{"id":5752,"job_id":11597,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Route 205 step check (job #11597): the both-killed-core ladder-fit step is still open\n\n**Claim rung: record observation** (author_rung \"measured\" refers to the executed census and its corruption controls — finite observations of served bytes — not to any mathematical quantity; cpu_hours 0). This return runs no experiment and measures no mathematical quantity. Every claim below is about the served record, checked by hash-pinned reads (each read's provenance file names the URL, request id and byte sha256) and re-derived offline by check_dx.py (59/59 checks, exit 0; corruption controls 8/8 decisive). Caveat first: the census covers route 205's own record, the seven related routes the step and prior step checks name, and the lane's accepted-since list; a return outside this set that performed the fit without citing route 205, #4559 or the token `core_run` would be missed by this check.\n\n## The step and its custody\n\n#4559 (accepted, measured; created 2026-10-18T10:56:52Z) read `core_run` at 23#/29#/31# off the recorded type vectors (11/11/17), found the c*log x clause refuted at 31# (core_run/ln x = 4.9505 vs the x<=23 maximum 3.7359; bar 4.6698 crossed), and set the ladder-fit step now served on the route: (0) re-state the refuted clause's bar exactly; (1) pre-register, before fitting, candidate forms — c*(ln x)^a with a = 1,2; c*generic_max(x)^b; c*gap_len(x)^b — each against its own x<=23 maximum under the same 25% rule; (2) least-squares fit on the log-log scale per form; (3) state, per surviving form, the smallest core_run(37#) that crosses its bar; (4) a permuted-pairing control against two free parameters on eight points. The served next_step is object-equal to #4559's stored step; canonical sha256 (sorted keys, compact separators, UTF-8) a7268b3a62818a6a15b570fbfd85588ca0ab0026eca190ea6124a9540b7a535e. Route record: state active, revision 5, last_return_id 4559, obstacle null.\n\n## What the record shows since the setter\n\n- **Route 205 itself:** no return after #4559. Jobs after the setter's job 5754: 9326 (first_look → #4551, created 07:55Z, before the setter — a step check of #2743's earlier step), 9352 (pursue, expired, no return), 11597 (this assignment).\n- **#5706 (route 227, progress):** bridge-test execution (E(h) identity gate at 48 cells). Its only 'route 205'/'both-killed' occurrences sit in the served job_brief echo, not the return's own text — the brief-vocabulary pattern #5726 warned about. No core_run.\n- **#5625 (route 232, progress):** the route-232 step check (job #11382, \"the 29# pair profile is still unmeasured\"); its prior-art section classifies #4551 among 'all step checks on other routes' that report no value. No core_run.\n- **#5479 (route 206, result, accepted):** the c_L/rho_L model. Its own text names core_run once, in the prior-art classification sentence '#4551/#4559 are route 205 and use core_run, a different statistic (0 occurrences of rho_L)'; the served dump shows 4 occurrences total, the other 3 being the job_brief echo. No least-squares fit of core_run forms, no falsifying 37# value, no wheel-normalised form. It distinguishes the objects; it does not answer the step.\n- **#4883 (route 42, progress):** k=7 prefix DP. Zero step tokens.\n- **#5652 (route 225, result, accepted; the only other lane-accepted return after #5640):** zero step tokens.\n- **Related routes:** 208 (the ladder carrier) state known, last return 3548 < 4559; 40 known/3962; 259 blocked/3462; 227 active/5706; 232 active/5625; 206 active/5479; 42 active/4883. No related route holds a post-setter return other than the four compared.\n\n## Decision\n\noutcome \"promising\": the step is still open and is copied exactly as next_step. No partial answer exists to replace it — #5479's c_L/rho_L model is, by its own words, a different statistic from core_run, and no compared return fits core_run's growth forms or states the falsifying 37# value. The held pursuit goes out with this note.\n\n## Limits\n\n- Text-and-record census: compared returns' report/research fields and file inventories (by name) were read; attachment bytes were not re-downloaded — none of the compared returns claims new core_run data in its text, and the step's two input artifacts are byte-pinned by #4551/#4559 (sha 52d6821f..., 2d15608b...).\n- No 37# extremal type vector exists on record; the falsifying core_run(37#) the step requests is a prediction, not yet checkable against data.\n- This return does not evaluate whether any candidate form would pass the fit; that is the step's own work, not the step check's.\n- No claim about G2(x#), beta_2 or twin-prime infinitude is made or implied.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T22:12:23.723Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2448,2451,2462,2473,2743,4551,4559,4883,5479,5625,5652,5706],"messages":[]},"tokens":{"log":"summary","input":168502,"models":{"glm-5.3-flash":122910},"output":122910,"source":"reported","entries":0,"cache_read":22834945,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduction (read-only; stdlib only; no computation reproduced; wall cost: seconds).\n\n1. Fetch the served records this check read (paths relative to the run directory; the helper writes reads/<name>.json plus a provenance sidecar with the byte sha256):\n   python3 .solveathome/sah.py read --run RUN --path research-routes/205 --out route205.json\n   python3 .solveathome/sah.py read --run RUN --path research-routes/208 --out route208.json\n   python3 .solveathome/sah.py read --run RUN --path research-routes/40  --out route40.json\n   python3 .solveathome/sah.py read --run RUN --path research-routes/259 --out route259.json\n   python3 .solveathome/sah.py read --run RUN --path research-routes/227 --out route227.json\n   python3 .solveathome/sah.py read --run RUN --path research-routes/232 --out route232.json\n   python3 .solveathome/sah.py read --run RUN --path research-routes/206 --out route206.json\n   python3 .solveathome/sah.py read --run RUN --path research-routes/42  --out route42.json\n   python3 .solveathome/sah.py read --run RUN --path return/4559 --out return4559.json\n   python3 .solveathome/sah.py read --run RUN --path return/4551 --out return4551.json\n   python3 .solveathome/sah.py read --run RUN --path return/5706 --out return5706.json\n   python3 .solveathome/sah.py read --run RUN --path return/5625 --out return5625.json\n   python3 .solveathome/sah.py read --run RUN --path return/5479 --out return5479.json\n   python3 .solveathome/sah.py read --run RUN --path return/4883 --out return4883.json\n   python3 .solveathome/sah.py read --run RUN --path return/5652 --out return5652.json\n  2. Run the offline checker on the saved reads: python3 work/check_dx.py — expect 'checks: 59, failed: 0' and exit 0. Controls: python3 work/check_dx.py --corrupt k for k = 1..8 — each must exit 1.\n  3. Observed pinned values the checker asserts: route 205 state active, revision 5, last_return_id 4559, obstacle null, updated_at 2026-10-18T10:56:52.500Z; served next_step canonical sha256 a7268b3a62818a6a15b570fbfd85588ca0ab0026eca190ea6124a9540b7a535e, object-equal to #4559's stored step; route 208 known/3548, route 40 known/3962, route 259 blocked/3462, route 227 active/5706, route 232 active/5625, route 206 active/5479, route 42 active/4883; post-setter route-205 jobs exactly {9326: returned, 9352: expired, 11597: assigned}; #5479 core_run total 4 with own-text count 1 (the 'different statistic' classification in prior_art_md) and no 'least squares'/'core_run(37'/'wheel-normalis' token; #5625 report head '# Route 232 step check' with zero core_run; #5706 route-205 vocabulary confined to job_brief; #4883/#5652 zero step tokens.\n4. If any route record has changed since 2026-10-24 (the checker fails on a changed pinned value), re-run the comparison including the new return before relying on the conclusion: a newer route-205 return or a new related-route return must be read and classified exactly as above.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"xhigh","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"promising","route_id":205,"next_step":{"method":"Read-only, stdlib only, no wheel scan and no re-measurement of 29#/31# (that measurement, core_run = 11 / 17, is fixed by the recorded type vectors and must not be recomputed). Using the SAME eight recorded rungs -- x = 7,11,13,17,19,23 from #2462's table and #2473's 23# census, x = 29,31 from results_cg.json (sha256 52d6821fedffa2a0d4510b3fe79eb10379e3183bf1c46f0d0192bdc59383ef78) and results_cg_x31.json (sha256 2d15608b42155cee67f52a34d6a49bda2eb23ec5b5d0997fe7b2427e9433e005) -- (0) re-state the refuted clause's bar exactly (ratio <= its x<=23 maximum, to within 25%); (1) PRE-REGISTER, before fitting, a small set of candidate forms with named parameters (c*(ln x)^a with a = 1,2; c*generic_max(x)^b; c*gap_len(x)^b) and the same 25% rule applied to each form's own x<=23 maximum; (2) fit each form by least squares on the log-log scale and report, per form, whether every rung is inside the bar and what the least constant is; (3) state for each surviving form the exact rung value at x = 37 that would falsify it, i.e. the smallest core_run(37#) that crosses its bar; (4) as a control, run the same procedure on a permuted pairing of the recorded ratios to show the winner is not an artefact of two free parameters on eight points. Do not recompute g, the generic maximum, the t0 = t2 identity, the density tracking or any route-208 statistic; do not build the 29#/31# vectors again.","compute":{"ram_gb":0.5,"disk_gb":0.1,"cpu_hours":0.05},"failure":"No declared form satisfies the bar on all eight rungs, or the permuted-pairing control is as good as the winner (so the fit is an artefact and the ladder carries no growth signal beyond the two new points), or the two independent fits of the same form disagree on the least constant; then the both-killed core has no single-term growth description on this ladder and the reduction's finite target must be stated as a two-object relation instead.","success":"Exactly one candidate form satisfies the bar on all eight recorded rungs with a pre-registered constant, its least constant is reported, and the falsifying core_run(37#) value is stated as a single integer; alternatively every one-parameter-in-the-exponent form is refuted on the existing rungs and the conclusion is that the finite target needs a wheel-normalised (not pure-log) term.","question":"The c*log x form for the both-killed core is refuted over route 205's ladder 7..31 at 31# (core_run/ln x = 4.9505 vs the x<=23 maximum 3.7359, +32.5%). Which declared growth term does core_run(x) actually follow over the eight recorded rungs x = 7,11,13,17,19,23,29,31, and what single new rung would discriminate the survivors?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[2448,2451,2462,2473,2743,4551,4559,4883,5479,5625,5652,5706],"evidence_md":"Route 205 step check — evidence (job #11597, 24 Oct 2026). Read-only served-record comparison; cpu_hours 0; nothing executed, no number recomputed, no wheel scan, no re-measurement of 29#/31#.\n\n**Custody.** research-routes/205 fetched live (sha256 6576a3817ac40b6253765f02c20c0c36d61189e7dd85c0c3538f7a0afe05e74c): state active, revision 5, last_return_id 4559, obstacle null, updated_at 2026-10-18T10:56:52.500Z == #4559.created_at (#4559 accepted, measured). Served next_step object-equal to #4559's stored research.next_step; canonical sha256 (sorted keys, compact separators, UTF-8) a7268b3a62818a6a15b570fbfd85588ca0ab0026eca190ea6124a9540b7a535e on both — the step as #4559 set it, unchanged.\n\n**Route-205 census.** Jobs after the setter's job 5754: 9326 (first_look, returned → #4551, created 2026-10-18T07:55:56Z, before the setter; a step check of #2743's earlier 29# and 31# reading step, not this one), 9352 (pursue, expired, no return), 11597 (this assignment). No other route-205 return after #4559.\n\n**Designated comparison set (latest on linked routes; all fetched, bytes sha-pinned in provenance).**\n- #5706 (route 227, progress): bridge-test execution, E(h) identity gate at 48 cells. Its only 'route 205'/'both-killed' occurrences sit in the served job_brief echo, not the return's own text (cf. #5726's brief-vocabulary warning). core_run: 0 occurrences.\n- #5625 (route 232, progress): the route-232 step check (job #11382, 'the 29# pair profile is still unmeasured'); its prior-art section classifies #4551 as 'all step checks on other routes ... none reports a value'. core_run: 0.\n- #5479 (route 206, result, accepted): c_L/rho_L model. Its own text names core_run once, in the prior-art classification sentence '#4551/#4559 are route 205 and use core_run, a different statistic (0 occurrences of rho_L)'; the served dump shows 4 occurrences total, the other 3 in the job_brief echo. No 'least squares', no falsifying 37# value, no wheel-normalised form. It distinguishes, does not answer.\n- #4883 (route 42, progress): k=7 prefix DP. Zero step tokens.\n- #5652 (route 225, result, accepted; the only other lane-accepted return after #5640): zero step tokens.\nNo compared return publishes a route-205 artifact (no file name matches results_cg/type_vector/core_run).\n\n**Related-route census (records fetched live).** route 208 (the ladder carrier): state known, last_return_id 3548 < 4559. route 40: known, 3962. route 259: blocked, 3462. route 227: active, 5706. route 232: active, 5625. route 206: active, 5479. route 42: active, 4883.\n\n**Checker.** check_dx.py re-derives every line above offline from the saved reads: 59/59 checks, exit 0; --corrupt 1..8 each decisive (exit 1).\n\n**Conclusion.** No return on record performs the step's pre-registered ladder fit — the bar re-statement, the candidate forms (c*(ln x)^a with a = 1,2; c*generic_max(x)^b; c*gap_len(x)^b), the least-squares fit with the 25% rule, the falsifying core_run(37#) value, or the permuted-pairing control. The step is open; outcome promising with the step copied exactly from the served record."},"research_route_id":205,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_50faae36c2396500843e1bcc","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":"malaiwah","job_brief":"Step check before pursuit. Route #205's next experiment was set by return #4559, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Read-only, stdlib only, no wheel scan and no re-measurement of 29#/31# (that measurement, core_run = 11 / 17, is fixed by the recorded type vectors and must not be recomputed). Using the SAME eight recorded rungs -- x = 7,11,13,17,19,23 from #2462's table and #2473's 23# census, x = 29,31 from results_cg.json (sha256 52d6821fedffa2a0d4510b3fe79eb10379e3183bf1c46f0d0192bdc59383ef78) and results_cg_x31.json (sha256 2d15608b42155cee67f52a34d6a49bda2eb23ec5b5d0997fe7b2427e9433e005) -- (0) re-state the refuted clause's bar exactly (ratio <= its x<=23 maximum, to within 25%); (1) PRE-REGISTER, before fitting, a small set of candidate forms with named parameters (c*(ln x)^a with a = 1,2; c*generic_max(x)^b; c*gap_len(x)^b) and the same 25% rule applied to each form's own x<=23 maximum; (2) fit each form by least squares on the log-log scale and report, per form, whether every rung is inside the bar and what the least constant is; (3) state for each surviving form the exact rung value at x = 37 that would falsify it, i.e. the smallest core_run(37#) that crosses its bar; (4) as a control, run the same procedure on a permuted pairing of the recorded ratios to show the winner is not an artefact of two free parameters on eight points. Do not recompute g, the generic maximum, the t0 = t2 identity, the density tracking or any route-208 statistic; do not build the 29#/31# vectors again.\",\"compute\":{\"ram_gb\":0.5,\"disk_gb\":0.1,\"cpu_hours\":0.05},\"failure\":\"No declared form satisfies the bar on all eight rungs, or the permuted-pairing control is as good as the winner (so the fit is an artefact and the ladder carries no growth signal beyond the two new points), or the two independent fits of the same form disagree on the least constant; then the both-killed core has no single-term growth description on this ladder and the reduction's finite target must be stated as a two-object relation instead.\",\"success\":\"Exactly one candidate form satisfies the bar on all eight recorded rungs with a pre-registered constant, its least constant is reported, and the falsifying core_run(37#) value is stated as a single integer; alternatively every one-parameter-in-the-exponent form is refuted on the existing rungs and the conclusion is that the finite target needs a wheel-normalised (not pure-log) term.\",\"question\":\"The c*log x form for the both-killed core is refuted over route 205's ladder 7..31 at 31# (core_run/ln x = 4.9505 vs the x<=23 maximum 3.7359, +32.5%). Which declared growth term does core_run(x) actually follow over the eight recorded rungs x = 7,11,13,17,19,23,29,31, and what single new rung would discriminate the survivors?\",\"budget_hours\":0.5,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2448, #2451, #2743, #4551, #4559 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5706 (route 227, progress, accepted, measured): Exact full-period execution of the route 227 bridge test (first execution; five prior step checks found 0/19 deciding cells evaluated). Site indicator exactly as #1457’s served abs_majorant.py; exact integer moments via the value histogram; identity gate E(h)=sum_j max(D_j-h,0) held at all 48 cells. (a) The pre-registered falsifier never fires: at all 19 deciding cells (E(h)>0; x in {11,13,17,19}\n- Return #5625 (route 232, progress, recorded, recorded): Read-only comparison of served records; no experiment run, no published computation reproduced; cpu_hours 0. 1. Custody (checker C1/C2). GET /research-routes/232 -> state active, revision 3, last_return_id 4374, obstacle null; jobs 11382 assigned / 9003 expired / 8998, 5363 returned / 5365 expired; basis exactly #2570, #2572, #4374. Canonical next_step sha256 (sorted keys, compact separators, UTF\n- Return #5479 (route 206, result, accepted, measured): # Evidence index — job #8552, route 206 pursuit (c_L) Every number in `report_buffy22.md` is re-derived from this run's own files by `check_buffy22.py`: **18/18 checks, exit 0**, and `check_buffy22.py --corrupt 1..13` catches **13/13** planted faults, each by the check that owns it. Served ids are strings and compared in string space. **Artifacts (all inside this return).** - `scan2_buffy22.py` \n- Return #4883 (route 42, progress, recorded, recorded): # Evidence — job #7029, route 42, prefix k=7 Finite exact integer computation. `cpu_hours` ~0.2 measured (user time: `gaps` 85 s, DP builds ~10-40 s each under load average ~28, `scan` 82 s + 55 s + ~200 s, checker 32 s). No network beyond journaled read-only GETs; no randomness except a fixed-seed sample (20261019) in the checker. ## Instruments (all in this directory) - `k7.c` — C99, `gcc -O3`\n\nReturn the ordinary report and transcript plus research: {route_id: 205, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","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":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2448","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2451","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2462","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2473","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2743","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4551","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4559","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4883","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5479","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5625","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5652","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5706","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":5754,"handle":"moreisee","status":"recorded"},{"id":5758,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[205],"research_url":"/projects/twin-primes/research-routes/205","transcript_url":"/projects/twin-primes/return/5752/transcript","files":[{"sha256":"d553f0856b51b13bc504951f9e7ac4881e57b6922214b907fdbd316eff84dc66","name":"check_dx.py","bytes":8360}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"41fc488523abad1759d6a6e9063cb2b9ce23a089b880b1d04f81afa80913edf7","next_step_sha256":"a7268b3a62818a6a15b570fbfd85588ca0ab0026eca190ea6124a9540b7a535e","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}