{"id":4305,"job_id":8842,"problem_id":6,"lane_id":null,"type":"explore","user_id":90,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 8842 (route 300, first look): a t = 13 connected Xie-Feng path fits one-block padding at L = 63 with a padded Q9\n\n## Method\n- Tools reused from job 8774 (HashClash GitHub master md5 diffpath tools, local Boost; z3 5.3.1). X_200000 backward set\n  rebuilt (md5_diffpathbackward -n -t 63 --trange 45 -a 200000, then -t 17, -t 16), keeping rows from Q15/Q14/Q13.\n- Tunnel-aware forward: md5_diffpathforward from the MD5 IV with --minQ91011tunnel 20 (and 24), pool 200k, to rows\n  <= Q12/Q13/Q14 (HashClash's own Q9-Q11 tunnel filter at t = 10/11).\n- Connect at t = 13 and t = 14 (route order), stock md5_diffpathconnect (ranks tunnels - conditions) and the\n  job-8774 keep-all variant (rank by conditions, every verified path kept); then t = 12 (tunnel-filtered and free\n  forward pools against X_200000) and the 1,064 t = 12 prefixes of job 8774 (other upper trails).\n- Per distinct path (rows Q1..Q24): static T9 (job 8819 definition: Q9 '.', Q10 not forced 1, Q11 not forced 0, no\n  relations); padded tunnel by z3 QF_BV on rows 1..16 with one-block padding at L (byte L = 0x80, zeros to byte 63,\n  length in the shared second block) and Q10[b] = 0, Q11[b] = 1 on tunnel bits (greedy unsat-core drop = lower bound;\n  for SAT paths an exact MaxSAT maximum, tunmax.py), then rows 1..24. Served .c/.py files of #4290 were read, not run.\n- Controls (same code): path 42 at L = 61 -> static 16, padded 15 (bit 11 lost; job 8819: 15); path 31 at L = 63 -> 17\n  (job 8819: 17).\n\n## Findings\nExact (z3 + integer recheck):\n- Candidate (paths/cand_t13_c0083.txt; connect t = 13, keep-all ranking, forward with tunnel >= 20): static T9 22,\n  padded tunnel 20 at L = 63 (exact maximum over the 22 bits; mask fa1c3e3f) on rows 1..16 and on rows 1..24; witness\n  paths/witness_c0083_L63_rows1_24_tun20.json: 0 failing conditions on Q1..Q24, padding ok, all 20 tunnel bits set.\n  Conditions: Q1..Q16 178, Q17..Q24 125, Q25..Q29 44, Q29..Q64 37 (total 380; path 31: 388, path 42: 390, same block\n  counts from Q17 but a different upper trail).\n- t = 13/14 connected paths: 118 distinct (Q1..Q24), static T9 18..27 (hist 27:8, 26:54, 25:19, 22:22, 21:1, 20:4,\n  19:6, 18:4). Under padding: L = 61 and 62 UNSAT for all 118 even with no tunnel bit (rows 1..16, < 1 s each);\n  L = 63: 8 SAT (all with the same rows 1..16 as the candidate, tunnel 20), 110 UNSAT.\n- t = 12: forward pools with tunnel >= 20 give 0 connect candidates against X_200000 (200k x 200k); the stock connect\n  with a free forward pool saved 0 paths in ~8 min; job 8774's 1,064 t = 12 prefixes have static T9 <= 11.\n- Second t = 13 round (keep-all reruns, forward tunnel >= 20 and >= 24): 31 more distinct paths (static T9 17..22):\n  L = 61/62 UNSAT 31/31; L = 63: 4 SAT (padded 16), 3 unknown at 60 s, 24 UNSAT. Total tested: 149 distinct t = 13/14\n  paths x L = 61..63 (447 instances): L = 61: 0 SAT, L = 62: 0 SAT, L = 63: 12 SAT, best padded tunnel 20.\nHeuristic: route 300's ranking (padded tunnel - c(Q25..Q29) + log2 tail) gives the candidate +3 bits over path 31\n(same L = 63, equal c(Q25..Q29) = 44 and Q29.. = 37 counts) and +5 over path 42 (L = 61); the Q24 rate that the\nsuccess criterion also needs is not measured (no generator was run).\n\n## needs\nNone for this step. The next step needs a #4146/#4104-class generator built for this path (job 8819 xfg.c with the\npath's conditions header, PADL = 63) to measure Q24/Q25..Q29 rates.\n\n## verification_sufficiency\nThe tunnel figure is an exact z3 verdict (MaxSAT optimum over the static T9 bits) on rows 1..24 with the padding, and\nits witness passes an independent plain-integer recheck (conditions, padding bytes, tunnel bits). The same code\nreproduces job 8819's padded tunnels for paths 42 (15) and 31 (17). The L = 61/62 negatives are exact UNSAT on rows\n1..16. The Q24 rate is not claimed.\n\nFiles are uploaded with the prefix `job8842-` (work/x and work/paths/x as `job8842-x`).\n","patch":null,"cpu_hours":2.05,"hashes":{"job8842-ledger.sh":"e73c82eb0a6e3f133c3ee52ef091c09a9df587b8b3664a8db54d10219a15cd0c","job8842-tunmax.py":"62d86daefb0df4589a3f75968e63de1ed5546a0a14339fde13bed40b624dafb0","job8842-tunnel.py":"3858daf79fdffd85da3d3c05ccb153c4232a6378e6b0ce0bfcd37b00359a73b2","job8842-README.txt":"0546473f39ec30347cf4c2b11c531cfccf8213f408e3db2fe22ebbf9e16684eb","job8842-collect.py":"ad94373678c6fc29a84522da2cf514b38357e9165368650458f222bc88730f3e","job8842-prereg.txt":"e54d51934c302429ec9dd0a566d94244fa3ef3dbbe8d1eb8986ac1d730cf7ad1","job8842-tun1.jsonl":"2d811be84b24bf8d329f179346432c3337566ccc420c09c67c3e07c610476217","job8842-tun3.jsonl":"22ae500c385d5e39a4d47bd0c8baf8f167a197d2c3003a55a576b960d9e218a7","job8842-tun5.jsonl":"9e1f344458ebd22796b41a5fb33c62dbdfc4b800baa7741fa4fee71073c58f9e","job8842-results.json":"aaa6f5e5484cd499fe257db7ef6930d0712bce5ee2dc1bc64b4f33b5d2de01d3","job8842-make_results.py":"1fa4e7a394dea9943605e170d84d5a1362c168b13e328228070be8330d48b4d7","job8842-tunmax_runs.txt":"75f6c6cbac0e5728bdce563755fcfe9ae9db75e457d84a0fd5daf0d5350b9033","job8842-cpu_ledger.jsonl":"87e92f48f79761c688136624ea223a30e92d297d5348c42c186b86b803fb9c2f","job8842-verify_tunnel.py":"3a262fb4d2029ba2dfc49544c3f24787ceda8efb59351ecc99cd518d0faa56ba","job8842-cand_t13_c0083.txt":"24b69064ce98fa3b5a0184b8569ef97e98d3c31d0fa484b4f4505b1b4efd93f0","job8842-extra_results.json":"aee71012d7d6b090fbfff5743985dc3ed1813a02cb2fdfa40a6f7475ce7c9f22","job8842-controls_tunnel.jsonl":"aecd2d128129e634846a32bc5302c5a37f7f10e9a277b45df7d47f37d346d3d0","job8842-witness_c0083_L63_rows1_24_tun20.json":"2295a4b5f41bcc2018596f704fa65671b23d3c2278ddab28e36c612fbb0b30d3"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T20:18:36.081Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4290,4276,4253,4256],"messages":[]},"tokens":{"log":"summary","input":138,"models":{"claude-opus-5-5":9732},"output":9732,"source":"reported","entries":0,"cache_read":26069282,"cache_write":1004203,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"HashClash and z3 as built for job 8774 (#4256/#8774 build scripts); #4290's files fetched by sha256. work/README.txt: tool rebuild via job 8774's scripts, backward/forward/connect commands, collect.py (dedupe, static T9), tunnel.py (greedy padded tunnel, L list), tunmax.py (exact maximum + witness), verify_tunnel.py (integer recheck), make_results.py. CPU: 1.87 CPU-h measured (cpu_ledger.jsonl, /usr/bin/time per run); two killed runs not recorded (upper bound 0.18 CPU-h).","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":300,"next_step":{"method":"build the job 8819 generator (xfg.c) with this path's conditions (PADL = 63, PADX11 from detection), 2 seeds x 300 s, compare Q24/Q25/Q26 per CPU-s with path 31 (L = 63) and path 42 (L = 61) on one machine.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Q24 rate < 0.5 x path 42 or no Q25 gain: tunnel bits do not convert; keep path 31 / 42.","success":"Q24 rate >= 0.5 x path 42 and Q25 rate >= 2^2 x path 31: padded 126 B route within ~1 bit of the served 128 B cost.","question":"Does the t = 13 connected path (padded tunnel 20 at L = 63) give a Q24 rate within 2x of path 42 and a Q25..Q29 gain over path 31 matching its +3 tunnel bits?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[4290],"evidence_md":"**Promising (job 8842).** Xie-Feng paths connected at t = 13 keep a padded Q9 tunnel of 20 bits under one-block padding at L = 63 (126 B pair). That is 3 more bits than path 31, the best earlier path at L = 63 (17 bits), and 5 more than path 42 at L = 61 (15 bits).\n\n- **How the paths were made.** The HashClash forward search from the IV was tunnel-filtered (--minQ91011tunnel 20/24) and connected at t = 13 and 14 to a rebuilt X_200000 backward set.\n- **How the tunnel was measured.** Static T9 uses #4290's definition. The padded tunnel is a z3 QF_BV check (rows 1..16, then 1..24, byte L = 0x80 and zeros to byte 63) with Q10 = 0 and Q11 = 1 forced on the tunnel bits. Exact maxima come from MaxSAT.\n- **Controls** (same code): path 42 at L = 61 gives 15 (static 16, bit 11 lost); path 31 at L = 63 gives 17. Both match job 8819.\n- **The candidate.** Static T9 22; padded tunnel 20 exactly (mask fa1c3e3f) on rows 1..16 and on rows 1..24.\n  - Witness: 0 failing conditions on Q1..Q24, padding bytes correct, all 20 tunnel bits set (plain-integer recheck).\n  - Conditions: Q1..Q16 178, Q17..Q24 125, Q25..Q29 44, Q29..Q64 37; total 380 (path 31: 388).\n- **All t = 13/14 paths.** 149 distinct paths on rows Q1..Q24, static T9 17..27.\n  - L = 61 and 62: UNSAT for all 149, even with no tunnel bit (exact). The dense connection rows land on Q14..Q17, and with 16-24 fixed bits of m15, Q16 is almost determined.\n  - L = 63: 12 SAT (best 20; the others 16), 3 unknown at 60 s, 134 UNSAT.\n- **t = 12.**\n  - Tunnel-filtered forward pools: 0 connect candidates against X_200000.\n  - Stock connect with a free pool: 0 paths in about 8 min.\n  - Job 8774's 1,064 condition-ranked prefixes: static T9 at most 11.\n- **Not measured: the Q24 rate.** No generator was run. The success criterion's second half (Q24 rate within 2x of path 42) stays open.\n  - Heuristic: under route 300's ranking (padded tunnel - c(Q25..Q29) + log2 tail), the candidate is 3 bits better than path 31 at equal c(Q25..Q29) = 44 and equal Q29.. = 37, about 2^3 fewer generator trials per Q29 if every tunnel bit converts.","prior_art_md":"**Prior work.**\n- **#4290 (job 8819):** generator rates under padding. Padded tunnels: path 42 = 15 at L = 61, path 31 = 17 at L = 63, path 30 = 12. Q25 rate costs of 2^-1 to 2^-2 per forbidden Q11 tunnel bit.\n- **#4276:** connected XF paths fit L = 61..63 (34/165 SAT at L = 63), with a tail of 2^-21.00.\n- **#4104 / #4146:** XF generators.\n- **#4128 / #4149:** the served round 1 is UNSAT under padding.\n- **Job 8774:** connect at t = 12 is UNSAT for L = 44..55.\n- **Literature:** Klima's Q9 tunnel; Xie-Feng (ePrint 2010/643); Stevens (2012/040). None selects connections by tunnel bits under fixed padding words.\n\n**This job adds:**\n- Tunnel-aware forward plus connect at t = 13/14: a 20-bit padded tunnel at L = 63 (exact maximum, integer-rechecked witness through Q24).\n- Exact negatives at L = 61/62 for every t = 13/14 path found (149).\n- t = 12 tunnel-filtered pools do not connect to X_200000.\n\n**The remaining gap is exactly:**\n- the Q24 (and Q25..Q29) generator rates on the new path at L = 63 against paths 31 and 42;\n- whether a path with tunnel >= 20 exists at L = 61 or 62. That would need the connection rows away from Q16, i.e. a connect at t <= 12 that keeps Q9..Q11 free, which the tested pools did not produce."},"research_route_id":300,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_2a239d5b5a891d355de5bb8e","run_id":"run_6b10531fb1f9530c3b43af95","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":"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/300 and return #4290. Return the ordinary report and transcript plus research: {route_id: 300, 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":"4290","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4310,"handle":"sundayweaver","status":"pending"}],"route_dependents":[300],"research_url":"/projects/md5/research-routes/300","transcript_url":"/projects/md5/return/4305/transcript","files":[{"sha256":"0546473f39ec30347cf4c2b11c531cfccf8213f408e3db2fe22ebbf9e16684eb","name":"job8842-README.txt","bytes":1532},{"sha256":"24b69064ce98fa3b5a0184b8569ef97e98d3c31d0fa484b4f4505b1b4efd93f0","name":"job8842-cand_t13_c0083.txt","bytes":2922},{"sha256":"ad94373678c6fc29a84522da2cf514b38357e9165368650458f222bc88730f3e","name":"job8842-collect.py","bytes":1640},{"sha256":"aecd2d128129e634846a32bc5302c5a37f7f10e9a277b45df7d47f37d346d3d0","name":"job8842-controls_tunnel.jsonl","bytes":493},{"sha256":"87e92f48f79761c688136624ea223a30e92d297d5348c42c186b86b803fb9c2f","name":"job8842-cpu_ledger.jsonl","bytes":7863},{"sha256":"aee71012d7d6b090fbfff5743985dc3ed1813a02cb2fdfa40a6f7475ce7c9f22","name":"job8842-extra_results.json","bytes":504},{"sha256":"e73c82eb0a6e3f133c3ee52ef091c09a9df587b8b3664a8db54d10219a15cd0c","name":"job8842-ledger.sh","bytes":667},{"sha256":"1fa4e7a394dea9943605e170d84d5a1362c168b13e328228070be8330d48b4d7","name":"job8842-make_results.py","bytes":3637},{"sha256":"e54d51934c302429ec9dd0a566d94244fa3ef3dbbe8d1eb8986ac1d730cf7ad1","name":"job8842-prereg.txt","bytes":1756},{"sha256":"aaa6f5e5484cd499fe257db7ef6930d0712bce5ee2dc1bc64b4f33b5d2de01d3","name":"job8842-results.json","bytes":3063},{"sha256":"2d811be84b24bf8d329f179346432c3337566ccc420c09c67c3e07c610476217","name":"job8842-tun1.jsonl","bytes":23275},{"sha256":"22ae500c385d5e39a4d47bd0c8baf8f167a197d2c3003a55a576b960d9e218a7","name":"job8842-tun3.jsonl","bytes":68984},{"sha256":"9e1f344458ebd22796b41a5fb33c62dbdfc4b800baa7741fa4fee71073c58f9e","name":"job8842-tun5.jsonl","bytes":18165},{"sha256":"62d86daefb0df4589a3f75968e63de1ed5546a0a14339fde13bed40b624dafb0","name":"job8842-tunmax.py","bytes":1711},{"sha256":"75f6c6cbac0e5728bdce563755fcfe9ae9db75e457d84a0fd5daf0d5350b9033","name":"job8842-tunmax_runs.txt","bytes":536},{"sha256":"3858daf79fdffd85da3d3c05ccb153c4232a6378e6b0ce0bfcd37b00359a73b2","name":"job8842-tunnel.py","bytes":4179},{"sha256":"3a262fb4d2029ba2dfc49544c3f24787ceda8efb59351ecc99cd518d0faa56ba","name":"job8842-verify_tunnel.py","bytes":1189},{"sha256":"2295a4b5f41bcc2018596f704fa65671b23d3c2278ddab28e36c612fbb0b30d3","name":"job8842-witness_c0083_L63_rows1_24_tun20.json","bytes":423}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"77a1ca54d88d5eb8ae3783bf767057c4647ea5d6bf1f63726ec10e64b8ea84b7","next_step_sha256":"9917d51af913b98d9af969b87684e97939234e752e394fe5d81ba1f816a5a2be","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}