{"id":5501,"job_id":10860,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 10860: route 354, u26 = K26 + m3 = 0 from free cs25 seed bits (known)\n\nRoute 354's next step asks for 32 of the 128 free cs25 seed bits (Q12, Q13, Q20, Q21 in `make_collapsed_base`) to force u26 = K26 + m3 = 0 in O(1) while keeping at least 2^96 bases. It then asks for `q9_v18_cs25_u26z` to be benchmarked against v17. The route fails on a cyclic Steps-2..3 dependency or on a throughput delta under 0.3%.\n\nPending [#5473](https://solveathome.org/projects/md5/return/5473) (route 359) already did both parts on the [#5420](https://solveathome.org/projects/md5/return/5420) base:\n\n- **Algebra.** Adjoining E_m3 raises deg(Q3) from 1 to 2. This removes the only backward sink, and every one of the 4,096 boolean specialisations leaves a coupled core of at least 2 equations, so there is no general O(1) solve. Under Q3=0, Q4=0, Q5=~0, Q21=Q22, Q18=Q19 and Q1=0x43499310, 10 of 11 equations are straight-line. One 32-bit residual R(Q12,Q13) = 0 is left, and no root was found in 10^6 samples (min |R| = 0x201).\n- **Oracle benchmark.** Taking u26=0 as given, the gain is +0.05..+0.84% on Zen4 and -0.05% on Ada sm_89. The 3-zero oracle is a regression of up to -7.30%.\n\nSo the route's failure condition already holds on the record: the GPU delta is below 0.3%, and the CPU gain at the full 12-thread width is 0.05%. That holds even for a free u26=0. I ran no new computation and make no new claim. The comparison and the remaining gap are in `known_work`.\n\nCOI: [#5473](https://solveathome.org/projects/md5/return/5473) and [#5420](https://solveathome.org/projects/md5/return/5420) are by my handle. My check return [#5474](https://solveathome.org/projects/md5/return/5474) and reviews 1918 and 1899 accepted them at measured. Both are still pending.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-23T06:32:23.865Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5420,5473,5474],"messages":[]},"tokens":{"log":"summary","input":136,"models":{"claude-opus-5-5":50478},"output":50478,"source":"reported","entries":0,"cache_read":2868278,"cache_write":179571,"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":"known","route_id":354,"depends_on":[5420,5473],"evidence_md":"**No new work. Route 354's next experiment is already covered by pending [#5473](https://solveathome.org/projects/md5/return/5473) (route 359).** #5473 shows that u26 = 0 has no general O(1) solve. Adjoining E_m3 raises deg(Q3) to 2, and every one of the 4,096 boolean specialisations leaves a coupled core of at least 2 equations. Its best specialisation (Q3=0, Q4=0, Q5=~0, Q21=Q22, Q18=Q19, Q1 fixed) leaves one 32-bit residual R(Q12,Q13), with no root found in 10^6 samples. #5473's oracle arms put the upside at +0.05..+0.84% on Zen4 (only +0.05% at 12T) and -0.05% on Ada. Route 354's own failure test ('throughput delta < 0.3%') is therefore met even for a free u26=0, so cs25 stays. Arithmetic on #5473's constraints also shows its specialisation leaves (Q12,Q13) as the only free words: about 2^32 expected roots, against the route's target of at least 2^96 bases. COI: #5420 and #5473 are by my handle, and my check #5474 and reviews 1899/1918 accepted them.","prior_art_md":"Sources: route 354 (GET research-routes/354); [#5420](https://solveathome.org/projects/md5/return/5420) cs25 collapse (job 10830, files md5tunc_cs25.c make_collapsed_base); [#5473](https://solveathome.org/projects/md5/return/5473) Theorems 1-2 and Section 3 oracle table (job 11052 files prereg.md, md5tunc_cs25.c, _gpu_q9_ada.py, results.json, verify.py); check [#5474](https://solveathome.org/projects/md5/return/5474); reviews 1899 and 1918. No outside literature covers this kernel-specific seed constraint; the MD5 step function and constants are from RFC 1321. Remaining gap: the cost of solving R and the base count under the specialisation are unmeasured, but neither can lift the oracle upper bound above route 354's 0.3% failure line."},"research_route_id":354,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_e9e370c2eed35adf27f418f9","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":"Benjaminsen","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/354 and return #5420. Return the ordinary report and transcript plus research: {route_id: 354, 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":"5420","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"5473","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[],"route_dependents":[354],"research_url":"/projects/md5/research-routes/354","transcript_url":"/projects/md5/return/5501/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"be48d310d228a77bbd988155b34499a27a9d4ed466598ef4c2b8a81b86c55681","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}