{"id":4279,"job_id":8805,"problem_id":6,"lane_id":35,"type":"explore","user_id":90,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #8805 - Route #288 (rescue) - Xie-Feng Q29 generator: fair compressions-equivalent cost and an exact Q9 pre-filter\n\n## Method\nCriterion (from the route's next step, fixed before the runs): success if the cost is <= 2^23.60 compressions-equivalent per\nverified Q29; stop if it stays > 2^25.0 after the Q9 pre-filter and vectorisation. \"Compressions-equivalent\" = generator\nCPU-s x an MD5 compression rate. We report it against (a) the 2^23.60/12.58M scalar convention of #4091/#4198 and (b) the best\nMD5 rate this machine reaches with the same thread layout (scalar and AVX2 8-lane), which is how a brute-force or md5sbc\ncompetitor would run.\n1. Generator: #4198's job8543-xfgen_route288.c (sha256 checked), AVX2-only build via job8616's make_portable.py (arm A2,\n   scalar; A2 and A3 give identical state counts per the source's ablation). Runs: 12 threads on 6 P-cores with HT, 90 s;\n   1 thread on one P-core with its sibling idle, 75 s. Every d>=28 record rechecked by our own MD5 steps (make_results.py).\n2. MD5 rates: md5bench.c (scalar 1/2/4 interleaved, AVX2 8-lane 1/2/3 interleaved, self-check MD5(\"\")), in the same two layouts,\n   plus #4198's built-in bench.\n3. Q9 pre-filter: (i) exact kept fraction f_k of the best filter that sees only R9 mod 2^k (q9win.c: image of all 2^23 Q9\n   choices, 24 real (Q7,Q8) states); (ii) implemented the exact filter at the sub1 level (Q25 bits 0..19 known, so R9 mod\n   2^15 known), same seed and work as a control (patch_prof.py XF_Q9PRE); (iii) oracle bound: same-seed runs with all of\n   Stage E skipped (XF_NOE) and with only the Q9 inversion skipped (XF_NOQ9).\n4. No AVX2 port of the AVX-512 arm: it uses 77 AVX-512 intrinsics (mask compares, vprold/vprord, gathers) on 16 lanes,\n   not a mechanical change. Instead the bound below grants the full A3/A2 speed-up from #4198's own ablation.\n5. GPU: not ported (the plan ports only if the fair cost is within ~2 bits of 2^25.0; it is 3.2-5.5 bits above).\n\n## Findings\nMEASURED (generator, A2):\n G1. 12 threads, 1,080.3 thread-s: Q27 257,604 (238.5/thread-s), Q28 802, Q29 50, Q30 4; fail 0, dup 0; q9_try/Q27 = 512.3.\n     1 thread, 75.0 s: Q27 32,417 (432.2/s), Q28 121, Q29 9. Pooled P(Q29|Q27) = 59/290,021 = 2^-12.26 (+-0.37 bit, 95%).\n     Cost: 20.61 thread-s/Q29 (12T; direct 21.61, 95% 16.4-29.1) and 11.37 CPU-s/Q29 (1 core; direct 8.33 from 9 hits).\n     All 923 d>=28 records recheck to their printed depth (0 disagreements).\n G2. MD5 rate per thread (Mcomp/s). 12T-HT: scalar 11.72 / 14.65 / 12.63 (1/2/4 streams), AVX2 46.5 / 68.3 / 74.1 (1/2/3\n     vectors). 1 core: scalar 14.86 / 24.62 / 31.32, AVX2 111.4 / 133.9; #4198's built-in bench 9.78.\n G3. Cost per Q29, log2 compressions-equivalent:\n       12T-HT: x 12.58M (#4198 convention) 27.95 | x scalar best 28.17 | x AVX2 best 30.51\n       1 core: x 9.78M (built-in bench) 26.73 | x 12.58M 27.09 | x scalar best 28.41 | x AVX2 best 30.50\n     Every value is > 2^25.0. The fair values (same thread layout, best scalar or best SIMD MD5) are 3.2-5.5 bits above the\n     stop line and 4.6-6.9 bits above break-even.\n G4. Time shares (same seed 8805200, 250,000 outer iterations, identical q22/q23/q24 in all arms): Stage E (Q25..Q27\n     enumeration plus Q9 inversion) is 40.3% of A2 time on a P-core (36.7% on an E-core); the Q9 inversion itself is 2.5%.\n     Even an oracle that made all of Stage E free gives at most 1.675x (0.74 bit).\nEXACT (q9win, 24 states; complete enumeration of the 2^23 Q9 choices):\n X1. The best possible pre-filter that knows R9 mod 2^k keeps on average f_k: k=7 (after sub0) 0.76; k=15 (after sub1)\n     0.296 = 1.76 bits; k=24 (after T, before sub_free2b) 0.0706 = 3.82 bits; k=32 0.001952 = 2^-9.00. Per state f_15 ranges\n     0.056-0.77. So #4198's statement that pre-filtering inside (sub1, sub2a) can only mean running more full inversions\n     misses that a partial, necessary condition exists: about 1.7 bits of the 2^-9 rejection is visible at the sub1 level,\n     and the 3-4 bits the route hoped for are visible only at the k=24 level, where at most 4 cheap iterations remain.\nMEASURED (the filter, P-core, same seed and work as the control):\n X2. Outputs identical (Q24 30,986,626; Q27 18,651; Q28 57; Q29 7). Rejected 737.3M of 1,058.3M sub1 nodes: 1.72 bits\n     recovered; q9_try 9,558,726 -> 2,916,451 (1.71 bits). CPU: control 43.51 s, filter 73.84 s, of which 34.99 s for 22,643\n     table builds (one per (Q7,Q8)). Net 0.589x (-0.76 bit); with the table free, 1.12x (+0.16 bit). Deferring the Q9\n     inversion stays the better choice in practice. #4198's conclusion holds; its argument was incomplete.\nHEURISTIC / BOUND:\n B1. Best case for this generator family on this machine: Stage E free (G4 oracle) and an AVX2 port that gets the full A3/A2\n     speed-up of #4198's 16-lane AVX-512 arm (53.83/32.32 ms = 1.67x): 2.79x (1.48 bits). This gives 7.39 thread-s/Q29 (12T),\n     2^26.69 vs scalar best, 2^29.03 vs AVX2 best. On 1 core: 4.08 s, 2^26.93 scalar best, 2^29.02 AVX2 best. Only with the\n     weakest single-stream scalar MD5 bench as the yardstick would it reach 2^25.25, which is still > 2^25.0.\n B2. GPU or AVX-512 cannot change a like-for-like cost by themselves. The cost is t_gen x R_md5 on the same device. Brute-force\n     MD5 is branch-free, register-only work and is about the best case for SIMD or GPU scaling (here AVX2 is 5.1x scalar per\n     thread). The generator is nested, data-dependent enumeration with per-level survival 2^-1..2^-9. So its SIMD/GPU gain\n     relative to MD5's is <= 1 unless shown otherwise. To reach 2^25.0 from 2^28.2-2^30.5 it would need to scale 9-45x\n     better than MD5 on the same device. #4198's 2^26.77 compares an AVX-512 generator with a scalar MD5 rate on Zen 4.\n     Measured against Zen 4's own SIMD MD5 rate, which was not measured here, it would rise by roughly log2 of that rate's\n     SIMD gain (heuristic; about 2 bits if it matches the AVX2/scalar ratio found here).\n B3. The Q8 tunnel: #4198's 0-free-bit proof was rechecked from the constants (T9 = 0x9f34ef7f, Q10 = C1[10] is 0 and Q11 is\n     1 on every T9 bit, so F(Q11,Q10,Q9) = 0 there). Not redone beyond that.\n\n## needs\nNothing beyond this machine. An AVX-512 machine is not decisive: B1 already grants the full measured AVX-512 gain, and the fair\ncost stays > 2^25.0.\n\n## verification_sufficiency\nEstablished: the counts in all same-seed 'prof' runs are deterministic, and the arms agree on q22/q23/q24. The filter arm\nreproduces the control's Q27/Q28/Q29 exactly. f_k is a complete enumeration per state, and its self-check passes (each record's\nown R9 lies in its image, 24/24). The mean f_32 equals 2^-9.00, matching the generator's measured q9_try/Q27 = 512. All 923\nd>=28 records recheck to their depth with independent MD5 code (MD5(\"\") self-test). md5bench self-checks pass. CPU times come from\n/usr/bin/time -v and the thread CPU clock.\nNot established: Q29 counts are small (50 and 9); the pooled estimate carries +-0.37 bit. The 12T rates are with HT on 6 cores.\nSingle-core runs ran concurrently on separate physical cores (shared turbo budget). No AVX-512 or GPU measurement was made (B1\ngrants the AVX-512 gain; B2 is heuristic). The f_k means are over 24 states (per-state spread is large: f_15 0.056-0.77).\n\nFiles are uploaded with the prefix `job8805-` (work/x and raw/x as `job8805-x`).\n","patch":null,"cpu_hours":0.699,"hashes":{"job8805-run.sh":"22c4c3e9a6e5da7eaadef54fc7824574294e80e66bedd9e33a8c4622f4ab5e38","job8805-q9win.c":"ecf3d95fa43613026394e6539fd519ab85023ce662dcf629b733fff6859bbf34","job8805-ledger.py":"d2b66e1e51759af0315eedffc37a0df689bfc27b0ac3b8c166a19de7546b110f","job8805-README.txt":"e12255cd8b3c20beb54ac7b71db3721a73bc5ff0da2f6ba5cfa7bc42951b8598","job8805-gen12.json":"e3b95d0fafdcf0141786923d23e9dcd332f6c5fd82c0714690a4f41e214001a5","job8805-gen1p.json":"7560c98ec93f0300916423c06cd4ee1a25896963ff30b0f1527cf7689641dee3","job8805-md5bench.c":"edc920c032ce42f3d15351513dff8c6230cb326d5851eedb692152a7a2b6e9c4","job8805-p_noE.json":"4c32145a0c4f506a484e32d3aab060b5d1a8774ef46143bb7e137f9dd3e037e1","job8805-q9win.json":"e6de7ea5fff20f27a2a4f05fc606e470a6a4cad8c6ff3cae706d2f2c70ffc001","job8805-md5_1e.json":"2fea224cf94fd760511614b2a4b44f61e4b57afd23d19655494946a4762c5d2e","job8805-md5_1p.json":"c6d38753558375e2c559584ca4696b8e55fd6d4ea06f4b8124b2a0c25f3b8822","job8805-pre_q9.json":"32ac7b270106abd6a006a3389ac225adcda0f2a302db813ce2961885a17897be","job8805-abl_noE.json":"c1b9a630b3c61e6e66c49a54bfc10fb8d2c90e81c7c12cfe4b25379f4bc8cee9","job8805-md5_12t.json":"f42882a3eea30cddc1892df523a6a1f3444ef828f65138ba052f05502b0a8db1","job8805-pre_ctl.json":"1221b94a62b0f0999fe6102908589316b1d70c59d77745a5bfac739df2199dd6","job8805-results.json":"6070c3ea3eb93a1ebb26881cab7202cb5f109cdd6e0db51c3a159a682cd32624","job8805-abl_full.json":"34dd0d53c337111b393b15bbd7c8d90c5368b80f2f25096dc293671151ff1a99","job8805-abl_noQ9.json":"8ae30ca260136a8e135fdf44796919445c71d239f08a6d32cf6e707e05f1815b","job8805-patch_prof.py":"beae5d87449b05262254c77601d55146610fd9e0887a4aa68ddd3950a44bab80","job8805-abl_full2.json":"3750c5f495ea3fb74771ad46dc75a169b875c4dfe30babd8d5dca0495d574293","job8805-make_results.py":"fd8fe79130ecc0f554fcea1911be32e82e26cb9a9968515c9e840309788b7dcd","job8805-cpu_ledger.jsonl":"8f929acd4dfa34f246d8baf10f138083d19544fae57b44b7f49027e715ec69be","job8805-make_portable.py":"4174ca5b10e4e7f98d5de3085affb3eb6c8bed0cc70777bafb1df67853f63329","job8805-gen12_records_d28plus.txt":"0a03500eb630ebebf09eef76be00798a474d1dba1f2cd11a8ab08460f40a0fff","job8805-gen1p_records_d28plus.txt":"099769a1cc8abc9e1647209b33d1e1cfb46d9a14fea0741b17b0a85e40e17893"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T17:32:16.146Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4198,4091,4146,4104],"messages":[]},"tokens":{"log":"summary","input":178,"models":{"claude-opus-5-5":46753},"output":46753,"source":"reported","entries":0,"cache_read":9855626,"cache_write":205433,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Fetch #4198's 11 files by sha256 into an empty directory; gcc and python3 only. See work/README.txt: make_portable.py -> patch_prof.py -> gcc; 'run' 12 threads 90 s and 1 thread 75 s; md5bench scalar 1/2/4 and avx2 1/2/3 in both layouts; 'prof 8805200 250000' with no variable, XF_NOE, XF_NOQ9, XF_Q9PRE; q9win on the run's records; make_results.py. Expected: G4 and X2 counts exactly; rates within machine noise.","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":"attempt_failed","evidence":"G1-G4, X1-X2, B1 in job8805-results.json (raw run outputs job8805-*.json); reproduction in recipe_md and job8805-README.txt.","statement":"Q9 pre-filtering (exact, 1.72 bits of the 2^-9 rejection recovered at the sub1 level) and vectorisation cannot bring the #4198 Xie-Feng Q29 generator below 2^25.0 compressions-equivalent per Q29. Measured 2^28.17 (scalar-fair) and 2^30.51 (AVX2-fair) on 12 threads. Best case with Stage E free and the full AVX-512 gain: 2^26.69 / 2^29.03.","assumptions":"Generator = #4198's design (Q22 search -> Q23 -> Stage D Q24 -> Stage E Q25..Q27 -> Q9 closure). Q29 conditions of #4091's pair-derived set. \"Compressions-equivalent\" uses the same machine's MD5 rate in the same thread layout. SIMD/GPU scale the generator no better than MD5 (B2, heuristic).","revisit_when":"A generator change cuts the cost per Q29 by >= 2^3.2 at fixed hardware. Stage E is only 40% of the time, so that change must cut Stage A-D cost per Q24 or raise P(Q29|Q27) = 2^-12.26. An example is a tunnel that re-randomises Q28/Q29 without rebuilding Q24..Q27, such as the 32-dimensional post-Q27 family proposed on route 294. Revisit also if a measured GPU port shows the generator scaling better than MD5 on the same device."},"route_id":288,"depends_on":[4198,4091],"evidence_md":"**Fair normalisation (measured, i7-12700, AVX2).** #4198's generator (scalar arm A2, AVX2-only build):\n- 12 threads (6 P-cores, HT), 1,080 thread-s: 257,604 Q27, 802 Q28, 50 Q29, all rechecked. That is 20.6 thread-s/Q29 using the\n  pooled P(Q29|Q27) = 2^-12.26 +- 0.37.\n- 1 core: 11.4 CPU-s/Q29.\n\nSame-layout MD5 rates per thread: scalar best 14.65 M/s (12T) and 31.3 M/s (1 core); AVX2 8-lane best 74.1 and 133.9 M/s.\n\nCost per Q29 (log2 compressions-equivalent):\n- 12T: 27.95 at #4198's 12.58 M; **28.17 scalar-fair; 30.51 AVX2-fair**.\n- 1 core: 26.73 at the built-in 9.78 M bench; 28.41 scalar-fair; 30.50 AVX2-fair.\n\nThe stop line is 2^25.0 and break-even 2^23.60.\n\n**Q9 pre-filter (exact + measured).** By complete enumeration of the 2^23 Q9 choices (24 states), a filter that knows R9 mod 2^k\nkeeps f_k: k=15 (after sub1) 0.296 = 1.76 bits; k=24 (after T) 3.82 bits; k=32 = 2^-9.00. So part of the rejection is visible\nearly, contrary to #4198's argument. Implemented exactly at sub1, same seed and work as control: identical Q27/Q28/Q29, 1.72 bits\nof rejection recovered, but net 0.59x with per-(Q7,Q8) table builds and 1.12x even if the tables were free. Stage E is only 40.3%\nof A2 time and the Q9 inversion 2.5%, so an oracle making Stage E free gives <= 1.675x. Deferring the inversion stays best in\npractice.\n\n**Bound.** Stage E free plus the full A3/A2 AVX-512 gain from #4198's ablation (1.67x) is 2.79x: 2^26.69 scalar-fair, 2^29.03\nAVX2-fair. Both are > 2^25.0. Only a mismatched yardstick (SIMD generator vs single-stream scalar MD5) gets near it (2^25.25).\n\n**GPU (heuristic).** The cost is t_gen x R_md5 on one device. Brute-force MD5 is the best-scaling SIMD/GPU workload, while the\ngenerator is divergent nested enumeration. A port lowers the like-for-like cost only if the generator scales better than MD5, by\n9-45x here. Not ported.\n\n**What it changes.** The route's next step (Q8 tunnel, Q9 pre-filter, AVX-512/GPU) cannot reach the stop line. The Q8 tunnel has\n0 bits (#4198, rechecked). The remaining 3.2-5.5 bit gap is in Stages A-D (about 60% of time) and in P(Q29|Q27) = 2^-12.26, not in\nthe Q9 inversion. #4198's 2^26.77 used a scalar rate for an AVX-512 generator, so on a same-SIMD basis it is about 2 bits higher\n(heuristic).","prior_art_md":"- Stevens, \"Single-block collision attack on MD5\", ePrint 2012/040 (abstract via search): average ~2^49.8 MD5 compressions.\n  It is the md5sbc baseline the route's break-even was set against (#4091: 2^23.60 per Q29 with the 2^-22.05 Xie-Feng tail).\n- Xie and Feng, ePrint 2010/643 (abstract via search): first single-block MD5 collision; method not disclosed.\n- Xie, Liu and Feng, ePrint 2013/170 (search summary; read in full by #4091): the 2010 attack is ~2^47 and a preserved attack is\n  claimed at ~2^41. No generator rate or per-Q29 cost is published.\n- Klima, ePrint 2006/105 (tunnels; cited by job 8616) and Return #4198 (generator, AVX-512 ablation, Q8 tunnel proof) are the\n  direct predecessors. #4146 is rejected; its duplicate-record issue was repaired in #4198.\n- No published md5sbc or brute-force throughput was found in 2 searches. Rates here are own measurements (scalar and AVX2 8-lane\n  MD5 on the same CPU and thread layout).\n- Remaining gap: no source gives a Xie-Feng-path generator at <= 2^25 compressions per Q29 on a same-hardware basis. The open\n  ingredient is a construction that lowers Stage A-D cost per Q24 or re-randomises Q28/Q29 cheaply after Q27, not a better Q9\n  inversion or wider SIMD."},"research_route_id":288,"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":"Inspect the decisive obstruction with a fresh perspective. Distinguish an unresolved task, failed attempt, refuted statement and scoped obstruction. Seek a repair, weaker requirement, new ingredient or alternate method. Preserve valid counterexamples and their exact scope. A successful rescue needs a distinct next experiment and evidence that the alternative avoids the obstruction. Reuse the prior search and search online for the changed ingredient, including failures in the source field. Do not rerun published computations here. Your findings start a new investment basis; explicitly list any earlier return still required in depends_on.\n\nRead GET <project base>/research-routes/288 and return #4146. Return the ordinary report and transcript plus research: {route_id: 288, 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. 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