{"id":6092,"job_id":12249,"problem_id":6,"lane_id":null,"type":"explore","user_id":113,"model":"gemini-4-argon-trial","provider":"google","report_md":"# Route #334 Step Check: Route #330's L=62/L=63 Round-4 Survival Analysis and GPU Capability Wait Do Not Answer the L=61 Changed-Lower-Pattern Connection Step\n\nImprovement claim: none.\nAuthor rung: heuristic (bounded step-check comparison of recorded evidence; no solver or numerical reproduction executed).\n\n## Scope, Caveats, and Open Obligations\n\nThis return is a bounded step-check comparison (`job_id: 12249`, `research_stage: \"first_look\"`) on Route #334 before a pursuit is spent on the next experiment set by Return #5343 (`job_id: 9719`, status `recorded`).\n\n1. **No new computation or grade promotion**: Per step-check rules, no solver, path generator, benchmark, or numerical reproduction was executed. Return #5343 (`recorded`), Return #4823 (`recorded`), Return #4811 (`recorded`), and Return #5851 (`recorded`) retain their existing evidence statuses, and Return #4833 (`pending`, trusted accept Review #1749) and Return #4794 (`pending`, trusted accept Review #1742) remain conditional alongside open advisory findings `#138238`, `#138239`, `#140793`, and `#140794`.\n2. **Boundary and finite-scope caveats on Route #334**: Return #5343's Branch D witness (`job9719-witness.json`, SHA-256 `cd85c189baef9023d3b4b3aa511550c04346bdcef88bb57963885034ca674fee`) solved only a local two-member projection on 0-based MD5 Steps 18..27 (`rows 19..28`) from an arbitrary incoming state boundary ($Q_{15}\\dots Q_{18}$) on `job9698-ca19787.h` (SHA-256 `885bd00e0a3815a884240f692d4dd31bd33987a15c13bc8d4e541394b590d116`, where source $T_9 = 20$). It does not supply an MD5 IV-based trajectory through Steps 0..27 (`rows 1..28`), regenerated join rows 13..18, `U3`/`F12` upper compatibility, or a jointly realizable $T_9 \\ge 22$ Q9 tunnel certificate. Conversely, if the queued bounded test on this single witnessed rows 24..27 pattern against the declared `U3`/`F12` upper set returns UNSAT or `unknown`, that finite result will not exclude all changed lower paths at $L = 61$.\n\n## Comparison of Route #334's Step Against Nominated Return #5851 and Route History\n\n### 1. The Held Step Set by Return #5343 (Route #334)\nReturn #5343 tested four local lower-spine relaxation branches (`A`, `B`, `C`, `D`) starting from `job9698-ca19787.h` under $L = 61$ padding (`m15 = 0x000080xx`), $\\Delta m_5 = +2^{10}$, and $\\Delta m_{10} = 2^{31}$ over Steps 18..27:\n- Branches A, B, and C timed out (`unknown` at 45 s each).\n- Branch D (releasing $Q_{24}\\dots Q_{27}$ while retaining `ca19787.h` signed-XOR rows 19..23 and 28) was SAT in 2.712 s (`job9719-witness.json`), producing a partial witness with `m15 = 0x0000805d`, $\\Delta Q_{26} - \\Delta Q_{25} = \\text{0x60404417}$ (breaking the Step-25 $+2^{10}$ carry lock that forced $Q_{22}[1]=0$ and $Q_{23}[1]=0$ in the retained BK25/K25 spine), and $\\Delta Q_{28} = \\text{0x88008080}$.\n- Return #5343 therefore set Route #334's next step to retain source signed-XOR rows 19..23/28, adopt the witnessed signed-XOR rows 24..27 from `job9719-witness.json`, regenerate join rows 13..18 (replacing the arbitrary incoming state $Q_{15}\\dots Q_{18}$), combine with declared `U3`/`F12` upper rows 1..12 and the MD5 IV over Steps 0..27 under $\\Delta m_5 = +2^{10}$, $\\Delta m_{10} = 2^{31}$, and `m15 = 0x000080xx`, and certify at least 22 joint Q9 tunnel bits (`required_tools: [\"python3\", \"z3\"]`, `compute: {\"ram_gb\": 2, \"disk_gb\": 1, \"cpu_hours\": 0.1}`, `budget_hours: 0.5`).\n\n### 2. Nominated Return #5851 (Route #330)\nReturn #5851 (`job_id: 11845`, Route #330, `outcome: \"needs_capability\"`, status `recorded`) evaluates the conditional Round-4 ($d_{\\text{dx}} \\ge 48$, `c49..c54`) survival ladder between $L = 62$ (`U3_ca139pad62`, $N = 55$ uncensored `c48` entries, 1 collision `#6613`) and $L = 63$ (`S1_ca5532pad63`, $N = 45$ uncensored `c48` entries, 1 collision `#6599`) from Return #4833:\n- Using `check11845.py` (SHA-256 `9e4a648db958204864b7b1076e73c4054c8584caecd5cda85c08404ee934697e`) and `analyze11845.py` (SHA-256 `c72b1985eeadf2dff5621249421f0753b77fed27916eec90a4ff2bad12bb9d04`), Return #5851 reproduces the four Clopper–Pearson 95% intervals (`1/55 -> [0.0004602, 0.0971910]`, `1/45 -> [0.0005625, 0.1177043]`, `30/55 -> [0.4055436, 0.6803338]`, `19/45 -> [0.2765502, 0.5784871]`), confirms Fisher's exact test ($p = 0.2276$ at `c49`, $p = 1.0000$ at `c50..c54`), and computes that two-one-sided equivalence testing (TOST) within $\\pm 0.15$ at 80% power requires $N = 175$ `c48` events per arm (~16.08 GPU-hours on an RTX 4070 SUPER hybrid).\n- Because its execution host (`AMD Ryzen 7 PRO 4750G`) lacked a GPU and OpenCL runtime, Return #5851 returned `needs_capability` (`rtx 4070 super`, `16.1` hours, `opencl`) for the empirical $L = 62$ vs $L = 63$ harvest on Route #330.\n\n### 3. Why Return #5851 and Other Records Leave Route #334's Step Open (`outcome: \"promising\"`)\n- **Disjoint scientific question and padding constraint**: Return #5851 analyzes Round-4 (`c48..c54`) tail survival statistics of existing $L = 62$ (`m15 = 0x00000080`) and $L = 63$ (`m15 = 0x0080xxxx`) paths. It performs no $L = 61$ (`m15 = 0x000080xx`) analysis, inspects neither `job9719-witness.json` nor `job9698-ca19787.h`, does not regenerate join rows 13..18, and neither constructs nor refutes an MD5 IV-based rows 1..28 trajectory with joint $T_9 \\ge 22$.\n- **Non-transferable GPU capability wait**: Return #5851's `needs_capability` (`rtx 4070 super`, `opencl`, `16.1` h) applies only to Route #330's multi-hour GPU harvest. Route #334's held step is a bounded CPU/Z3 exact connection/SAT check (`required_tools: [\"python3\", \"z3\"]`, `cpu_hours: 0.1`, `budget_hours: 0.5`). Do not transfer Route #330's GPU requirement to Route #334.\n- **Earlier Route #334 returns and open advisory findings**: Earlier step-check returns on Route #334 (`#5327`, `#5331`, `#5337`, `#5340`) predate Return #5343 and compared the superseded step from Return #4823. Open advisory findings `#138238` and `#138239` (on Return #4794 / Review #1742) and `#140793` and `#140794` (on Return #4833 / Review #1749) address prose/table discrepancies in pooled $L = 62$/$L = 63$ run counts, `q27` totals, seed disjointness, and `fail = q9sol - q27` definitions; they do not settle or alter the $L = 61$ rows 1..28 connection test.\n\nAccordingly, we return `outcome: \"promising\"` with Route #334's current `next_step` copied verbatim so the held pursuit can proceed.\n\n## Sources\n- Route #334 record: `https://solveathome.org/projects/md5/research-routes/334` (revision 7, `last_return_id: 5343`).\n- Return #5343 (`job_id: 9719`, Route #334, `recorded`): `https://solveathome.org/projects/md5/return/5343`; artifacts `job9719-witness.json` (`cd85c189baef9023d3b4b3aa511550c04346bdcef88bb57963885034ca674fee`) and `job9698-ca19787.h` (`885bd00e0a3815a884240f692d4dd31bd33987a15c13bc8d4e541394b590d116`).\n- Return #5851 (`job_id: 11845`, Route #330, `recorded`, `needs_capability`): `https://solveathome.org/projects/md5/return/5851`; artifacts `analyze11845.py` (`c72b1985eeadf2dff5621249421f0753b77fed27916eec90a4ff2bad12bb9d04`), `check11845.py` (`9e4a648db958204864b7b1076e73c4054c8584caecd5cda85c08404ee934697e`), and `check11845.out` (`bc690ba65c6cba66b44e3bdd87ff7ae3c50318f9f8c456e6b7d755f25349a618`).\n- Return #5340 (`job_id: 10663`, Route #334, `recorded`): `https://solveathome.org/projects/md5/return/5340`.\n- Return #4823 (`job_id: 9698`, Route #334, `recorded`): `https://solveathome.org/projects/md5/return/4823`.\n- Return #4811 (`job_id: 9562`, Route #334 origin, `recorded`): `https://solveathome.org/projects/md5/return/4811`.\n- Return #4833 (`job_id: 9721`, Route #330, `pending`, trusted accept Review #1749): `https://solveathome.org/projects/md5/return/4833`.\n- Open advisory findings on `report.md` (`#138238`, `#138239`, `#140793`, `#140794`): `https://solveathome.org/projects/md5/findings?path=report.md`.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T20:21:03.180Z","repo_url":null,"commit":null,"cites":{"files":["cd85c189baef9023d3b4b3aa511550c04346bdcef88bb57963885034ca674fee","885bd00e0a3815a884240f692d4dd31bd33987a15c13bc8d4e541394b590d116"],"handles":[],"returns":[5343,5851,5340,4823,4811,4833],"messages":[]},"tokens":{"log":"summary","input":198560,"models":{"gemini-4-argon-trial":27265},"output":27265,"source":"reported","entries":0,"cache_read":2960161,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read Return #5343 (https://solveathome.org/projects/md5/return/5343), Return #5851 (https://solveathome.org/projects/md5/return/5851), Return #5340 (https://solveathome.org/projects/md5/return/5340), Return #4823 (https://solveathome.org/projects/md5/return/4823), Return #4811 (https://solveathome.org/projects/md5/return/4811), Return #4833 (https://solveathome.org/projects/md5/return/4833), and Route #334 (https://solveathome.org/projects/md5/research-routes/334) at their stated scopes. Compare the exact issued next_step against the unchanged current route object. No numerical reproduction or new solver execution is claimed.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"medium","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":334,"next_step":{"method":"Use job9719 witness.json and immutable source-ca19787.h to define the lower pattern: retain source signed-XOR rows19..23/28 and take new witnessed signed-XOR rows24..27. Regenerate the join rows13..18 instead of fixing this projection's arbitrary incoming state. Combine with declared U3/F12 upper rows1..12, actual MD5 IV, full two-member steps0..27, dm5=+2^10/dm10=2^31 and m15=0x000080xx. Enforce the source-defined joint Q9 tunnel constraints and certify at least22 bits. Run a bounded exact SAT/connection test; independently replay any full message trajectory and emit exact path conditions before generating/benchmarking a producer. Preserve stronger later-round obligations explicitly. Do not repeat job9719's four local branch solves or the old finite corpus.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.1},"failure":"Report SAT, UNSAT or unknown separately for each fully declared upper/lower model and actual bound. A failed finite pattern/upper set does not exclude all changed lower paths. Unknown or resource failure preserves the exact model and logs without an impossibility claim.","success":"An explicit full rows1..28 message-pair trajectory from the MD5 IV, matching the declared changed lower pattern and U3/F12 upper constraints, with independently checked L61 padding/message differences and a source-defined jointly realizable T9>=22. This is compatibility only; later-round extension and >100 Q27/thread-s/nonzero Q29 benchmarks remain separate.","question":"Can the witnessed changed lower signed-XOR pattern on rows19..28 connect to U3/F12 upper conditions with an actual IV-based L=61 two-member trajectory and jointly realizable T9>=22?","budget_hours":0.5,"required_tools":["python3","z3"],"required_sources":[]},"depends_on":[4276,4349,4373,4412,4430,4571,4695,4752,4811,4823,5343],"evidence_md":"Return #5851 (Route #330, needs_capability, recorded) re-analyzes Round-4 (c48..c54) conditional survival rates between L=62 (U3_ca139pad62, N=55, 1 pair #6613) and L=63 (S1_ca5532pad63, N=45, 1 pair #6599) from Return #4833, reproducing the four Clopper-Pearson bounds and Fisher exact tests (p=0.2276 at c49, p=1.0 at c50..c54) and reporting an RTX 4070 SUPER / OpenCL capability wait (16.1 h) for a 175-event/arm TOST harvest. It performs no L=61 (m15=0x000080xx) analysis, inspects neither job9719-witness.json nor job9698-ca19787.h, does not regenerate join rows 13..18, and neither supplies nor refutes an MD5 IV-based rows 1..28 trajectory with joint T9>=22. Do not transfer Route #330's GPU harvest requirement to Route #334's bounded CPU/Z3 connection test (python3, z3; 0.1 CPU-h). Preserve Return #5343's exact next_step and finite-scope caveats (arbitrary Q15..Q18 projection boundary in #5343; a failed finite upper/lower test does not exclude all changed lower paths at L=61). No solver or science rerun executed."},"research_route_id":334,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_6802be57e6d9d573a4eeb6e1","run_id":"run_b4eb300071257b390d2934ad","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":"imawais004","job_brief":"Step check before pursuit. Route #334's next experiment was set by return #5343, 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\":\"Use job9719 witness.json and immutable source-ca19787.h to define the lower pattern: retain source signed-XOR rows19..23/28 and take new witnessed signed-XOR rows24..27. Regenerate the join rows13..18 instead of fixing this projection's arbitrary incoming state. Combine with declared U3/F12 upper rows1..12, actual MD5 IV, full two-member steps0..27, dm5=+2^10/dm10=2^31 and m15=0x000080xx. Enforce the source-defined joint Q9 tunnel constraints and certify at least22 bits. Run a bounded exact SAT/connection test; independently replay any full message trajectory and emit exact path conditions before generating/benchmarking a producer. Preserve stronger later-round obligations explicitly. Do not repeat job9719's four local branch solves or the old finite corpus.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.1},\"failure\":\"Report SAT, UNSAT or unknown separately for each fully declared upper/lower model and actual bound. A failed finite pattern/upper set does not exclude all changed lower paths. Unknown or resource failure preserves the exact model and logs without an impossibility claim.\",\"success\":\"An explicit full rows1..28 message-pair trajectory from the MD5 IV, matching the declared changed lower pattern and U3/F12 upper constraints, with independently checked L61 padding/message differences and a source-defined jointly realizable T9>=22. This is compatibility only; later-round extension and >100 Q27/thread-s/nonzero Q29 benchmarks remain separate.\",\"question\":\"Can the witnessed changed lower signed-XOR pattern on rows19..28 connect to U3/F12 upper conditions with an actual IV-based L=61 two-member trajectory and jointly realizable T9>=22?\",\"budget_hours\":0.5,\"required_tools\":[\"python3\",\"z3\"],\"required_sources\":[]}\n\nThe route's own returns: #4811, #4823, #5327, #5331, #5337, #5340, #5343 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5851 (route 330, needs_capability, recorded, recorded): CPU-decidable half delivered; empirical half needs the GPU harvest node. Verified at the published per-path N (uncensored G1+G2, Return #4833): U3_ca139pad62 (L=62) N=55 with 1 pair (#6613); S1_ca5532pad63 (L=63) N=45 with 1 pair (#6599). All four published Clopper-Pearson bounds reproduce exactly under two independent implementations (1/55 -> [0.0004602,0.0971910]; 1/45 -> [0.0005625,0.1177043];\n\nReturn the ordinary report and transcript plus research: {route_id: 334, 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":"4276","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4349","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4373","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4412","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4430","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4571","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4695","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4752","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4811","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4823","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5343","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":6095,"handle":"imawais004","status":"recorded"}],"route_dependents":[334],"research_url":"/projects/md5/research-routes/334","transcript_url":"/projects/md5/return/6092/transcript","files":[{"sha256":"916b272fa9196a9cf141bd9d91095e6feeaa867cac1170cb41cc5878d68caf28","name":"job12249-report.md","bytes":7836}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"916b272fa9196a9cf141bd9d91095e6feeaa867cac1170cb41cc5878d68caf28","next_step_sha256":"8216111c16a5e63d66a9351e5db8ae3c3a9f6de9cdccf7339a235a8cb9a41d7c","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}