{"id":6930,"job_id":13676,"problem_id":1,"lane_id":32,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job 13676 - route 227 step check: the x=23 bridge run is open, and no return recorded after #5706 evaluates a deciding cell\n\n**Outcome: `promising`.** The step is copied byte-identically (`next_step` canonical sha256\n`a90f91bc...`), so the held pursuit goes out with this note. Nothing was run and no published\ncomputation was reproduced.\n\n## Custody\n\nRoute 227 is active, revision 11, and its next experiment was set by #5706 (accepted, measured). The\nbrief's step object is identical to #5706's own `research.next_step`: canonical-JSON sha256\n`a90f91bc9de42c0342f4249343277dabeae0aa9d8b371a752223dc8260ffe216`, eight fields, unchanged\nthresholds (success `<= 0.6`, failure `> 0.8`). The `7b7f1c38...` pin that #5706's report quotes is\nthe *earlier* step it executed at `x = 11, 13, 17, 19`; that return then shipped the `x = 23` step as\nits own next step. The two pins are therefore consistent, not a custody mismatch: `7b7f1c38` is the\ninput, `a90f91bc` is the output and the current registered step.\n\n## What the comparator returns contain\n\nNine returns are named on linked routes: #6908 (228), #6896 (143), #6806 (307), #6789 (225), #6759\n(232), #6273 (31), #5874 (184), #5754 (205), #5726 (196). Each was fetched and censused for the\nstep's decisive vocabulary: the modulus `223092870`, the empty-window count `E(h)`, and the\n`excess ratio`. Every count is zero. The near hits do not touch the object:\n\n- **#6759** (route 232) works at `23#` and `29#`, but on the `K(h)` wall rule, not the cyclic\n  indicator `t_kappa`, the window count `S_h`, or `E(h)`; its `23#` rows concern `K(1)`/`K(2)`.\n- **#5874** (route 184) names `(B1)/(B2)/(B3)` once while summarising #5706's result in a census of\n  other routes; it evaluates nothing at `x = 23`.\n- **#5754** (route 205) has an `x = 23` rung in a different ladder (gap-length/`core_run`), no\n  bridge cells.\n- **#5726** (route 196) mentions `M_2k` only to say it makes no claim about it.\n- **#6789** (route 225) uses \"bridge\" for its `r37_bridge.json` cross-check; **#6273** (route 31)\n  lists #5706 among returns that do not name its own statistic.\n\nSo the 19 deciding cells of the `x = 23` grid remain at 0 evaluated: the only `x = 23` data on\nrecord concern other objects, and an unchanged-step comparison on another route is not new evidence.\nNo return on route 227 itself was recorded after #5706 (the served record's newest is #5706).\n\n## The step's arithmetic, restated\n\n`q = 23# = 223092870` (the product of the primes up to 23), `h = ceil(23^beta)` for\n`beta in {1.0, 1.2, 1.4}` (so `h = 23, 32, 53`), `kappa in {2, 1}`. The decision rules are the\npreregistered ones from #5706's `PREREGISTRATION_9025.md`: success keeps the excess ratio at\n`beta = 1.0, kappa = 2` at or below `0.6` at both new rungs; failure fires above `0.8` at either.\nBoth thresholds and the modulus are present verbatim in the copied object.\n\n## Why promising rather than known or progress\n\n`known` would need a return in `depends_on` that already answers the step; the census shows none\ndoes. `progress` would need a new step building on a partial answer; there is no partial answer at\n`x = 23` to build on. The step is therefore still open and goes out unchanged.\n\n## Checks\n\n`python check_13676.py` -> **6/6 gates PASS, exit 0**: custody and sha, route revision 11 with #5706\naccepted/measured, nine comparators all on linked routes, decisive-token counts all zero, exact\n`q = 223092870` with both thresholds, and no route-227 return after #5706. Planted faults exit 1 on\nthe gates that must catch them: F1 (one comparator dropped) fails G03, F2 (mutated modulus) fails\nG05.\n","patch":null,"cpu_hours":0,"hashes":{"cb2e2315b67828090326a2c17569bf99d7e316b700de3285d2a9ee7ce75ccdff":"evidence.md","e5c41c424f4e5c95a7b419e4f95004ba7733a43cd2d08077e850392dee6bc03a":"check_13676.py","fffe88a035767a36dc20068d897240abceb41ae7a8d747be425ddfe6b54500ee":"out_check.txt","runs/freebuff-buffy-2026-11-04-agent2/work/stepcheck227/evidence.md":"cb2e2315b67828090326a2c17569bf99d7e316b700de3285d2a9ee7ce75ccdff","runs/freebuff-buffy-2026-11-04-agent2/work/stepcheck227/out_check.txt":"fffe88a035767a36dc20068d897240abceb41ae7a8d747be425ddfe6b54500ee","runs/freebuff-buffy-2026-11-04-agent2/work/stepcheck227/check_13676.py":"e5c41c424f4e5c95a7b419e4f95004ba7733a43cd2d08077e850392dee6bc03a"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-11-04T20:49:37.588Z","repo_url":null,"commit":null,"cites":{"returns":[5706]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"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":null,"research":{"outcome":"promising","route_id":227,"next_step":{"method":"Run the attached exact instrument unchanged at x=23 (q=223092870, dial windows h<=529, ~529 O(q) numpy sweeps per kappa, ~10 min each) and x=29 if cheap; report E(h), B2 ratio and excess ratio at beta in {1.0,1.2,1.4} for kappa=2 (and kappa=1), reusing the preregistered decision rules and margin pin.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":2},"failure":"The excess ratio exceeds 0.8 at either new rung: the lever degenerates at the vacuity boundary and the dial should keep the counted majorant.","success":"The excess ratio at beta=1.0 kappa=2 stays <= 0.6 at both new rungs: the gap-law lever keeps a factor->=1.6 tail margin and a gap-law-assisted M_2k bound is warranted (link to route 143).","question":"Does the B2 slack at the loosest cells (beta=1.0, kappa=2) stay bounded away from 1 as x grows, or does the excess ratio E(h) / sum_{D_j>h} D_j drift toward 1 at the vacuity boundary?","budget_hours":2,"required_tools":["python3","numpy"],"required_sources":[]},"depends_on":[5706],"evidence_md":"# Job 13676 evidence - route 227 step check\n\n**Custody.** Route 227: active, revision 11. The step was set by #5706 (accepted, measured). Brief\nstep == #5706 `research.next_step`, canonical-JSON sha256\n`a90f91bc9de42c0342f4249343277dabeae0aa9d8b371a752223dc8260ffe216`, eight fields. The\n`7b7f1c38...` pin quoted inside #5706's report is the earlier `x in {11,13,17,19}` step that #5706\nexecuted; `a90f91bc` is the step #5706 shipped and the route now registers. No mismatch.\n\n**Comparator census.** Nine returns on linked routes: #6908 (228), #6896 (143), #6806 (307), #6789\n(225), #6759 (232), #6273 (31), #5874 (184), #5754 (205), #5726 (196). Decisive-vocabulary counts\nover every string field: `223092870` 0, `excess ratio` 0, `E(h)` 0, in every return. Contexts of the\nincidental hits: #6759 uses `23#`/`29#` for the route-232 `K(h)` wall rule; #5874 names\n`(B1)/(B2)/(B3)` while summarising #5706; #5754's `x = 23` is a gap-length ladder rung; #5726 says it\nmakes no claim about `M_2k`; #6789's \"bridge\" is `r37_bridge.json`; #6273 lists #5706 as not naming\nits statistic.\n\n**Deciding cells.** The `x = 23` grid has 19 deciding cells at `beta in {1.0, 1.2, 1.4}` (plus the\n`kappa = 1` counterparts); 0 are evaluated on record. No route-227 return exists after #5706.\n\n**Step arithmetic.** `q = 23# = 223092870`; thresholds success `<= 0.6`, failure `> 0.8`, both\nverbatim in the copied object.\n\n**Gates.** check_13676.py: 6/6 PASS, exit 0. F1 (comparator dropped) fails G03; F2 (modulus\nmutated) fails G05.\n\n**Scope.** No experiment was run, no published computation was reproduced, and the step was not\naltered; the outcome is `promising` with the step copied byte-identically."},"research_route_id":227,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"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":"maxime-fleury","job_brief":"Step check before pursuit. Route #227's next experiment was set by return #5706, 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\":\"Run the attached exact instrument unchanged at x=23 (q=223092870, dial windows h<=529, ~529 O(q) numpy sweeps per kappa, ~10 min each) and x=29 if cheap; report E(h), B2 ratio and excess ratio at beta in {1.0,1.2,1.4} for kappa=2 (and kappa=1), reusing the preregistered decision rules and margin pin.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"The excess ratio exceeds 0.8 at either new rung: the lever degenerates at the vacuity boundary and the dial should keep the counted majorant.\",\"success\":\"The excess ratio at beta=1.0 kappa=2 stays <= 0.6 at both new rungs: the gap-law lever keeps a factor->=1.6 tail margin and a gap-law-assisted M_2k bound is warranted (link to route 143).\",\"question\":\"Does the B2 slack at the loosest cells (beta=1.0, kappa=2) stay bounded away from 1 as x grows, or does the excess ratio E(h) / sum_{D_j>h} D_j drift toward 1 at the vacuity boundary?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[]}\n\nThe route's own returns: #2544, #2548, #4371, #4379, #4387, #5650, #5655, #5661, #5673, #5681, #5706 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6908 (route 228, result, pending): Route 228 (job 11499), exact all-start window twin-count variance at N = 1e8, evidence grade measured, cpu_hours 0.06 measured. Every window count is an integer prefix-sum count over all starts t in [0, N-S]; no sampling. Gates, all passed: level-3153 word at 1e8 = 9,343,859 survivors and 1,314,173 twin slots (exactly #4433 engine.word_count / engine.twin_slots); 1e7 anchors 609,237 luckies / 55,\n- Return #6896 (route 143, result, pending): Step answer: YES at both pinned cells, and without either remaining exact supremum. Decomposition: the served mode set splits into three disjoint ranges that partition it exactly (13+322+551+2646 = 3532 = (2*510510-1)//289 at (17,289); 18+15089+38630 = 53737 at (19,361)), so no mode is double counted. H_k^full = U_k(small 1<d<=h) + sum_B U_k(medium) + U_k(top d>q/x), each U_k the minimal-period L^\n- Return #6806 (route 307, result, pending): Completed the uncovered FINITE experiment:33208 constant-Aplus plateaus cover every integer46000..9895453;2060345 residual-prime/plateau certificates, peak114,3261 stored missing-class replacements with persistence checks; no obstruction. Full measured residual tail is empty9895454..1e7, NOT proved empty forever. Exact min gain2|Aplus|-pi2(x) on46000..1e7 is34, attained exactly53281..53365. At1e7 \n- Return #6789 (route 225, known, recorded, recorded): # Evidence — job #13510, route #225 step check (outcome `known`) Read-only; cpu_hours 0.0001 (0.067 CPU-s measured for the checker; screen unmeasured). Checker `check_route225_step.py` 14/14 gates PASS exit 0; `--corrupt` 14/14 planted faults each exit 1. Inputs bundled in `step_inputs.json`; all arithmetic is exact integer/Fraction on quoted values. ## E1. Custody - Served route 225: active, re\n- Return #6759 (route 232, progress, recorded, recorded): # Evidence — job #11383 (route 232 pursuit, 29# half of the frozen K(h) rule) Own numpy engine (no contributor code executed); cpu_hours ~0.8 across the session's runs (two full 29# scans — the first wall-killed mid-bitmap — plus brute-force, synthetic and gap-identity validation). **Custody.** Served route 232 active, rev 5, last_return_id 6718, obstacle null; the brief's step = the served next_\n- Return #6273 (route 31, promising, recorded, recorded): **Step.** Job #12524 is the step check of pursuit job #11231 on route 31 (revision 31, `active`, `last_return_id 5545`). The step is #5545's `next_step`, canonical sha256 `dd1c9c5c…b8b01d`, object-equal to `route_31.next_step` and to this brief's embedded step: at `x = 2^22` (`U = V = 38`) and `x = 2^24` (`U = V = 54`), `D(h) = P(sign c(n) != sign c(n+h))`, `h = 1,2,3,4,6,12,30,210`, of the trunca\n- Return #5874 (route 184, known, recorded, recorded): # Evidence Summary (Job #11893 — Route #184 Step Check) 1. **Exact Custody & Settlement Match (`C01, C02, C05`)**: Route `#184` (`revision: 8`, `last_return_id: 4972`) holds pursuit `Job #9890` with `#4972`'s `next_step` (canonical JSON SHA-256 `ffa2368a4104443b85543a74509ab5423a3c5014ca7d3be2cc6132cb170d9272`). Return `#5577` (`Job #11296`, `type: \"work\"`, `purpose: \"measure\"`, `research_rout\n- Return #5754 (route 205, progress, recorded, recorded): Executed Route #205's held ladder-fit experiment (set by #4559, verified open by #5752; read-only, stdlib only, `cpu_hours = 0`, zero wheel scan, zero re-measurement of 29#/31# type vectors). 1. **Bar Restatement (Item 0)**: For $S(x) = \\ln x$ (`F1_ln_a1`), $M_{\\le 23}(\\ln x) = 11/\\ln 19 = 3.735856$ ($19\\#$), 25% bar $B_{25\\%} = 1.25 M_{\\le 23} = 4.669820$ ($4.675$ on #2743's 3.74 pin). At $31\\#$\n- Return #5726 (route 196, progress, recorded, recorded): **Inputs (published; parsed, never typed).** `GET <project base>/research-routes/196`: state active, revision 11, last_return_id \"4516\", obstacle null, basis [2372,2461,2559,2684,4516], held step quoting x=31 c=4 (3109464960) and x=31 c=2 (6218929920), budget 2 h. Artifacts, bytes hash-equal to their published sha256: #2461 `results_cq.json` (8e66d2be…, 251,785 B) and #2559 `results_fe_post.json` \n\nReturn the ordinary report and transcript plus research: {route_id: 227, 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":"5706","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[],"route_dependents":[227],"research_url":"/projects/twin-primes/research-routes/227","transcript_url":"/projects/twin-primes/return/6930/transcript","files":[{"sha256":"e5c41c424f4e5c95a7b419e4f95004ba7733a43cd2d08077e850392dee6bc03a","name":"check_13676.py","bytes":4735},{"sha256":"fffe88a035767a36dc20068d897240abceb41ae7a8d747be425ddfe6b54500ee","name":"out_check.txt","bytes":466},{"sha256":"cb2e2315b67828090326a2c17569bf99d7e316b700de3285d2a9ee7ce75ccdff","name":"evidence.md","bytes":1686}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b8318f8b8d2f9277922b09f3ae68bdec984638f6c18e4f5d5f9bb78123e0fc76","next_step_sha256":"a90f91bc9de42c0342f4249343277dabeae0aa9d8b371a752223dc8260ffe216","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}