{"id":4296,"job_id":8774,"problem_id":6,"lane_id":null,"type":"explore","user_id":90,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 8774 (route 298, first look): Xie-Feng dM with a fresh round 1 from HashClash forward + connect at t = 12:\n\n## Method\n- Rebuilt the predecessor's backward sets with HashClash (GitHub master, MIT; Boost 1.88 local static build):\n  md5_diffpathbackward -n -t 63 --trange 43 -a 200000, then -t 19 --trange 3 -a 200000, from the collision state.\n  X = Xie-Feng dM (m5 +2^10, m10 +2^31), S = route 296 dM (m1 +2^10, m6 +2^31). Check vs #4253: best raw\n  conditions X from Q21/25/29/33/37 = 137/77/37/23/17 (#4253: 138/77/37/23; served XF path 154/79/37/23), S from\n  Q21 = 148 (#4253: 147). Rows Q13..Q64: best 250 (X), 253 (S).\n- Fresh round 1: start path = MD5 IV as constant rows; md5_diffpathforward --normalt01 -t 0 --trange 11 -a 200000\n  -q 64 (rows <= Q12). Best Q1..Q12: 23 conditions (X), 67 (S). (Brief: -t 1 --trange 10 after the helper's\n  start path; this starts one step earlier from an equivalent IV path.)\n- Connect at t = 12 (lower <= Q12, upper >= Q13), patched md5_diffpathconnect: rank by total conditions, round-1\n  check_path_collfind off, keep every verified path, bestmaxcomp not raised after the first path (see correction).\n  X: 114,187 candidate pairs, 73 verified per final snapshot, 1,169 saved paths, 1,064 distinct Q1..Q16 prefixes,\n  best 391 conditions on Q1..Q64. S: 484 candidates, 100 distinct prefixes, best 445. S with the served (shifted XF)\n  round 1 rows 1..12 as the single lower path: 0 candidates.\n- Padding check (padscan.py, z3 5.3.1 QF_BV, one worker per CPU): steps 0..15, Q1..Q16 free, m by inverting the\n  steps, member b with m + dM, every bit condition of the prefix on Q1..Q16, and member a's bytes >= L fixed\n  (0x80, zeros, 8L in m14, m15 = 0). Controls: served S rows 1..12 at L = 48 SAT (as #4213); best X and S prefixes\n  without padding SAT; all three witnesses rechecked on plain integers (0 failing conditions, padding ok).\n- Padding-aware attempts (extension): HashClash's path model has no message values, so fixed padding words cannot\n  be passed to forward/connect; padding was moved into z3 instead: (a) only an upper path's rows imposed, rows below\n  free (\"any round 1\") with padding (zfree.py); (b) HashClash forward rows Q1..Q8 + upper Q13..Q16, rows Q9..Q12\n  free; (c) backward continued into round 1 (from the best 20k X paths, -t 15 --trange 5 -a 50000) so the\n  padding-determined rows come from backward, rows Q1..Q8 free.\n\n## Findings\nExact (z3, controls SAT):\n- X: all 1,064 distinct connected prefixes are UNSAT at every L = 44..55 (12,768 instances, each <= ~2 s).\n- S fallback: all 100 distinct prefixes UNSAT at every L = 48..55 (800 instances).\n- First failing row tracks the first padding-fixed word (best X prefix): L = 44 (m11 fixed) UNSAT from row 12,\n  L = 48 (m12) from row 13, L = 55 (m13 top byte) from row 14; all shorter prefixes SAT.\n- Round-1-backward X paths (rows Q9..Q16, 128 conditions) with Q1..Q8 entirely free: UNSAT at L = 48 and 52 for 4/4\n  paths (~1 s each), i.e. no round 1 at all fits those entries; at L = 55 unknown at 300 s (portfolio below).\nMeasured/heuristic:\n- Why: a fully fixed word m_w makes Q_{w+1}..Q16 functions of Q_{w-3}..Q_w (128 bits). The connected prefixes\n  carry 174-183 conditions on Q_{w-3}..Q16 (min over 1,064: 183 for L44-47, 180 for L48-51, 174 for L52), because\n  connect at t = 12 puts its dense rows (25-30 conditions each) exactly on Q10..Q15, the padding-determined block.\n- Upper entries alone are light (X_200000 rows Q13..Q16: 47-49 conditions; S: 45). With any round 1 below them,\n  z3 is unknown at 900 s for 8 X entries at L = 44 and 4 S entries at L = 48; HashClash forward rows Q1..Q8 +\n  free Q9..Q12: unknown at 1200 s (L = 44, 48). So \"no round 1 at all reaches the cheapest entries\" is open.\n- L = 55 portfolio (6 round-1-backward X paths x seeds, rows Q9..Q16, Q1..Q8 free): all 14 runs unknown at 1650-1800 s (no SAT, no UNSAT).\nCorrection to #4256 (job 8641): its connect patch raised bestmaxcomp to 0 after the first verified path, which makes\nconnect's tunnel prefilter skip almost every later (lower, upper) pair; its \"best connected\" counts came from a\ntruncated connect search. Its forward/backward floors (350+ conditions vs 244 at L = 32) are unaffected.\n\n## needs\nNone for this step (all runs fit this machine).\n\n## verification_sufficiency\nEvery UNSAT is an exact z3 verdict on a stated encoding; the encoding is validated by three SAT controls with integer\nrechecks and by #4213's L = 48 result. Paths, prefixes and per-instance results are in results.json and the run\nlogs; one re-run of padscan.py on any prefix file reproduces its verdict in seconds. The negative is scoped to the\nsearched beams and to connect at t = 12; it is not a lower bound for other round-1 constructions.\n\nFiles are uploaded with the prefix `job8774-` (work/x and work/paths/x as `job8774-x`).\n","patch":null,"cpu_hours":15.43,"hashes":{"job8774-zfree.py":"07ec5d21b329d20e7c2653436a0b08df616418db5e56216e1f6ff0045a9b9d40","job8774-ledger.sh":"b69df7261a39ba84d5dd360808ca2fbf9d026c6f7d805444999e7ea00ba0ba7d","job8774-README.txt":"8321fe9feccafb7c17279c54263f854a318e3ea05839b9d45b6dc6c91655d01b","job8774-padscan.py":"f71a9693fd0a1d58700afdb8d396f69526914cda04490f45baf7585da50665be","job8774-prereg.txt":"b87f99c707f68ebcdffed69cb29c4ee89c2690a726c20a595e491168332b5cb1","job8774-build_hc.sh":"d1336bc1338666a64bb97fa26fb685c2775a03a0ef5489263a846d9a9fc4fd88","job8774-results.json":"d7f75f6718964a1e95c5b647099501d20c0e7e77d3709d1d4ac9c3eeecc7d0ef","job8774-showpaths.cpp":"fc2aa1c20637f4576f32711f864f85cabe250b974a79883984c6d3584bae5b60","job8774-build_boost.sh":"2300f51f51be1aa01655d9cbb1e00444a6adb2b3349b2799c13e54a0163e0ef3","job8774-make_results.py":"afecd36121d55caed87ce90007323fb91938170e9b1c475d4c9d779ec439d706","job8774-cpu_ledger.jsonl":"ab60ce751420d8e635bbc4f4cfe9509bb78d52aa0dfc04c3d54afdeab2334bce","job8774-connect_j8774.diff":"e4b69aac12dc40bca8ea70f4e372feeb2b906c2a685d24b02003baac27676df9","job8774-X_connected_best_full.txt":"64d8edfd1b43ee97db5ea625457822078cf14bd5f1c20cea2f34e2d6cb13389c","job8774-X_round1_backward_u00.txt":"bc51943567dad8d98d0a68c6a300d09e6b2dbe2a56ce03769c098085538a7433","job8774-X200000_entry0_Q13_Q16.txt":"3b7ad980649e0b3ff39f1a6dd68d666a7db3b3cc01e237f6eef16728c0b50742","job8774-S_connected_best_prefix.txt":"bedfd5ab5cc18895ff53ab729d293d9baf55bde003908feeb98e5a28175d42c6","job8774-X_connected_best_prefix.txt":"a1f91fb2de72a08eca1df87296e761d81417e6671254591de5efa8b57a13f326","job8774-ctl_S_served_rows12_L48.json":"7c30bf8629b78cd11c7bdad8b946e4a0ed41ce93ba7072b7287b76b9bc24aadc","job8774-ctl_S_pre000_rows16_nopad.json":"d37685d4aeb5f5c1184fb6900524446b0ce217d553ff80a0a25ce38bb115aa50","job8774-ctl_X_pre000_rows16_nopad.json":"e0f1228f17b3aa2e2c86ad1e43f7b61931a0c8ccb19c4d3804ec5762fb970c70"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T19:27:35.877Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4253,4213,4128,4149,4276,4256],"messages":[]},"tokens":{"log":"summary","input":194,"models":{"claude-opus-5-5":15132},"output":15132,"source":"reported","entries":0,"cache_read":27989268,"cache_write":2500798,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Build Boost and HashClash (job8774-build_boost.sh, job8774-build_hc.sh with job8774-connect_j8774.diff) in a scratch dir $WORK; python3 with z3-solver. work/README.txt lists every command; build_boost.sh, build_hc.sh, connect_j8774.diff rebuild the tools (~2 CPU-min); backward X/S ~0.37 CPU-h each, forward seconds, connect ~10 CPU-min each, padding scans ~3 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":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"13,568 UNSAT instances in job8774-results.json; the first failing row tracks the first padding-fixed word (row 12 at L = 44, 13 at L = 48, 14 at L = 55); round-1-backward rows Q9..Q16 with Q1..Q8 free are UNSAT at L = 48 and 52, unknown at L = 55 after 1800 s.","statement":"Connecting at t = 12 puts HashClash's dense connection rows (25-30 conditions each) on Q10..Q15, the rows that equal-length padding determines; every connected Xie-Feng round 1 found (1,064 distinct prefixes, L = 44..55) and every S round 1 (100 prefixes, L = 48..55) is z3-UNSAT under padding over steps 0..15.","assumptions":"HashClash beams of 200k (forward from the IV, X_200000 / S_200000 backward sets rebuilt to match #4253), connect at t = 12 only, with the bestmaxcomp pruning fix; prefixes deduplicated on Q1..Q16; z3 QF_BV with SAT controls rechecked on integers.","revisit_when":"A round 1 that keeps Q_{w-3}..Q16 under ~128 conditions (connect at t <= w-4 with a light upper part, or a path search that carries the padded words), or an 'any round 1' SAT run (CaDiCaL/kissat, cube-and-conquer) that decides the light X_200000 entries (rows Q13..Q16), which z3 left unknown at 900-1200 s."},"route_id":298,"depends_on":[4253],"evidence_md":"**Blocked (scoped negative), job 8774.** For the Xie-Feng dM (m5 +2^10, m10 +2^31), fresh round-1 paths do connect to the cheapest backward trails. None of them is compatible with equal-length padding at any L = 44..55. The route's fallback, S (m1 +2^10, m6 +2^31) at L = 48..55, gives the same verdict.\n\n- **Sets.** The X_200000 and S_200000 backward sets were rebuilt with HashClash using job 8645's recipe. They match #4253: X raw C(21/25/29/33) = 137/77/37/23 (#4253: 138/77/37/23); S C(21) = 148.\n- **Forward and connect.** A forward pool of 200k from the MD5 IV fed md5_diffpathconnect at t = 12, ranked on total conditions.\n  - X: 114,187 candidate pairs; 1,064 distinct round-1 prefixes on Q1..Q16; best path 391 conditions on Q1..Q64.\n  - S: 100 distinct prefixes; best 445. The served shifted round 1 gives 0 connect candidates.\n- **Exact (z3 QF_BV over steps 0..15, prefix conditions plus padding of bytes >= L).**\n  - All 12,768 X instances (1,064 prefixes x 12 values of L) are UNSAT.\n  - All 800 S instances (100 x 8 values of L) are UNSAT.\n  - Controls are SAT with integer rechecks: S served rows 1..12 at L = 48 (as #4213), and the best X and S prefixes without padding.\n  - The first failing row follows the first fixed word: L = 44 from row 12 (m11), L = 48 from row 13 (m12), L = 55 from row 14 (top byte of m13).\n- **Mechanism (count).**\n  - A fixed word m_w makes Q_{w+1}..Q16 functions of Q_{w-3}..Q_w, which is 128 bits.\n  - Connect at t = 12 puts its dense rows (25-30 conditions each) on Q10..Q15, exactly in that block.\n  - The connected prefixes carry at least 174-183 conditions on Q_{w-3}..Q16.\n- **Padding-aware variants.** HashClash's path model carries differences and bit conditions but no message values, so the padded words cannot be passed to it. Padding was therefore imposed in z3:\n  - X backward continued into round 1, so the determined rows come from backward (Q9..Q16, 128 conditions), with Q1..Q8 entirely free: UNSAT at L = 48 and 52 for 4 of 4 paths, i.e. no round 1 at all fits them. At L = 55: unknown at 1650-1800 s for 6 paths (14 seeded runs).\n  - The light X_200000 entries alone (Q13..Q16, 47-49 conditions) with any round 1 below them: z3 unknown at 900 s at L = 44. The same holds for S at L = 48, and with HashClash rows Q1..Q8 fixed (1200 s). This case stays open.\n- **Correction to #4256.** Its connect patch raised bestmaxcomp after the first verified path, which truncated those connect searches. Its forward/backward floors stand.","prior_art_md":"**Prior work and what this job adds.**\n- **#4128/#4149:** the served XF path forces m15 bit 29 = 1, so there are 0 padded cores at L = 44..55. Re-signed rows 12-16 are UNSAT for L = 44..63. This covers one round 1 only (XF's own).\n- **#4276** (pending): 165 XF paths. Under padding, L63 34/165, L62 10 and L61 9 are SAT. Its L55/56/60 UNSAT verdicts were tested only on the 34 paths selected for L = 63, so they do not cover L <= 60 with paths chosen for those paddings.\n- **#4253:** backward-trail costs for X and S (rebuilt here, matching).\n- **#4213:** the served shifted round 1 fits L = 48..55.\n- **#4256:** padding fixes Q14..Q16 at L = 55; dM' over budget.\n- **Literature:** Xie-Feng (ePrint 2010/643), Xie-Liu-Feng (2013/170) and Stevens (2012/040) construct single-block paths with full message freedom. None constrains rows Q12..Q16 by short-message padding.\n\n**This job closes:** fresh HashClash round-1 paths connected at t = 12 to the cheapest backward sets, chosen without regard to L, against every L = 44..55 (X) and 48..55 (S). All are UNSAT, exactly.\n\n**The remaining gap is exactly:**\n- whether any round 1 at all (not one from connect at t = 12) reaches a light X_200000 / S_200000 entry (rows Q13..Q16, about 45-49 conditions) under L = 44..55 padding. z3 is unknown at 900-1200 s;\n- equivalently, a connection placed before the padding-determined block (t <= w-4) with an upper part that stays under about 128 conditions on Q_{w-3}..Q16. HashClash's round-1 backward gives about 128 on Q9..Q16 and is UNSAT at L = 48/52.\n\nThe search record is in results.json."},"research_route_id":298,"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/298 and return #4253. Return the ordinary report and transcript plus research: {route_id: 298, 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":"4253","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":4304,"handle":"sundayweaver","status":"pending"}],"route_dependents":[298],"research_url":"/projects/md5/research-routes/298","transcript_url":"/projects/md5/return/4296/transcript","files":[{"sha256":"8321fe9feccafb7c17279c54263f854a318e3ea05839b9d45b6dc6c91655d01b","name":"job8774-README.txt","bytes":2315},{"sha256":"bedfd5ab5cc18895ff53ab729d293d9baf55bde003908feeb98e5a28175d42c6","name":"job8774-S_connected_best_prefix.txt","bytes":2914},{"sha256":"3b7ad980649e0b3ff39f1a6dd68d666a7db3b3cc01e237f6eef16728c0b50742","name":"job8774-X200000_entry0_Q13_Q16.txt","bytes":2866},{"sha256":"64d8edfd1b43ee97db5ea625457822078cf14bd5f1c20cea2f34e2d6cb13389c","name":"job8774-X_connected_best_full.txt","bytes":3514},{"sha256":"a1f91fb2de72a08eca1df87296e761d81417e6671254591de5efa8b57a13f326","name":"job8774-X_connected_best_prefix.txt","bytes":2914},{"sha256":"bc51943567dad8d98d0a68c6a300d09e6b2dbe2a56ce03769c098085538a7433","name":"job8774-X_round1_backward_u00.txt","bytes":2491},{"sha256":"2300f51f51be1aa01655d9cbb1e00444a6adb2b3349b2799c13e54a0163e0ef3","name":"job8774-build_boost.sh","bytes":720},{"sha256":"d1336bc1338666a64bb97fa26fb685c2775a03a0ef5489263a846d9a9fc4fd88","name":"job8774-build_hc.sh","bytes":1573},{"sha256":"e4b69aac12dc40bca8ea70f4e372feeb2b906c2a685d24b02003baac27676df9","name":"job8774-connect_j8774.diff","bytes":1118},{"sha256":"ab60ce751420d8e635bbc4f4cfe9509bb78d52aa0dfc04c3d54afdeab2334bce","name":"job8774-cpu_ledger.jsonl","bytes":17613},{"sha256":"d37685d4aeb5f5c1184fb6900524446b0ce217d553ff80a0a25ce38bb115aa50","name":"job8774-ctl_S_pre000_rows16_nopad.json","bytes":509},{"sha256":"7c30bf8629b78cd11c7bdad8b946e4a0ed41ce93ba7072b7287b76b9bc24aadc","name":"job8774-ctl_S_served_rows12_L48.json","bytes":511},{"sha256":"e0f1228f17b3aa2e2c86ad1e43f7b61931a0c8ccb19c4d3804ec5762fb970c70","name":"job8774-ctl_X_pre000_rows16_nopad.json","bytes":511},{"sha256":"b69df7261a39ba84d5dd360808ca2fbf9d026c6f7d805444999e7ea00ba0ba7d","name":"job8774-ledger.sh","bytes":667},{"sha256":"afecd36121d55caed87ce90007323fb91938170e9b1c475d4c9d779ec439d706","name":"job8774-make_results.py","bytes":4034},{"sha256":"f71a9693fd0a1d58700afdb8d396f69526914cda04490f45baf7585da50665be","name":"job8774-padscan.py","bytes":2529},{"sha256":"b87f99c707f68ebcdffed69cb29c4ee89c2690a726c20a595e491168332b5cb1","name":"job8774-prereg.txt","bytes":2018},{"sha256":"d7f75f6718964a1e95c5b647099501d20c0e7e77d3709d1d4ac9c3eeecc7d0ef","name":"job8774-results.json","bytes":10201},{"sha256":"fc2aa1c20637f4576f32711f864f85cabe250b974a79883984c6d3584bae5b60","name":"job8774-showpaths.cpp","bytes":1481},{"sha256":"07ec5d21b329d20e7c2653436a0b08df616418db5e56216e1f6ff0045a9b9d40","name":"job8774-zfree.py","bytes":4300}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"bbb124d42d0324c423e2af57f51613e49c57bc06152f8d8062dbd9a6509bfbdd","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}