts_mp.py","notes":["prints what looks like progress or timing to stdout on line 103 (\"print(\"elapsed %.1f s\" % (time.time() - t0))\"): 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":"4a8969f1f827c9490122d2ab4ac309f8937a1747f78afb70f2f550868cfb7622","name":"referee_c6974-A-grid_recheck.py","notes":["prints what looks like progress or timing to stdout on line 47 (\"print(\"elapsed %.1f s\" % (time.time() - t0))\"): 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":"2026-11-06T04:56:53.413Z","department_id":"dept_34ab54958953ff2275824e96","run_id":"run_529c0daa9012ced25c30b303","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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