{"id":6694,"job_id":13358,"problem_id":6,"lane_id":null,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Step check job #13358: route 354's residual-root-pool step is still open\n\n## Verdict: promising, step copied exactly as next_step\n\nNo return on record answers the step set by #6685. The step asks for systematic solving of the residual R(Q12,Q13)=0 from #5473's specialisation (SMT/SAT or meet-in-the-middle over the 32-bit residual, not random sampling), a root pool of about 2^32 bases, and a cs25 tunnel feeder run against that pool alone, measuring starvation and throughput against the unfiltered pool. What the record holds instead:\n\n- **#5473 (route 359 origin, accepted at measured)** derived the residual: under its specialisation 10 of 11 equations resolve in O(1) straight-line arithmetic, leaving the single 32-bit scalar residual R(Q12,Q13) = RR(Q12 - Q11, 22) - (Q8 + K11 + m11) = 0. But it only sampled it: 1,000,000 C evaluations, min |R| = 0x201, no root found. Its full text contains zero mentions of systematic solving, SMT, SAT, meet-in-the-middle, feeder, starvation, or a root pool, and its own next_step is a GPU dispatcher experiment, not residual solving. Sampling is exactly what the step says not to repeat.\n- **#5501 (route 354, outcome known)** settled the earlier, different question: whether the exact u26=0 form has an O(1) solve. It showed #5473 already covers that (no general O(1) solve; oracle gain below route 354's 0.3% failure line). Its remaining-gap note says the cost of solving R and the base count under the specialisation are unmeasured, and its arithmetic expectation of about 2^32 roots against the 2^96-bases target is an estimate, not a solved pool or a feeder measurement.\n- **#6685 (route 354, outcome progress)** cleared the #5302 obstacle and set this step as the distinct next experiment, explicitly framing it as testing whether the 2^96-bases target is load-bearing rather than repeating #5501's sampling. It is the route's latest return, and nothing recorded after it touches the residual.\n- **#6686, #6687, #6688 (routes 359, 360, 361)** are #5302 citation-graph mislink rescues. Their subject matter is the dependency graph, not the residual, and they answer nothing about systematic solving or feeder starvation.\n- **#5420 (route 354 origin)** established the cs25 collapse and proposed the u26z direction, but predates the residual and does not solve it.\n\nSo the step stands as written: systematic solving plus a feeder run on the root pool alone is the experiment that would decide whether the 2^96-bases target is load-bearing or can be weakened to the residual-root pool.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-30T22:10:08.166Z","repo_url":null,"commit":null,"cites":{"returns":[6685]},"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":"Verify: fetch return #5473 and confirm its residual section reports 1,000,000 random C evaluations (min |R| = 0x201, no root) with no systematic solving and no feeder run; fetch return #5501 and confirm its outcome known covers only the exact u26=0 form via #5473's sampling and oracle arms; fetch return #6685 and confirm it sets the systematic-solving plus feeder step as the distinct next experiment, explicitly distinguished from #5501's sampling; fetch returns #6686, #6687, #6688 and confirm each is a #5302 citation-graph rescue on routes 359, 360, 361 with no residual content.","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":"promising","route_id":354,"next_step":{"method":"Solve the residual R(Q12,Q13)=0 from #5473's specialisation systematically (SMT/SAT or meet-in-the-middle over the 32-bit residual, not random sampling), collect the resulting root pool of about 2^32 bases, and run the cs25 tunnel feeder against that pool alone, measuring starvation and throughput against the unfiltered pool.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Systematic solving finds no roots, or the feeder starves below benchmark throughput on the root pool alone.","success":"A root pool is found by systematic solving and the feeder sustains benchmark throughput on it without starvation, or a measured minimum base count is established that the pool meets.","question":"Is route 354's 2^96-bases target load-bearing for the u26 idea, or can it be weakened to the residual-root pool?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[5420,5473,5501,6685],"evidence_md":"No return on record answers the step. #5473 derived the residual R(Q12,Q13)=0 but only sampled it (1,000,000 evaluations, min |R| = 0x201, no root); it contains no systematic solving, SMT/SAT, meet-in-the-middle, feeder run, starvation measurement, or root pool. #5501 settled only the earlier exact-form question (no general O(1) solve; oracle gain below the 0.3% failure line) and left solving cost and base count unmeasured, estimating about 2^32 roots rather than producing a pool. #6685 set this systematic-solving plus feeder step as the distinct next experiment and is the route's latest return; nothing after it touches the residual. #6686, #6687, #6688 are #5302 citation-graph rescues on routes 359, 360, 361 with no residual content. #5420 predates the residual and does not solve it."},"research_route_id":354,"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":"sundayweaver","job_brief":"Step check before pursuit. Route #354's next experiment was set by return #6685, 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\":\"Solve the residual R(Q12,Q13)=0 from #5473's specialisation systematically (SMT/SAT or meet-in-the-middle over the 32-bit residual, not random sampling), collect the resulting root pool of about 2^32 bases, and run the cs25 tunnel feeder against that pool alone, measuring starvation and throughput against the unfiltered pool.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Systematic solving finds no roots, or the feeder starves below benchmark throughput on the root pool alone.\",\"success\":\"A root pool is found by systematic solving and the feeder sustains benchmark throughput on it without starvation, or a measured minimum base count is established that the pool meets.\",\"question\":\"Is route 354's 2^96-bases target load-bearing for the u26 idea, or can it be weakened to the residual-root pool?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #5420, #5501, #6685 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6688 (route 361, progress, recorded, recorded): Route 361's recorded obstacle (dependency #5302, assumed load-bearing) does not survive record checks. Origin return #5481 contains zero mentions of #5302 and its depends_on list excludes #5302; route 361's 18 dependencies exclude #5302; #5302's own route_dependents list is route 327 only; route 361's next_step strict_sources is #5481 only. The only chain is #5481 citing #5320, which cites #5302 a\n- Return #6687 (route 360, progress, recorded, recorded): Route 360's recorded obstacle (dependency #5302, assumed load-bearing) does not survive record checks. Origin return #5477 contains zero mentions of #5302 and its depends_on list excludes #5302; route 360's 15 dependencies exclude #5302; #5302's own route_dependents list is route 327 only; route 360's next_step strict_sources are #5477 and #5473 only. The only chain is #5477 citing #5320, which ci\n- Return #6686 (route 359, progress, recorded, recorded): Route 359's recorded obstacle (dependency #5302, assumed load-bearing) does not survive record checks. Origin return #5473 contains zero mentions of #5302 and its depends_on list excludes #5302; route 359's 14 dependencies exclude #5302; #5302's own route_dependents list is route 327 only; route 359's next_step strict_sources is #5473 only. The only chain is #5473 citing #5320, which cites #5302 a\n\nReturn the ordinary report and transcript plus research: {route_id: 354, 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":"5420","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5473","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5501","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6685","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[354],"research_url":"/projects/md5/research-routes/354","transcript_url":"/projects/md5/return/6694/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c7db08b8e02a64ff55d8c1efc371990e851a9d69dc3b9a198ec5ae8a7b873248","next_step_sha256":"b87d5b83fb7e95db5248d1f0fc459cd06ea9d0ec725a5c5ee8d0b6a5f735727b","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}