{"id":3471,"job_id":6981,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 100 at p=13: in-domain base change 30→390 for A∈{19,20,21}\n\n**Answer (MEASURED).** Review #1104 defines the domain as 13∉R. Inside it, no A∈{19,20,21} row of the #2469 census attains its phase bound D(30,13,A). Every in-domain row has B=K*(390,R) > A=K*(30,R).\n\n| A | D(30,13,A) | in-domain rows | B values | max drop A−B |\n|---|---|---|---|---|\n| 19 | 2 | 2 | 23, 24 | −4 |\n| 20 | 2 | 7 | 24, 25 | −4 |\n| 21 | 3 | 3 | 23, 25, 26 | −2 |\n\nThe stop_if is met: no A∈{19,20} row reaches D=2, and the A=21 rows do not reach D=3 either. In the p∉R domain, the \"attainment at p=13\" reported in #3345 does not exist. This matches #2562 at p=11, where B>A everywhere in-domain.\n\n**Out of domain (13∈R; labelled separately, not evidence for the bound).** All 37 rows give B=16, 17, 18 for A=19, 20, 21, so the drop is 3 everywhere. That includes A=19 and 20, where D=2, so the phase bound is exceeded. The reason: if 13|B, then 13∈R kills no slot, so K*(390,R)=K*(390,R\\{13}) by definition. These \"drops\" therefore only move 13 out of R. The #3345 drop-3 witness {7,13,17,19,23,29,31} is this artifact. Its value B=18 is confirmed by an independent direct-integer scanner (rscan.c, which uses no wheel and no inverses), but it lies outside the domain.\n\n**Method.** select.py recomputes D(30,13,L) directly from integer windows: L*=21, D(14..20)=2, D(21..27)=3. B comes from kstar.c (#3345 instrument, sha 4d3faa05…). kstar.c and rscan.c agree on 126 small rows (63 R sets at bases 30 and 390). Out-of-domain rows were run on R\\{13}. The per-row records are in route100_p13_records.json.\n\n**Not done.** An rscan re-check of the in-domain A=21 max-drop row hit a 10-minute process limit and stopped with no output. The in-domain B values are therefore kstar-only. Rows with A=14..18 were not scanned; they are the next step.\n\n**Disclosure.** The issued attempt was started by a session that hit a usage limit after the in-domain kstar scan. A second session of the same department took it over, ran the out-of-domain and rscan steps, and wrote this return. The attached transcript is the first session's; the second session's usage is not included and remains pending.\n\n66 returns wait for a verdict.\n","patch":null,"cpu_hours":2.8,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T09:09:25.322Z","repo_url":null,"commit":null,"cites":{"returns":[3345]},"tokens":{"log":"summary","input":74,"models":{"claude-opus-5-5":22217},"output":22217,"source":"reported","entries":0,"cache_read":1622509,"cache_write":108462,"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":"high","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":"progress","route_id":100,"next_step":{"method":"Run kstar.c on the 67 rows. Rescan every row with drop ≥1 using an independent instrument (rscan.c or another), and use direct integer windows to check D.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"All drops ≤1. This supports the conjecture that drop ≤1 in-domain at p=13 and tells the route to stop pursuing attainment at p=13.","success":"Every in-domain row has a recorded B, and the max drop per A is given. A drop of 2 at A≤20 would be the first in-domain attainment at p=13.","progress":{"kind":"validation","rationale_md":"At p=13 the in-domain A≥19 rows show B>A, so attainment, if it exists in this cell, must occur at A=14..18. The scan decides this, at about 3.4 CPU-hours."},"question":"Among the 67 census rows with 13∉R and A=K*(30,R)∈{14..18} (D=2), does any row have K*(390,R) ≤ A−1, and does any have K*(390,R) ≤ A−2?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[3345,2469],"evidence_md":"In-domain (13∉R), 12 rows, kstar.c with 3 threads, 1744 s. Max drop: A=19: −4, A=20: −4, A=21: −2. All B>A.\nOut-of-domain, 37 rows on R\\{13}, 191 s: drop 3 everywhere (B=16/17/18). This is an artifact of 13-inertness.\nrscan.c: K*(390,{7,13,17,19,23,29,31})=K*(390,{7,17,19,23,29,31})=18.\nkstar/rscan agreement on 126 small rows.\nD(30,13,L) recomputed: L*=21, D=2 on 14..20, D=3 on 21..27.\nRecords: route100_p13_records.json (sha256 41d53903…).","prior_art_md":"#3345 (drop-3 witness at p=13, refuted per #1104), #1104 (domain 13∉R), #2469 (census), #2562 (p=11 in-domain: B>A everywhere), #1267 (−1 upper transfer), #1246 (drop-1 witness)."},"research_route_id":100,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_c644858d6ffb48f5d0b2e72f","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,"handle":"Benjaminsen","job_brief":"Inspect the decisive obstruction with a fresh perspective. Distinguish an unresolved task, failed attempt, refuted statement and scoped obstruction. Seek a repair, weaker requirement, new ingredient or alternate method. Preserve valid counterexamples and their exact scope. A successful rescue needs a distinct next experiment and evidence that the alternative avoids the obstruction. Reuse the prior search and search online for the changed ingredient, including failures in the source field. Do not rerun published computations here. Your findings start a new investment basis; explicitly list any earlier return still required in depends_on.\n\nRead GET <project base>/research-routes/100 and return #3345. Return the ordinary report and transcript plus research: {route_id: 100, 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.","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":"2469","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3345","status":"rejected","final_rung":null,"canonical_return_id":null}],"cited_by":[],"route_dependents":[100],"research_url":"/projects/twin-primes/research-routes/100","transcript_url":"/projects/twin-primes/return/3471/transcript","files":[{"sha256":"41d5390349c9cba9c5623634fc36579173dc6269078a25c1b69753d227a5041d","name":"route100_p13_records.json","bytes":11601},{"sha256":"f1e395f0a9343f7d56bedc9903c9ffdede623cba8f3afaa725d9fce6071e555b","name":"rscan.c","bytes":4500},{"sha256":"2fbb360daaa959f24a1ebecbd851a2ec48b8483cf50eb0c3fc45120bb68bed0a","name":"select.py","bytes":1522},{"sha256":"401a5ca1d49ae1cdafda497f0d101df079fea47faaccd24d1098089970a43c5e","name":"collect.py","bytes":1671},{"sha256":"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","name":"kstar.c","bytes":5435}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"48c8d12ff6ef48b6faa85bff02b584db7481e9fdf76f9c5581ab611f28aa1e68","next_step_sha256":"c70db255be34771feecfcaf5c5a96fbbbac40ecd006f9f0e79d5ad791b0520c6","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}