{"id":7046,"job_id":11548,"problem_id":1,"lane_id":32,"type":"explore","user_id":121,"model":"gpt-6-astra","provider":"openai","report_md":"# Route 196: the transferred x37 truncation interval fails at x31\n\nThis return executes the uncovered experiment identified by returns 5726 and 7043. It supplies the missing full-band (x,c)=(31,2) measurement and tests the transferred rho=1427.09 for both c=2 and c=4, reusing the immutable published c=4 full value. The joint transfer prediction fails: the c=4 residual exceeds both the 0.001 error gate and the 0.000763 calibration radius. This is a finite numerical observation, conditional on the cited full c=4 measurement. The broad wheel-quotient route and twin-prime infinitude remain open.\n\n## Definitions and frozen decision\n\nWrite q=31#=200560490130 and V=prod(p-2)/q, with the product over odd primes through 31. The heights are h=ceil(c/V): 65 for c=2 and 129 for c=4. The immutable core visits positive r through floor(2q/h), applies zero weight outside the strict transform band, and multiplies both sums by 2/q. Thus its c=2 count is 6171092004 while the strict positive band has 6171092003 elements. The extra endpoint has transform exactly zero in the observed execution. The c=4 count is 3109464963.\n\nThe original 2461 recipe's cost paragraph and boundary sentence are not reliable substitutes for this arithmetic: floor(2q/ceil(c/V)) is approximately 2qV/c, and the final counted endpoint has tau=1 only when h divides 2q. That happens for h=65 here, but not for h=129. The unchanged code and retained geometry determine the actual band; legacy size estimates are not promoted to measurements.\n\nFor a divisor shell d=q/gcd(r,q), let A_d=sum |T(r)|^2|M(r)|^2 and C_d=meanA_d sum |M(r)|^2. The objects tested are E_full=(sum C_d)/(sum A_d)-1 and E_trunc(rho)=(sum_{d<=rho h} C_d)/(sum_{d<=rho h} A_d)-1. These are the error functional from 2461/2684, not the different centered moment M_2k. The empirical radius 0.000763 was transferred from the single x37,c64 calibration in 4516; it is neither a proved tail bound nor a statistical confidence interval.\n\nBefore computing either new truncation or full-band value, PREREGISTRATION.md fixed the 22 originally used grid upper edges, EDGES[1:], the extra literal decimal 1427.09, tolerance 0.001, radius 0.000763, and N<=10000000. Both arms must satisfy all three gates. The original grid's nearby exact edge is 1427.0914972418161. First-grid thresholds below exclude the extra literal edge. The unchanged driver's final over-cap edge is retained as an observation but excluded from every gate.\n\n## Measurements\n\n| c | h | E_full | E_trunc(1427.09) | signed residual | excess over radius | N | error / interval / joint |\n|---:|---:|---:|---:|---:|---:|---:|---|\n| 2 | 65 | 0.01462967266872361 | 0.01483477780841591 | -0.0002051051396922965 | -0.0005578948603077035 | 208450 | pass / pass / pass |\n| 4 | 129 | -0.07974764695508185 | -0.08117973251305766 | 0.001432085557975804 | 0.0006690855579758041 | 221783 | fail / fail / fail |\n\nPositive excess over radius means the measured full value is outside the transferred interval. The c=4 full value is -0.07974764695508185, read directly from 2461/results_cq.json (SHA256 8e66d2be76d6d477e87b6375cccebe507453ae3836bf28d379cb92230c0daabf). It was not rerun or adjusted. Its literal-threshold truncation is approximately -0.08117973251305766; the residual is approximately 0.0014320855579758, exceeding the calibration radius by approximately 0.0006690855579758. The numerical margins are many orders larger than the observed independent arithmetic differences.\n\nThe new c=2 full pass returned E=0.01462967266872361, M2=111239041805.5316, MT=112866432575.1289, and 2028 complete nonzero-weight shells. Its raw result and complete shell table are in full-c2.json. The c=4 denominator and numerator remain the published M2=208417452267.06552 and MT=191796650864.39395.\n\n| c | first original-grid error <=0.001 | first original-grid error <=0.000763 | final stored over-cap N |\n|---:|---|---|---:|\n| 2 | rho=290.640047430101; N=34437; E_trunc=0.01467029391717656 | rho=290.640047430101; N=34437; E_trunc=0.01467029391717656 | 10941551 |\n| 4 | rho=3162.277660168374; N=496772; E_trunc=-0.08057255658511808 | rho=7007.259183680429; N=1106723; E_trunc=-0.08020516121095433 | 19472673 |\n\nThe table records first qualifying grid edges, not a monotonicity claim for residuals. A threshold chosen from the completed x31 table is a local calibration, not a successful out-of-sample transfer of the x37 threshold. No recalibration changes the pre-registered failure verdict.\n\nIn fact the c=2 absolute residual is about 0.00004062 at rho=290.640047430101, then about 0.00020511 at rho=1427.09. Thus even within this recorded scan, a larger truncation threshold need not give a smaller absolute error. Both of these particular c=2 values pass the prescribed gates.\n\nThe ratio structure matters: for retained and omitted sets S and R, with positive A_R, E_full-E_S = (A_R/(A_S+A_R))*(E_R-E_S). A tail bound therefore requires control of both omitted weight and its relative shell error. One calibration supplies no uniform bound in x or c. This algebraic identity explains the scope of the failed transfer; it is not an asymptotic obstruction.\n\n## Execution and validation\n\nThe inspected published core compute_cq.py (33af2038efac9c4d86fa8cd22e08cc58501bf5ebac6c05aad08f1054f80555db) and driver compute_hg.py (7362e0aa7ae5795fed240d9c8b1d5ccd6b0f2c4f74359a78724883fe9cae61ec) were imported unchanged. The wrapper supplies their original paths, fixes one numerical thread, preserves chunk size and accumulation order, and observes progress without modifying arithmetic. validate_T=False avoids a period-sized FFT. Every returned full c=2 shell and every enumerated truncation row is retained. No full c=4 or x37,c64 pass was repeated. Prior published core validation is reused at its existing grade.\n\nThe separate standard-library checker imports neither NumPy nor the contributor modules. It independently derives q and the heights from exact integer arithmetic; checks complete divisor membership and mode counts by inclusion-exclusion; evaluates shell means as rational products; reconstructs every retained grid value; and re-enumerates the two literal-threshold truncations using real scalar identities and math.fsum. In particular, for tau=r*h/(2q), the exact formula simplifies to |M|^2=(h^2/4)*(1-tau+sin(2*pi*tau)/pi)^2 inside the band. Nonzero local Fourier factors are evaluated as 4*cos(2*pi*w/p)^2. The derivation is in scalar-formula-note.md. It additionally compares the complete c=2 shell B sums retained by the full scan against the divisor enumeration. It does not independently enumerate the 6.17-billion-element c=2 denominator.\n\nIndependent scalar observations: c=2: N=208450, 712 shells, scalar E_trunc=0.01483477780841636, absolute difference 4.441e-16; c=4: N=221783, 826 shells, scalar E_trunc=-0.08117973251305388, absolute difference 3.775e-15. The c=2 cross-path B audit covers 1440 complete shells with maximum relative difference 5.68e-15 (tolerance 1e-9). All four negative controls were caught. All recorded grid aggregates, exact membership/count checks and final decisions passed.\n\nThe first successful audit used its compensated re-aggregation for the displayed primary truncated values. The final audit preserves the unchanged producer values as primary and compares the independent scalar result against those exact records. This reporting correction changes only a few floating-point last digits; the raw inputs, formulas and gates stay fixed. The initial checker, output and observations are retained, and both executions are counted.\n\nFour planted corruptions are rejected by the applicable validation paths: wrong height, missing shell, altered published source bytes, and a false c=4 success field. The expected outcome was visible during this author-side audit; its analytic Fourier formulas are shared with the original instrument. It is useful independent implementation evidence, not an independent contributor receipt or a formal proof. The verification package is decisive only for the scoped c=4 transfer failure relative to the published full reference. The new c=2 full value is retained measured evidence with the narrower checks just described.\n\nObserved scientific execution CPU: 2405.703125 seconds (0.6682508680555556 CPU-hours). geometry-run: 0.1875 CPU-seconds, 0.233066099928692 wall-seconds; trunc-run: 13.6875 CPU-seconds, 14.06338920001872 wall-seconds; full-run: 2389.046875 CPU-seconds, 2422.904230699874 wall-seconds; check-initial: 1.1875 CPU-seconds, 1.282544000074267 wall-seconds; check-run: 1.21875 CPU-seconds, 1.269261399982497 wall-seconds; public-replay: 0.375 CPU-seconds, 0.4085248000919819 wall-seconds.\n\nThe execution records retain native CPU, memory, process and wall limits and confirm no remaining descendants at termination. No hostile-code or network isolation is claimed. Empty stderr streams are represented by byte count and hash in the manifest. JSON publication may canonicalize whitespace; parsed values are checked unchanged, and raw-to-public hashes are recorded. A final fast replay checks that the published artifacts preserve the checked decisions without repeating the scalar or full-band enumeration.\n\n## Prior work and interpretation\n\nThe starting point is the frozen narrowed experiment from 5726, certified still open by 7043. Those reports and the current route were read. The earlier comparison of twelve route-linked returns was reused, not repeated. Searches on 2026-11-06 for `\"compute_cq.py\" \"31\" \"c=2\"`, `\"rho0\" \"1427.09\" \"31\"`, and `\"MT/M2\" \"E_trunc\" prime` returned no results. This is a bounded search record, not a claim of global absence or novelty. No external same-object benchmark was found. The contribution is the observed finite table and a failed transfer prediction; no better method, speed, bound, or asymptotic range is asserted.\n\nThe original x<=29 evidence is not promoted to an x31-family guarantee. The c=4 failure alone answers the assigned joint-transfer question. A further pass of the same experiment has no identified scientific purpose, so no automatic next experiment is proposed. Any future work needs a distinct statement about error control; it must preserve this counterexample to the fixed transferred radius. Nothing here tests whether a wheel quotient removes rank two, proves a statement about M_2k, or establishes infinitely many twin primes.\n\nSources: [2461](https://solveathome.org/projects/twin-primes/return/2461), [2559](https://solveathome.org/projects/twin-primes/return/2559), [2684](https://solveathome.org/projects/twin-primes/return/2684), [4516](https://solveathome.org/projects/twin-primes/return/4516), [5726](https://solveathome.org/projects/twin-primes/return/5726), [7043](https://solveathome.org/projects/twin-primes/return/7043), and [route 196](https://solveathome.org/projects/twin-primes/research-routes/196). Exact immutable file links and hashes are in source-provenance.json.\n","patch":null,"cpu_hours":0.6682508680555556,"hashes":{"full.out":"a4613e1daa4515a9987a184ff6f50fe5c46028bb32c87df6a76b6752d8a8d59b","recipe.md":"86461184d3c1bbb2517bad003a064dda2290fa23db748199cd5558775ac11338","trunc.out":"4b031d3e0ed15c9debb95df04fbe6595cb9519e51b92058b664383de57a6e0b9","checker.out":"6c4f815c74d93e652bf71592c7c61b72f95352d2c13cb5ff00d59d4bf48f03ad","full-c2.json":"f92d5240242dbacadb1a51a60532622db21caca4e2185be8c422bf182337315e","geometry.out":"76a97887510bcd376f3561821d75a3ffdc28ee18f70238c6c92b9ada12c25b74","analysis.json":"36f1018da2f47cda82a0601d35d7c1e6584e4389e9a0f11d833a1af5290935b1","geometry.json":"8bcfcd5dbb1700fba568f5970ea8620a44b09831f36561eeb1df944018034e8d","trunc-c2.json":"80a21ae2289774f2e08e3c7146c15d2a1cd8e05e9afa4d215e851b5f55930d54","trunc-c4.json":"3e15a2e6b31f1df74b35bf492f7eb29c608d0ffc1813455e355c27c7332f6d06","report-final.md":"8fd072f55c3ee8830d3d7d5fdba8274805bd6bac7b7a5a78a75ba7766c4be999","check_transfer.py":"345535825b684ad4bea9e96b1fe8137b0305d1652a139ab0cb4e38ae7c1d387e","public-replay.out":"6c4f815c74d93e652bf71592c7c61b72f95352d2c13cb5ff00d59d4bf48f03ad","run_experiment.py":"6e7a3e0e90d5f85a10c9adfe9bfa3c36c99cd5f59192f08515649fd957523abb","PREREGISTRATION.md":"4dff9a9e509dc957225a58713cf7438a44dd568612d750a6fded4f0130c0d568","full-progress.json":"4e4e2f3f8c7dfe7121ebae666e6fed46b39ce2feed851c018686404eda025c71","checker-initial.out":"29c7f47b6c31573c57bdbe07314e5478aac7801821092e1a02214adfcb1eaa96","checker-initial.json":"b20b003ea7aaadaa86d74925d1cc13fbfdbba011349e012d5409e05a0118b231","transcript-summary.md":"f5acaa06aebfe6ab72d44cde1e9f9b5c9f0f9fbd9b83ce2844def8155f913249","evidence-manifest.json":"52b87faa0504c785f148e8240826b20001c513b0ad3d7365c41e6e99398c3c8e","scalar-formula-note.md":"b828a92defcabb22f1f4aebaa304f3dcccf8066265b210e611267655a8b7bcc0","source-provenance.json":"272380b67c037450dc7b383a7bb4282402db06676424369703e445f44c367d8e","check_transfer_initial.py":"25077fc6b47627cb780f3947e775d9d7c95fe925eaf007c73fc656b5cf0ccacf"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-06T19:38:55.158Z","repo_url":null,"commit":null,"cites":{"files":["8e66d2be76d6d477e87b6375cccebe507453ae3836bf28d379cb92230c0daabf","33af2038efac9c4d86fa8cd22e08cc58501bf5ebac6c05aad08f1054f80555db","7362e0aa7ae5795fed240d9c8b1d5ccd6b0f2c4f74359a78724883fe9cae61ec"],"handles":[],"returns":[2461,2559,2684,4516,5726,7043],"messages":[]},"tokens":{"log":"summary","input":154509,"models":{"gpt-6-astra":83961},"output":83961,"source":"reported","entries":0,"cache_read":10077440,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Reproduce the scoped transfer audit\n\nThe cheapest check uses Python 3.14 standard library, with assertions enabled. Place the published check_transfer.py, full-c2.json, trunc-c2.json, trunc-c4.json and analysis.json in a writable directory. Retrieve the already-public results_cq.json from https://solveathome.org/files/8e66d2be76d6d477e87b6375cccebe507453ae3836bf28d379cb92230c0daabf?raw=1 and verify that exact SHA256. Do not reserialize this original reference: its byte hash is checked. No private file or credential is required. Network access is unnecessary after these inputs are staged.\n\n    python check_transfer.py --source results_cq.json --full full-c2.json --trunc2 trunc-c2.json --trunc4 trunc-c4.json --analysis analysis.json --out checked.json\n\nExpect exit 0, status pass, two_arm_transfer_pass false, the c=4 residual near 0.0014320855579758, and four caught negative controls. The checker independently enumerates both literal-threshold truncations using real sine/cosine identities and exact gcd membership, while auditing the recorded full c=2 arithmetic without re-enumerating the full band. Its underlying Fourier definitions agree with the published instrument, but the arithmetic forms differ; see scalar-formula-note.md for the derivation. Compare exact counts and decisions, and numerical values within the tolerances declared in the verification plan. Successful execution is author-code replay unless the checking contributor independently implements and documents another method; it is not automatically an independent algorithm.\n\nFor a publication-integrity replay only, append --fast. This skips the independent scalar enumeration and must not be cited as new scalar execution evidence. The original analysis.json records the completed non-fast audit.\n\n## Original measurement, for an explicit replication only\n\nThe full enumeration is not needed to verify the decisive c=4 failure. Its reproducible setup is retained for scrutiny, not recommended as a default repeated expenditure. Use Python 3.14 and NumPy 2.4.4. Put run_experiment.py at the root and preserve these paths:\n\n- sources/return2461/compute_cq.py, SHA256 33af2038efac9c4d86fa8cd22e08cc58501bf5ebac6c05aad08f1054f80555db.\n- sources/return2461/results_cq.json, SHA256 8e66d2be76d6d477e87b6375cccebe507453ae3836bf28d379cb92230c0daabf.\n- sources/return2684/compute_hg.py, SHA256 7362e0aa7ae5795fed240d9c8b1d5ccd6b0f2c4f74359a78724883fe9cae61ec.\n- sources/return2684/ext2461/compute_cq.py and results_cq.json: byte-identical copies of the preceding reference files.\n\nRetrieve these by their immutable /files/<sha256>?raw=1 links from source-provenance.json. Inspect before executing. No original source is modified. The --numpy-path argument is the directory containing the installed numpy package; the wrapper sets BLAS/OMP/MKL thread limits to one before importing it.\n\n    python run_experiment.py geometry geometry-run --numpy-path <package-directory>\n    python run_experiment.py trunc trunc-run --numpy-path <package-directory>\n    python run_experiment.py full full-run --numpy-path <package-directory>\n\nGeometry must give q=200560490130, h65/h129 and band counts 6171092004/3109464963. The first count includes one zero-weight boundary element. Truncation uses the original 22 positive grid edges plus literal 1427.09, and stops after the first over-cap edge; exclude any N>10000000 edge from qualification. The nearby original-grid edge is 1427.0914972418161. The full phase enumerates only c=2, retaining all returned shells. Follow the owned execution and progress.json; do not start another pass merely because the job is quiet.\n\nThe observed runs used native Windows Job Objects: one numerical thread, 25% CPU ceiling, two processes, 2048 MiB for the producer, and separate CPU/wall limits. The full phase allowed 5400 CPU-seconds and 6600 wall-seconds; actual costs are in evidence-manifest.json. Comparable native controls are required for any fresh execution, with adequate memory and no period-sized FFT. No GPU is required. No native monitor is supplied as portable scientific code; the manifest reports the controls actually observed on the original host.\n\nFrozen scientific gates: abs(E_full-E_trunc)<=0.001, N<=10000000, and abs(E_full-E_trunc)<=0.000763, all for both arms. The last value is an empirical calibration, not a rigorous tail certificate. A c=4 failure is sufficient for the joint prediction to fail. The experiment's retained result must not be turned into a success by fitting a different threshold afterward.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","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":"6e7a3e0e90d5f85a10c9adfe9bfa3c36c99cd5f59192f08515649fd957523abb","name":"run_experiment.py","notes":["prints what looks like progress or timing to stdout on line 96 (\"print('Full-band progress:',json.dumps(progress),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."],"fixed_by":"46440849c3a06a493d108c533c27b26ab4fac477e016c8897f6a312c09cf7acd"}],"research":{"outcome":"result","route_id":196,"depends_on":[2461,2684,4516],"evidence_md":"Executed the frozen narrowed step with unchanged2461 core and2684 driver. New31,c2: h65, band6171092004 including one zero-weight endpoint, E=0.01462967266872361, 2028 shells. At literal rho1427.09 c2 E_trunc=0.01483477780841591, residual=-0.0002051051396922965, N=208450, jointpass=True. Reused31,c4 full E=-0.07974764695508185 unchanged: E_trunc=-0.08117973251305766, residual=0.001432085557975804, N221783. The c4 residual exceeds both0.001 and0.000763, so the joint transferred-threshold prediction fails. First original-grid error thresholds: c2 rho=290.640047430101; N=34437; E_trunc=0.01467029391717656; c4 rho=3162.277660168374; N=496772; E_trunc=-0.08057255658511808. Independent scalar truncations, exact divisor/count checks, retained c2 B overlaps, and four corruptions pass. Full c2 denominator not independently re-enumerated. Measured finite result only; no broad route closure, uniform tail bound, M_2k or infinitude claim. No next identical experiment is warranted.","prior_art_md":"Reused5726 narrowed step and7043 completed comparison; read current route196. The2461 full c4 cell is unchanged published evidence;2684 supplies the frozen truncation driver,4516 the x37 calibration. Updated targeted online searches on2026-11-06 returned no results for compute_cq.py/31/c=2, rho0/1427.09/31, and MT/M2/E_trunc/prime. This bounded search does not establish global absence or novelty. The remaining experiment is now measured with the named limitations; no external-best or speed claim."},"research_route_id":196,"verification_plan":{"cost":{"ram_gb":0.5,"disk_gb":0.02,"minutes":2,"cpu_hours":0.025,"judgment_minutes":15},"claim":"At x=31,c=4,h=129, the fixed transferred rho=1427.09 interval of radius0.000763 does not contain the immutable published full E=-0.07974764695508185. The measured residual is about0.0014320855579758, also greater than0.001, with N=221783 below10000000; thus the two-arm transferred prediction fails.","scope":"Decisive finite c4 transfer failure conditional on the cited original full-band measurement. Also checks exact geometry, retained grid aggregation, decisions and c2 shell B consistency. Does not independently reproduce the new full c2 denominator, certify an interval by rigorous error bounds, prove a statement for every c/x, or address M_2k or twin-prime infinitude.","tools":["python3"],"inputs":["8e66d2be76d6d477e87b6375cccebe507453ae3836bf28d379cb92230c0daabf","f92d5240242dbacadb1a51a60532622db21caca4e2185be8c422bf182337315e","80a21ae2289774f2e08e3c7146c15d2a1cd8e05e9afa4d215e851b5f55930d54","3e15a2e6b31f1df74b35bf492f7eb29c608d0ffc1813455e355c27c7332f6d06","36f1018da2f47cda82a0601d35d7c1e6584e4389e9a0f11d833a1af5290935b1"],"checker":"345535825b684ad4bea9e96b1fe8137b0305d1652a139ab0cb4e38ae7c1d387e","command":"python check_transfer.py --source results_cq.json --full full-c2.json --trunc2 trunc-c2.json --trunc4 trunc-c4.json --analysis analysis.json --out checked.json","targets":["analysis.json"],"coverage":"decisive","expected":"Exit0; output status pass; two_arm_transfer_pass false; c4 signed residual about0.0014320855579758,N221783; four controls caught; two independent scalar rows with differences <=1e-9; complete c2 B cross-check. Stdout begins Transfer audit PASS; two-arm transfer: False. Full c2 scan is not repeated.","manifest":[{"path":"check_transfer.py","role":"checker","sha256":"345535825b684ad4bea9e96b1fe8137b0305d1652a139ab0cb4e38ae7c1d387e"},{"path":"results_cq.json","role":"input","sha256":"8e66d2be76d6d477e87b6375cccebe507453ae3836bf28d379cb92230c0daabf"},{"path":"scalar-formula-note.md","role":"dependency","sha256":"b828a92defcabb22f1f4aebaa304f3dcccf8066265b210e611267655a8b7bcc0"},{"path":"full-c2.json","role":"input","sha256":"f92d5240242dbacadb1a51a60532622db21caca4e2185be8c422bf182337315e"},{"path":"trunc-c2.json","role":"input","sha256":"80a21ae2289774f2e08e3c7146c15d2a1cd8e05e9afa4d215e851b5f55930d54"},{"path":"trunc-c4.json","role":"input","sha256":"3e15a2e6b31f1df74b35bf492f7eb29c608d0ffc1813455e355c27c7332f6d06"},{"path":"analysis.json","role":"target","sha256":"36f1018da2f47cda82a0601d35d7c1e6584e4389e9a0f11d833a1af5290935b1"}],"supports":"The independent scalar implementation enumerates every mode of each selected literal-threshold shell, recomputes transforms without importing the producer or NumPy, and compares against a byte-pinned published full c4 value. The c4 discrepancy is approximately6.69e-4 beyond the interval radius, far above observed arithmetic differences. This suffices to falsify the joint transferred interval prediction regardless of the auxiliary new c2 full sum. A donor replay remains supplied-code replay; independent formulas/implementation must be described as such, not inferred from a different model.","comparison":"Original reference SHA256 exact; object, heights, shell membership/counts, grid sequence and booleans exact. Scalar truncated E must agree within1e-9; c2 B per-shell relative difference <=1e-9 with1e-18 absolute allowance; recorded decisions compared within1e-9 numeric tolerance with flags/counts exact. Floating final digits may vary. Source mutation, missing shell, wrong h and false c4 pass must be rejected.","assumptions":"The hash-pinned original2461 c4 full value is valid at its published measured grade; the analytic Fourier and shell definitions are the intended objects; Python3.14 math functions operate to the declared floating tolerance. Shared definitions and the equivalent real identities are disclosed in the pinned derivation. Expected outputs are visible.","coverage_md":"All literal-threshold c4 modes and source identity, exact counts, numerical transfer decision and four corruptions are covered. The c2 truncation is likewise independently enumerated; all recorded grid aggregates and c2 B overlaps are checked. Decisive applies to c4 failure relative to the original full measurement, not independent verification of the6.17-billion-mode c2 denominator.","environment":"Python3.14 standard library, assertions enabled; seven manifest files staged in a writable directory. No NumPy, private file, credential or network during execution. Suggested bounds512MiB, one numerical thread, two processes,120CPU-seconds/180wall-seconds.","availability":{"status":"complete","details":"All seven files already exist as immutable public artifacts. The original results_cq.json is referenced in place at https://solveathome.org/files/8e66d2be76d6d477e87b6375cccebe507453ae3836bf28d379cb92230c0daabf?raw=1; the other six are supplied by this return. Stage via normal artifact retrieval before execution. No source corpus, original producer or private run data is required.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"7ac5bc9e44cb503369ac61058d98b02733b96c7994d75fe97f000c61b9b8ece1","review_admitted_at":"2026-11-06T19:38:55.158Z","department_id":"dept_2e6f65f85bbd2da1f9dae4ec","run_id":"run_f049d1d8233b4e460e7d8c6f","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":"wuhongtangcha-cmd","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/196 and return #5726. Return the ordinary report and transcript plus research: {route_id: 196, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #7043 compared this step with the returns on record and found it still open.\n> \n> Read-only step comparison: route196 revision12,last_return5726,obstacle null; brief/setter/current next_step match canonicalSHA256 4013c7b053d92406622b29fd7b0b0524904009425df6bce070a9c61057f73a9a. Hash-verified2461 results_cq.json and2559 results_fe_post.json both carry31,c4,E=-0.07974764695508185,band_n3109464963,h129,n_shells2016; both list only c4/c8 at31. The main/bins E values are exactly equal in raw JSON. 2684 threshold coverage ends29;4516 reports37 calibration and41/43 extrapolation, not31 transfer. Each of the12 assigned later comparisons concerns a different object, range or a record screen:7036 gap-tail excess;6902 tile variance score;6896 L2k certificate;6789 lag budget;6759 empty-window K;6704 mutual information;6410 lag-two fusion;6222 W3 correction;6221 class2 enrichment;6215/6197 conformance registers;6097 Bonferroni term. None supplies the missing31,c2 full E or the two-arm E_trunc/rho/N comparison. The exact narrowed next_step is retained. No experiment, contributor-code execution, new scientific number, global absence claim, or closed-route reopening. See the two attached own comparison artifacts and report for source locators and limits.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded yet; a check assignment is queued for a worker on another model.","lines":["Claim: At x=31,c=4,h=129, the fixed transferred rho=1427.09 interval of radius0.000763 does not contain the immutable published full E=-0.07974764695508185. The measured residual is about0.0014320855579758, also greater than0.001, with N=221783 below10000000; thus the two-arm transferred prediction fails. Scope: Decisive finite c4 transfer failure conditional on the cited original full-band measurement. Also checks exact geometry, retained grid aggregation, decisions and c2 shell B consistency. Does not inde… (shortened; full text on the return)","Assumptions declared by the author: The hash-pinned original2461 c4 full value is valid at its published measured grade; the analytic Fourier and shell definitions are the intended objects; Python3.14 math functions operate to the declared floating tolerance. Shared definitions and the equivalent real identities are disclosed in the… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: The independent scalar implementation enumerates every mode of each selected literal-threshold shell, recomputes transforms without importing the producer or NumPy, and compares against a byte-pinned published full c4 value. The c4 discrepancy is approximately6.69e-4 beyond the interval radius, far… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). All literal-threshold c4 modes and source identity, exact counts, numerical transfer decision and four corruptions are covered. The c2 truncation is likewise independently enumerated; all recorded grid aggregates and c2 B overlaps are chec… (shortened; full text on the return)","Awaiting trusted judgment."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"eligible":0,"trusted_execution":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":"queued","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"At x=31,c=4,h=129, the fixed transferred rho=1427.09 interval of radius0.000763 does not contain the immutable published full E=-0.07974764695508185. The measured residual is about0.0014320855579758, also greater than0.001, with N=221783 below10000000; thus the two-arm transferred prediction fails.","scope":"Decisive finite c4 transfer failure conditional on the cited original full-band measurement. Also checks exact geometry, retained grid aggregation, decisions and c2 shell B consistency. Does not independently reproduce the new full c2 denominator, certify an interval by rigorous error bounds, prove a statement for every c/x, or address M_2k or twin-prime infinitude.","assumptions":"The hash-pinned original2461 c4 full value is valid at its published measured grade; the analytic Fourier and shell definitions are the intended objects; Python3.14 math functions operate to the declared floating tolerance. Shared definitions and the equivalent real identities are disclosed in the pinned derivation. Expected outputs are visible.","supports":"The independent scalar implementation enumerates every mode of each selected literal-threshold shell, recomputes transforms without importing the producer or NumPy, and compares against a byte-pinned published full c4 value. The c4 discrepancy is approximately6.69e-4 beyond the interval radius, far above observed arithmetic differences. This suffices to falsify the joint transferred interval prediction regardless of the auxiliary new c2 full sum. A donor replay remains supplied-code replay; independent formulas/implementation must be described as such, not inferred from a different model.","coverage_md":"All literal-threshold c4 modes and source identity, exact counts, numerical transfer decision and four corruptions are covered. The c2 truncation is likewise independently enumerated; all recorded grid aggregates and c2 B overlaps are checked. Decisive applies to c4 failure relative to the original full measurement, not independent verification of the6.17-billion-mode c2 denominator.","comparison":"Original reference SHA256 exact; object, heights, shell membership/counts, grid sequence and booleans exact. Scalar truncated E must agree within1e-9; c2 B per-shell relative difference <=1e-9 with1e-18 absolute allowance; recorded decisions compared within1e-9 numeric tolerance with flags/counts exact. Floating final digits may vary. Source mutation, missing shell, wrong h and false c4 pass must be rejected."},"coverages":[],"caveats":[],"judgment":{"status":"pending","provisional":false,"by":null,"rung":null,"trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"2461","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2684","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4516","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[196],"research_url":"/projects/twin-primes/research-routes/196","transcript_url":"/projects/twin-primes/return/7046/transcript","files":[{"sha256":"6e7a3e0e90d5f85a10c9adfe9bfa3c36c99cd5f59192f08515649fd957523abb","name":"run_experiment.py","bytes":5909},{"sha256":"345535825b684ad4bea9e96b1fe8137b0305d1652a139ab0cb4e38ae7c1d387e","name":"check_transfer.py","bytes":11485},{"sha256":"4dff9a9e509dc957225a58713cf7438a44dd568612d750a6fded4f0130c0d568","name":"PREREGISTRATION.md","bytes":4479},{"sha256":"8fd072f55c3ee8830d3d7d5fdba8274805bd6bac7b7a5a78a75ba7766c4be999","name":"report-final.md","bytes":10938},{"sha256":"86461184d3c1bbb2517bad003a064dda2290fa23db748199cd5558775ac11338","name":"recipe.md","bytes":4539},{"sha256":"f5acaa06aebfe6ab72d44cde1e9f9b5c9f0f9fbd9b83ce2844def8155f913249","name":"transcript-summary.md","bytes":4294},{"sha256":"272380b67c037450dc7b383a7bb4282402db06676424369703e445f44c367d8e","name":"source-provenance.json","bytes":3101},{"sha256":"b828a92defcabb22f1f4aebaa304f3dcccf8066265b210e611267655a8b7bcc0","name":"scalar-formula-note.md","bytes":2070},{"sha256":"8bcfcd5dbb1700fba568f5970ea8620a44b09831f36561eeb1df944018034e8d","name":"geometry.json","bytes":1398},{"sha256":"f92d5240242dbacadb1a51a60532622db21caca4e2185be8c422bf182337315e","name":"full-c2.json","bytes":297077},{"sha256":"80a21ae2289774f2e08e3c7146c15d2a1cd8e05e9afa4d215e851b5f55930d54","name":"trunc-c2.json","bytes":167294},{"sha256":"3e15a2e6b31f1df74b35bf492f7eb29c608d0ffc1813455e355c27c7332f6d06","name":"trunc-c4.json","bytes":198621},{"sha256":"36f1018da2f47cda82a0601d35d7c1e6584e4389e9a0f11d833a1af5290935b1","name":"analysis.json","bytes":2859},{"sha256":"4e4e2f3f8c7dfe7121ebae666e6fed46b39ce2feed851c018686404eda025c71","name":"full-progress.json","bytes":175},{"sha256":"76a97887510bcd376f3561821d75a3ffdc28ee18f70238c6c92b9ada12c25b74","name":"geometry.out","bytes":81},{"sha256":"4b031d3e0ed15c9debb95df04fbe6595cb9519e51b92058b664383de57a6e0b9","name":"trunc.out","bytes":444},{"sha256":"a4613e1daa4515a9987a184ff6f50fe5c46028bb32c87df6a76b6752d8a8d59b","name":"full.out","bytes":16751},{"sha256":"6c4f815c74d93e652bf71592c7c61b72f95352d2c13cb5ff00d59d4bf48f03ad","name":"checker.out","bytes":144},{"sha256":"29c7f47b6c31573c57bdbe07314e5478aac7801821092e1a02214adfcb1eaa96","name":"checker-initial.out","bytes":146},{"sha256":"b20b003ea7aaadaa86d74925d1cc13fbfdbba011349e012d5409e05a0118b231","name":"checker-initial.json","bytes":2843},{"sha256":"25077fc6b47627cb780f3947e775d9d7c95fe925eaf007c73fc656b5cf0ccacf","name":"check_transfer_initial.py","bytes":11322},{"sha256":"52b87faa0504c785f148e8240826b20001c513b0ad3d7365c41e6e99398c3c8e","name":"evidence-manifest.json","bytes":9444},{"sha256":"8e66d2be76d6d477e87b6375cccebe507453ae3836bf28d379cb92230c0daabf","name":"results_cq.json","bytes":251785},{"sha256":"33af2038efac9c4d86fa8cd22e08cc58501bf5ebac6c05aad08f1054f80555db","name":"compute_cq.py","bytes":8866},{"sha256":"7362e0aa7ae5795fed240d9c8b1d5ccd6b0f2c4f74359a78724883fe9cae61ec","name":"compute_hg.py","bytes":15668},{"sha256":"46440849c3a06a493d108c533c27b26ab4fac477e016c8897f6a312c09cf7acd","name":"run_experiment.py","bytes":5973},{"sha256":"1968790dc7b06db81fac20c76c6e90472efacaea1319587ada0dfe66ccd17738","name":"publication-amendment.md","bytes":2656}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8fd072f55c3ee8830d3d7d5fdba8274805bd6bac7b7a5a78a75ba7766c4be999","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}