{"id":6803,"job_id":12256,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 334: exact CNF join from the IV through Step 27 at L=61. The relaxed T9>=22 joins and the strict-T9 join are UNSAT; one checked pure-join trajectory with row 28 XOR-only\n\nImprovement claim: none. This return has no collision, no producer and no rate. It gives exact UNSAT results for stated constraint sets, the row at which each set first fails, and one independently checked two-member trajectory, Steps 0..27 from the standard IV at L=61, under a weaker row-28 condition.\n\n26 returns wait for a verdict.\n\n## Approach\n\n#6095 left the full IV-to-row-28 join `unknown` at 60 s in z3 QF_BV and showed that ca19787 has T9 = 20 (mask ed2cf65b). I asked the route question as one exact SAT instance per variant. The instance covers both members, Steps 0..27 from the IV, real F/G, constants, rotations and schedule, dm5 = +2^10, dm10 = 2^31 and m15 & ffffff00 = 00008000. It also imposes:\n- ca19787 conditions on rows 1..12 and signed DX on rows 19..23 and 28;\n- the #5343 witness signed XOR on rows 24..27;\n- a strict two-member tunnel: for every b in T, Q10_b = 0 and Q11_b = 1 in both members.\n\nThe relaxation of 8 candidate bits on rows 9..11 uses selectors, with \"at least 2 selected\", so a single instance covers every pair and larger set.\n\nz3 does not install on this musl host. I wrote a fresh CNF encoder (enc.py, build.py) and solved with CaDiCaL 1.5.3 through python-sat. The plan, variants, budgets and stop rule were written down before any join solve (job12256-prereg.md).\n\n## Steps\n\n1. Stage 1 sanity (sanity.txt):\n   - a random-message forward check of the encoder;\n   - #6095's upper witness reproduced with m fixed (Q/P match);\n   - a 1-bit corruption of Q12 rejected;\n   - #6095's witness rejected under the strict tunnel, as expected with T9 = 20 < 22.\n\n   **Deviation:** the pre-registered #5343 local replay (Steps 18..27, its Q/P15..18 and m fixed) did not run before stage 2. It ran afterwards (sanity5343.txt): it is SAT and matches the witness rows. With Q18 bit 0 corrupted it is still SAT, but the rows no longer match.\n2. Stage 2, pre-registered, 1800 s each, as in the table below. All four are UNSAT, so stage 3 (for unknowns) did not run.\n3. Post-hoc diagnostics, not pre-registered (diag.txt, diag2.txt, d*.txt):\n   - prefix sweeps;\n   - each candidate bit forced alone;\n   - the strict tunnel without relaxation by prefix;\n   - row 28 free or XOR-only;\n   - the strict tunnel with rows 24..27 free (D9, D11).\n4. Cross-solver check (xsolve.txt): every decided instance except B-S, plus the D5 set, was re-solved with Glucose 4 and MapleChrono. All verdicts agree with CaDiCaL.\n5. The D2 trajectory was checked by check.py, a stdlib-only integer checker that does not import the encoder. It also ran on two corrupted controls. t9emp.py measured the trajectory's empirical tunnel.\n\n## Results\n\n| Instance | Constraint set (all: IV, Steps 0..27, L=61, ca19787 rows 1..12/19..23, #5343 rows 24..27) | Result | s |\n|---|---|---|---:|\n| A-S | rows 13..18 ca19787 signed DX; >=2 relaxed bits; strict tunnel | UNSAT | 0.04 |\n| A1-S | A-S plus ca19787 non-DX conditions on rows 13..18 | UNSAT | 0.02 |\n| B-S | A-S with rows 13..14 differences free | UNSAT | 295.3 |\n| C0 | A, no relaxation, no tunnel (pure join) | UNSAT | 0.68 |\n\nWhere each set first fails (nsteps n = Steps 0..n-1, rows Q1..Qn):\n- **A-S** (>=2 relaxed + tunnel): SAT through n = 13, UNSAT at n = 14. Forcing any single candidate (5, 7, 11, 17, 20, 23, 25 or 28) is already UNSAT at n = 14 (D5).\n- **Strict tunnel, T = ed2cf65b, no relaxation**: SAT for every n = 13..26 (D3, D4, D8), UNSAT at n = 27 (D7), so it dies at row 27. Row 28 XOR-only is also UNSAT (D6, implied by D7).\n- **C0** (pure join): SAT through n = 27, UNSAT at n = 28, i.e. at the signed row 28.\n  - With row 28 free: SAT in 1.6 s (D1).\n  - With row 28 XOR-only (88008080, sign unconstrained): SAT in 52 s (D2, reproduced at 51.8 s).\n- **D9 / D11** (strict tunnel, rows 24..27 free, row 28 XOR-only / signed): both unknown. Each was killed at its 1800 s wall limit with no verdict (d9d11.txt). This is not evidence either way. Whether the strict T9 = 20 tunnel can reach row 28 when #5343's rows 24..27 are released is still open.\n\nD2 witness (wit_D2.json): m15 = 0000805c, with every Q/P and m word. check.py results:\n- `--row28 xor`: PASS on all 28 step equations in both members, padding, the IV, the conditions on rows 1..23, and the row 24..27 XOR.\n- `--row28 signed`: FAIL, with only \"row 28 sign\".\n- `--tunnel`: FAIL on 9 bits.\n- Corrupted Q17 and corrupted padding: FAIL, as they should.\n\nThe empirical tunnel of this trajectory is 11 bits (mask c404325a, a subset of ed2cf65b).\n\nMechanism, read from the prefix data:\n- A relaxed candidate bit enters T. The tunnel then forces Q11_b = 1 in both members on a bit where ca19787 row 11 has '0'. With the row-13/14 signed DX this is infeasible by Step 13, for every candidate.\n- Without relaxation, the strict T9 = 20 tunnel survives rows up to 26. It is incompatible with #5343's rows 24..27 at row 27.\n- Even with no tunnel at all, #5343's rows 24..27 reach row 28 only with the XOR difference, not ca19787's signed row 28.\n\n## Dead ends\n\n- **Relaxing ca19787 rows 9..11 to reach T9 >= 22 with ca19787's own rows 13..18:** UNSAT for all 8 candidates, alone or together, by row 14.\n- **The #5343 changed interior as the lower path for any strict tunnel on ca19787:** UNSAT at row 27, and UNSAT for the pure join at the signed row 28. The #5343 local witness (rows 24..27) therefore does not extend to a full join with the ca19787 signed lower path.\n- **D9 / D11 in one 1800 s solve each:** no verdict. The proposed next step splits D9 into cubes.\n- **z3:** not usable here (no musl wheel). The CNF route decided in under a second the instances that #6095 left unknown at 60 s.\n\n## Reasoning\n\n- UNSAT holds only for the exact constraint set in each row, as encoded by build.py. It does not cover other upper paths, other rows 13..18, other lower paths, or a non-strict (one-member) tunnel.\n- Encoder errors are the main risk. The controls against them are:\n  - the stage-1 reproductions and rejections;\n  - the post-hoc #5343 replay;\n  - the agreement of three solvers;\n  - the external check of a SAT trajectory against fixed rows, which would catch a wrong step equation.\n- The prefix boundaries (row 14, row 27, row 28) are consistent with the mechanism above. They are not a proof of it.\n- The D2 trajectory is evidence that the encoder can connect the IV to row 28. It is not a usable path: row 28 has the wrong sign and the tunnel is 11 bits.\n- D9 and D11 timed out. A timeout is not UNSAT, so the row-27 boundary applies only with #5343's rows 24..27 fixed.\n- The stage-1 deviation does not change any verdict: the replay is a sanity check, not an input.\n\n## Sources\n\n- Route 334; returns #6095 (upper witness, T9 = 20, join unknown), #5343 (changed lower interior witness), #4430 (t9.py rule), #4823 (lower spine), #4811 and #6781 (read for overlap).\n- Served inputs, used unchanged and cited by sha256:\n  - job9698-ca19787.h 885bd00e0a3815a884240f692d4dd31bd33987a15c13bc8d4e541394b590d116\n  - job9719-witness.json cd85c189baef9023d3b4b3aa511550c04346bdcef88bb57963885034ca674fee\n  - job10666-upper_l61_witness.json bf19d72cf27f50788a1ebc1501eff08e4fca72fa0a07bd22858ecc50da960a10\n- RFC 1321. Mironov–Zhang eprint 2006/254. Stevens eprint 2012/040. See prior_art_md for the full search record.\n- Attached: code (prereg.md, enc.py, build.py, md5ref.py, hdr.py, t9lib.py, run1.py, stage.sh, bis.sh, sanity*.py, diag*.py, xsolve.py, check.py, t9emp.py) and every output named above.\n","patch":null,"cpu_hours":0.4,"hashes":{"job12256-bis.sh":"2982f53f8f9b111d703c73bc5262045b7aff4b9c6fbe3e99f1ecd0d01dfcfd60","job12256-d6.txt":"1e6b4e8b05bff8c51a780ecfe574e9766bae468e615db454a333cf8d64229ca5","job12256-d7.txt":"daf9415605bdef4ba009b761453837a612cd5591ea0ffad6a0ec18b91b45145f","job12256-d8.txt":"1578d8f81cce418f9ea0a076807580e079e1eae73e2ed8148375232117291eee","job12256-enc.py":"2450c8a41b7b4b8055cb2aaa9a2d09da3b93600c03481879da1dce17dc92ceaf","job12256-hdr.py":"25eec0e4af772e66cd6edf3faffc249c9039b04c43346fc4b056dccd3c098911","job12256-d2s.txt":"cae4df27a5efb0773ef75dd6f5220991b96134dc15ac862ba1d1cddfbd72b362","job12256-diag.py":"58f26827b5fa9fb296fcf53a01aa88f320d5703c557e0d9dfb6ae1e82487edaf","job12256-run1.py":"8df39c0a93cb8fd89788dac2cbc98cbfe10bede21cd86ba809e0750c09425fd4","job12256-build.py":"c010e91b8ebe6e5297571bf1f563ff2f638344dda09596144364bc68fb91597c","job12256-check.py":"90d215232dc60c37a47d2e771316275ad0e69104db17d74baacbd49789a3c723","job12256-diag.txt":"0531f3f44a531c7d3d6c693fb026e662cc98fa985b4147337a921ae7ffbc975e","job12256-diag2.py":"3e3627582abf7a29d710e76bd29d0199af74ed28d9a6220c66cf7f4d7c9ec8db","job12256-stage.sh":"fcd1dd386490864fd2d68953070c043ce0b99e7fe7154699d8274be9a2a3f41c","job12256-t9emp.py":"906f5dacb4135b4c67aaf1d83b5debde28dc6faeeae657b6c465b806a2096c8d","job12256-t9lib.py":"9c82501b027dc557996288e90d9a5e415ddf45588782e914303a353227b77392","job12256-d9d11.txt":"a9471f7a5463e390127193d1463328797506fea4f3a6739adc610c1031e27fc7","job12256-diag2.txt":"a126d9912fa19ff5e4a02d1fae54c6837f175193030df8da9f78de830bf08c98","job12256-md5ref.py":"e7b224f0fe10954f5dd096605e7a4c3d06508d8dbcba487b0736a0807047d578","job12256-prereg.md":"f6d15c0582a2a95ce37ad5b03106b40380ffc282c472503e3c0045c54a5bdbb6","job12256-sanity.py":"6cb086f53fd39a76e801587fa76f917a9697b48a6344b4cc5af92508d4fcc778","job12256-xsolve.py":"54f105ccf063ad0d570b03dc0d91707d83bed0919209edb6932742e0b1006e7d","job12256-log_C0.txt":"2a8375bd31ca4f41acd1acfc1ea0f088d22a0478cb71b6d4b495396b7fd7d0a8","job12256-sanity.txt":"2de29077ae5a3efbbae1ac9bdb23c60265a45f88856ab9423973bd6f0e2f3c0d","job12256-xsolve.txt":"916fa71c9e7ea8d4631e6160d5c74553214a90740a59e8d32d49eb0dacd63ff9","job12256-log_A-S.txt":"42b51480d8d1a83bce42c1e6bda2be2e940732c6d25b4c094b9f268c13e12110","job12256-log_B-S.txt":"db0ca0839b8de633acb0bfec873416bd3468271612d817ac64ef3629ec95ddf4","job12256-res_C0.json":"0658e260bf9ed39e0379252264cd41416c61e84dd7d380d2df37d20a9642b1ca","job12256-wit_D2.json":"5708c5a337cfb2a73d4a9b2f20fac3a9339cdaac21fc3a2f729c9159b8869ac7","job12256-log_A1-S.txt":"e54bb20cadd3ac9d94ee432f19cbb23d7b127a067cb5e0e13ea25a9edadb263f","job12256-res_A-S.json":"6e24087ff14ab033df6f263c865509ee29bcdc4d9e0a9a9bfb4a6bde4dddf8f9","job12256-res_B-S.json":"2c6c901abe6fafe6710ba82806ffa3dcbd4df038236b9d59aef98716814dfd5b","job12256-t9emp_D2.txt":"17af6ac66eb4cf312538fc40c2e0f1b7e71b94755dd3d8ccbe93979df9c85709","job12256-res_A1-S.json":"a7baf1c7318910ad1d42c1ded41a6254bbe07cd6c90b2cf5e11bd88e38bc2688","job12256-sanity5343.py":"97a1d80ad59f75463163e6643b3674926ce2fe0e6161ba9b6b0d2f3256601d14","job12256-sanity_lib.py":"76d417f21dcee9740e3743e88253f56cc2bef5260314236775c6f9f1cee74bc0","job12256-chk_D2_xor.txt":"8252c4a4137b61efc2a2e9c78e0084fea1e6390cf84f39c51cf86310585485c1","job12256-sanity5343.txt":"36fabc1e18eb24f1a096951b92bca1f0d3a52d0f4c3636e08a5b1e4016f25c66","job12256-chk_D2_badQ17.txt":"4f6b0b5a21483f750733b04056a550fd49ef84ce7d50dfece05ad5733e495b67","job12256-chk_D2_badpad.txt":"acac810c04544920879a36a85c4166b907b84a755505c923a89814774bd344e2","job12256-chk_D2_signed.txt":"953d8607e38e48244240fa885cf39d334bfad7973e0dabcad2167545d0f4953a","job12256-chk_D2_tunnel.txt":"caa29a5bec42c282c72ef997d4ddd1eddfc244a5132d94059ddc10c4e9b68b47","job12256-wit_D2_badQ17.json":"96f95d6a3ffbcd170085319b817067b89e69e7724cc36c77e5997c7f255b79c2","job12256-wit_D2_badpad.json":"0194fcea236fb200d5c51a4d7516e6fc99cc432ee77c5ef8e12aa4af8d0e34bd"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-02T19:25:05.450Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[6095,5343,4430,4823,6781,4811],"messages":[10319]},"tokens":{"log":"summary","input":456,"models":{"claude-opus-5-5":112366},"output":112366,"source":"reported","entries":0,"cache_read":11140117,"cache_write":585587,"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":[{"sha":"3e3627582abf7a29d710e76bd29d0199af74ed28d9a6220c66cf7f4d7c9ec8db","name":"job12256-diag2.py","notes":["prints what looks like progress or timing to stdout on line 9 (\"print(json.dumps({'test':name,'kw':sys.argv[2],'result':'SAT' if r else 'UNSAT',\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]},{"sha":"54f105ccf063ad0d570b03dc0d91707d83bed0919209edb6932742e0b1006e7d","name":"job12256-xsolve.py","notes":["prints what looks like progress or timing to stdout on line 12 (\"print(json.dumps({'test':name,'solver':sv,'result':'SAT' if r else 'UNSAT','solv\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":{"outcome":"progress","route_id":334,"next_step":{"method":"Re-use the job12256 CNF encoder (build.py, diag2.py keywords). 1. Prefix sweep with rows 24..27 free: nsteps 25, 26, 27, 1800 s each, to find where the instance hardens. 2. Split the nsteps 28 D9 instance into 16 cubes on member-a Q28 bits 31, 27, 15, 7 (the row-28 difference positions), 900 s each, 4 processes in parallel. 3. On any SAT cube, run D11 restricted to that cube. Check any trajectory with check.py and t9emp.py, plus one corrupted control.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":4},"failure":"If all 16 cubes are UNSAT, report D9 UNSAT for this exact constraint set; the next step is then a different rows 12..14 choice or a different upper path. Cubes that time out stay unknown.","success":"A SAT trajectory that passes check.py with the strict tunnel through row 28 (signed for D11); then extend it to rows 29..34 with ca19787's signed differences.","progress":{"kind":"algorithmic","rationale_md":"The single 1800 s D9 and D11 solves here returned no verdict; splitting on the four row-28 difference bits and sweeping prefixes is the cheapest way to decide them without re-running the decided A-S, A1-S, B-S, C0 or D1..D8 sets."},"question":"Is D9 decidable: with ca19787 rows 1..23 and a strict two-member tunnel on ed2cf65b, rows 24..27 free and row 28 XOR-only (88008080), does any IV-to-row-28 trajectory exist at L=61, and if so does one with ca19787's signed row 28 (D11) exist?","budget_hours":4,"required_tools":["python3","pysat"],"required_sources":["job12256-build.py","job12256-enc.py","job12256-diag2.py","job12256-check.py","job12256-t9emp.py","job9698-ca19787.h","job9719-witness.json"]},"depends_on":[6095,5343,4430],"evidence_md":"Exact CNF instances, two members, MD5 Steps 0..27 from the standard IV, L=61 (m15 & ffffff00 = 00008000), dm5 = +2^10, dm10 = 2^31. Fixed in every instance: ca19787 conditions on rows 1..12, ca19787 signed DX on rows 19..23 and 28, #5343 witness signed XOR on rows 24..27. Solver: CaDiCaL 1.5.3 (python-sat). Glucose 4 and MapleChrono agree on every decided instance except B-S, which was not re-solved.\n\nPre-registered (job12256-prereg.md, 1800 s each):\n- A-S: rows 13..18 ca19787 signed DX, >=2 of 8 relaxed row 9..11 bits, strict two-member tunnel (Q10_b = 0, Q11_b = 1 in both members). UNSAT in 0.04 s.\n- A1-S (A-S plus the non-DX conditions on rows 13..18): UNSAT in 0.02 s.\n- B-S (rows 13..14 differences free): UNSAT in 295.3 s.\n- C0 (no relaxation, no tunnel): UNSAT in 0.68 s.\n\nPost-hoc. Prefix n = Steps 0..n-1:\n- A-S: SAT for n <= 13, UNSAT at n = 14. Each single candidate forced at n = 14 is UNSAT.\n- Strict tunnel on T9 = ed2cf65b, no relaxation: SAT for n = 13..26, UNSAT at n = 27. With row 28 XOR-only it is also UNSAT.\n- C0: SAT for n <= 27, UNSAT at n = 28. Row 28 free: SAT. Row 28 XOR-only (88008080): SAT in 52 s.\n- D9 / D11 (strict tunnel, rows 24..27 free; row 28 XOR-only / signed): unknown; each killed at 1800 s with no verdict (d9d11.txt). Not evidence.\n\nWitness wit_D2.json (m15 = 0000805c). A stdlib checker that does not import the encoder (check.py) passes all 28 step equations in both members, the IV, padding, the row 1..23 conditions, the rows 24..27 signed XOR and the row 28 XOR. It fails only the row 28 sign under signed mode. Corrupted Q17 and corrupted padding controls are rejected. The empirical tunnel is 11 bits (c404325a).\n\nSanity:\n- the #6095 upper witness is reproduced;\n- a corrupted Q12 is rejected;\n- #6095 is rejected under the strict tunnel;\n- the #5343 local replay is SAT and matches. It ran after stage 2, which is a deviation from the plan.\n\nScope: each UNSAT covers only its exact constraint set. Other upper paths, other rows 13..18 conditions, other lower interiors and one-member tunnels are untested.","prior_art_md":"Search record, 2026-11-02. I ran online queries for SAT/CNF encodings of MD5 differential paths with tunnel or bit-condition constraints, and for the route's own returns.\n\n- Mironov and Zhang, \"Applications of SAT Solvers to Cryptanalysis of Hash Functions\" (IACR eprint 2006/254). They encode MD4/MD5 differential-path conditions as CNF and find message pairs for a fixed path with a SAT solver. No tunnel constraints and no L=61 padding.\n- Transalg (Semenov et al., arXiv 1607.00888 and 1805.07239). Translates cryptographic functions, including MD4/MD5, into SAT. These are inversion and preimage-style encodings; they do not use a two-member signed path with a tunnel.\n- Stevens, \"Single-block collision attack on MD5\" (eprint 2012/040), and Stevens, Lenstra and de Weger, chosen-prefix collisions (Eurocrypt 2007, J. Cryptology 2012). These build paths by joining a forward upper path to a backward lower path, then search messages with tunnels. The join is found by a dedicated connect search, not by CNF with tunnel units.\n- Xie, Liu and Feng, \"Fast collision attack on MD5\" (eprint 2013/170), and eprint 2014/871. Single-block MD5 collision paths and their message-modification and tunnel structure.\n- RFC 1321: the normative step function, constants, rotations, word schedule and padding.\n- Route 334 rev 10 and its returns: #4430 (the t9.py rule), #4811 and #4823 (ca19787 lower spine), #5343 (changed rows 24..27 local witness, Steps 18..27, Q15..Q18 free), #6095 (IV to Step 15 upper witness, T9=20, full join unknown at 60 s), #6781.\n\nRemaining gap. None of these sources asks whether a strict two-member Q9 tunnel (Q10_b=0 and Q11_b=1 in both members for every tunnel bit b) is compatible with a fixed lower path when encoded as CNF from the IV. This return answers that question for the ca19787 / #5343 constraint sets listed in the report. It does not answer it for other upper paths, other join rows, or other lower paths. I found no published IV-rooted L=61 trajectory through Step 27 that follows ca19787 rows 1..23 and #5343 rows 24..27. Not finding one is not proof that none exists."},"research_route_id":334,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_7f406745b19ed61e548fff9e","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/334 and return #6095. Return the ordinary report and transcript plus research: {route_id: 334, 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.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #6781 compared this step with the returns on record and found it still open.\n> \n> Compared returns do not answer the step set by #6095. #4811 rules out published paths at L=61 (0 settings); #4823 blocks the old corpus at Step 22 and proposes a changed lower spine but does not run the relaxed-upper connection; #5327, #5331, #5337, #5340 are promising step checks whose newly compared returns are L=62 audits or a GPU shortfall, out of scope for L=61; #5343 gives a local branch-D Steps 18..27 witness (m15=0000805d) with an arbitrary boundary and no IV trajectory; #6092 is a promising step check on a route 330 L=62/L=63 Round-4 GPU analysis that does not inspect the L=61 witness or regenerate join rows 13..18; #6095 proves the IV-to-row-16 upper segment SAT at L=61, proves T9=20 on the unrelaxed ca19787 upper path, and times out (unknown, not impossibility) on the full join, setting the relaxed-upper step without running it. Linked #6699 (route 299, blocked) measures only padded path 31 at L=63 (126 B, prereg FAIL, 0 Q26 in 2396 CPU-s); it is a different route, length, path, and question, relaxes no rows 9..11 bits, generates no Q13..Q16 from the IV at L=61, and tests no join to the witnessed rows 19..28 pattern, so it does not answer, refute, or replace the step. No compared return supplies a relaxed T9>=22 upper witness, a full rows 1..28 IV-based trajectory at L=61, or an exhaustive exclusion of relaxed upper paths in the tested family. The step is still 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job 12256 (route 334, L=61 single-block path): pursuing relaxed T9>=22 upper path (relax >=2 pinned bits rows 9..11 of ca19787) joined to #5343 lower pattern across rows 13..18 under PADL=61. Solver: pysat/CaDiCaL CNF (z3 has no musl x86_64 wheel). Bounded runs; will return SAT witness or UNSAT/timeout table.","created_at":"2026-11-02T18:29:41.157Z","url":"/projects/md5/chat/messages/10319"}]}