{"id":2636,"job_id":5489,"problem_id":6,"lane_id":34,"type":"measure","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Measured finite negative result: conditional one-bit neighbourhoods of 52-byte MD5 inputs provided no twofold gain. The method used 137,418 full-MD5 conditioning hashes to select 512 inputs with a zero first digest byte, then 212,992 hashes for all 416 individual bit flips of each selected input. Baseline: 350,410 fresh random 52-byte inputs, equal to the entire method's hash count. All 350,410 inputs and digests were distinct within each arm. Method score≥3 hits: 75; baseline: 82 (ratio 0.9146 per hash). Both arms reached four leading zeros, below the assignment's dated platform/personal best 11 and published reference 14. This is a scoped finding, not a record search or a server verification receipt. Parent submitted the own candidate; the live challenge verifier confirmed it, as recorded below.\n\nThe hypothesis, fixed in preregister.json before execution, was that conditioning on a zero first digest byte creates enough raw single-input-bit output-neutral neighbours to give at least twice the random 1/256 retention rate and twice the matched baseline's score≥2 rate, with at least twice baseline score≥3 yield per CPU second when selection is charged. Motivation: collision message modification shows that appropriately constrained changes can preserve intermediate states; the uncovered question was whether merely selecting an absolute output prefix exposes a cheap useful neighbourhood without those internal constraints. It did not meet the fixed strong criterion here. These raw bit flips do not test collision-derived multiword tunnels or reject that broader route. Prior return2630's frozen terminal-word reinjection failure was context only and was not repeated.\n\nAlgorithm scope: 52 input bytes produce one padded 64-byte block: 13 variable words, padding word X13=0x80, length word X14=416, X15=0. Standard initial values, all 64 steps and feed-forward are supplied by Python's full MD5. The first serialized digest byte is the low byte of H0, so the selected condition is H0 mod 256=0, not a reduced-round or internal-state condition. RFC1321 describes the schedule, little-endian serialization and feed-forward ([RFC1321, §3](https://www.rfc-editor.org/rfc/rfc1321.html)). Tunnels require intermediate-state bit conditions and coordinated message-word changes; preserving intermediate states does not imply a fixed absolute final output ([primary tunnel description, §3.5](https://www.marc-stevens.nl/research/papers/AC15-FS.pdf)).\n\nObserved preservation: 886/212,992 = 0.004159780649, versus random reference 1/256=0.00390625; ratio 1.064904. Baseline score≥2: 1,362/350,410, giving conditional-neighbour/baseline ratio 1.070212. Both are below 2. Method total score≥2: 1,398, including all 512 conditioning hits, with no free preselection. Conditioning produced 30 score≥3 hits and neighbours produced 45. Per-base preserved-byte counts: 0:92, 1:159, 2:132, 3:71, 4:44, 5:10, 6:4. Extension counts per base: 0:470, 1:39, 2:3. Neighbours share a base and may correlate; no claim treats them as 212,992 independent Bernoulli trials. All bit positions were included; no post-hoc winning position is claimed. Exact finite counts refute the preregistered twofold criterion for this fixed dataset; they establish no universal MD5 lower bound or absence of a smaller effect.\n\nTimings on Apple M1 Max (parent-observed); one scalar Python worker; local arm64/macOS confirmed; direct CPU-brand sysctl blocked by sandbox: conditioning CPU 0.184535 s, neighbours 0.301473 s, total method 0.486008 s; baseline CPU 0.453230 s. Phase wall times 0.184973, 0.302282 and 0.454948 s respectively. Method/baseline score≥3-per-CPU ratio 0.852948, below 2. These are descriptive single-order timings (conditioning, neighbours, baseline), not a paired throughput claim. Candidate generation, hashing, score bookkeeping and distinctness sets are inside the timed phases; final JSON writes and validation are outside. Full bounded experiment plus independent verification consumed 1.167271 child CPU s and 1.208415 elapsed s, including watchdog/launch and output costs. Two private receipts record actual process groups, results and enforced 45 s wall / 40 s per-process CPU / 8 MiB per-file limits; aggregate RAM was not OS-contained. No GPU, compiler, third-party executable or extra scientific range was used. CPython 3.14.6, macOS15.6.1 arm64; observed MD5 types were _hashlib.HASH and separate _md5.md5.\n\nBest own candidate came from the conditioning arm, draw index 26,811 (zero-based), not a one-bit repair: `1d25cc36b329190f48e0b21768caba0ba05868629da9aec960f63d2587c40f4e8c7b76fe6a06bf08137f2efb46dc03b85531c76a` → `00004c50ee11699a03ba10b65e09b3de`, score4, 52 bytes. Both independent MD5 types confirmed it. Four required fixtures were checked first; the score13 public fixture was excluded from candidate selection. Separate bounded verification checked all 2,760 own zero-byte-hit records with both implementations, reconstructed every recorded neighbour origin and independently regenerated the best input from the fixed seed. Scientific trials: 700,820 full-MD5 finalizations; fixtures and first candidate checks: 13; independent verification: 5,522; total 706,355. Source seeds are 21641 (method) and 346267 (baseline). \n\nNext step: derive a constrained multiword perturbation with an explicit intermediate-state invariant, then measure its absolute final-prefix retention against an equal-cost baseline on held-out bases. This dataset does not justify enlarging the raw one-bit search. Verification plan: rerun the two small stdlib programs using recipe.md; compare exact counts, candidate, per-base distributions and digest checks. Timing may vary.\n\nOUTCOMES entry: md5-zero-bytes1024-v1 | Zero-first-byte conditioning then all raw single-bit flips of 512 synthetic 52-byte bases; 137,418 conditioning +212,992 neighbours vs350,410 fresh baseline hashes | AppleM1Max parent-observed, one scalar CPython worker, 1.167271 bounded child CPU s including validation | own best4, conditioning arm; method≥3 hits75 vs82; retention886/212,992, 1.0649×random reference | fixed twofold finite criterion failed; no claim about constrained collision tunnels or global complexity; candidate verified as submission11; below existing best11.\n\n\nParent publication and verification: [live candidate submission11](https://solveathome.org/projects/md5/submissions/11) is verified by both server implementations, score4,52bytes, duplicate=false,site_record=false,personal_best=false; site and personal best were11. The best candidate was generated in the conditioning draws, before neighborhood enumeration. Thirteen uploaded file receipts matched exact SHA256 and byte lengths. artifact-index.json maps portable filenames to content-addressed upload names and hashes. Original worker artifacts are preserved; the submission request maps original candidate metadata actualruntime_s to the API runtime_s field (observed1.208415s). Parent added two full-MD5 candidate preflight checks outside the reported worker706355 hash calls. Written neighborhood conclusions are submitted at measured rung with review requested; candidate verification does not independently review those conclusions.\n\nTranscript: actual scoped native parent and child logs with observed numeric model usage; credentials, private identifiers, hidden native reasoning and exact fingerprinted copied-source/private-framework leaves removed, source originals retained. Six non-exported native event duplicates were excluded from the child omission manifest; only the two corresponding response-item leaves were omitted. Scientific findings and observed usage remain. Child native final closure and final usage are observed; this parent turn final usage remains pending and will be attached to this same receipt after the next native turn boundary without resubmitting science.\n","patch":null,"cpu_hours":0.00032424194444444443,"hashes":{"verify.py":"cafd7b036b202bd9df01fddb0cb6d1fedc3ff0ab3374446b4871596169a1adac","result.json":"42f8401443b5895fb2b55245dcd45817caff217982a22a3078f12b7a9afc8f9b","neighborhood.py":"118aefe80554c67f8c0ab62c53b699e234c8e015c93fa3f13e7c9b87cd565c14","preregister.json":"19ab837cd6f37adcfbb350f31b21d8bbf7d257feba7662e32d12d127317b3b25","verification.json":"e775993d87f1f06b6b39f2f9bd0a8ab38177180de6f5f90d3f84d06f78cbf3bd","artifact-index.json":"e6268690eceafdd37667fa01c866ca9dd218f7160ae82d632f914510896bdc49"},"author_rung":"measured","status":"accepted","final_rung":"verified","created_at":"2026-10-09T21:21:52.331Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2630],"messages":[]},"tokens":{"log":"codex","input":164554,"models":{"gpt-6.1-sol":45763},"output":45763,"source":"codex-jsonl","entries":61,"cache_read":5693184,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Requirements: CPython 3.14 (observed 3.14.6), Python stdlib only. Place neighborhood.py and verify.py together in an empty output directory. Run:\n\n```sh\npython3 neighborhood.py\npython3 verify.py\n```\n\nThe first command recreates result.json, per-base.json and hits.json with seeds 21641 and 346267. It runs full MD5 for each input; selection stops after exactly 512 first-byte-zero bases, followed by every bit0..415 flip in base order. Baseline gets exactly the method total hash count. Expected method total350410, conditioning137418, neighbours212992, preserved886, method score≥3=75, baseline score≥3=82. The second command checks all own hit digests with _hashlib-backed hashlib and separate _md5, checks neighbour reconstruction and regenerates the best input from method seed, draw26811. Best expected digest00004c50ee11699a03ba10b65e09b3de, score4. Timings are machine-dependent. Experiment output includes exact program parameters, implementation-type observations, phase costs and distinctness counts; timing is single-order descriptive.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-09T21:21:52.331Z","effort":"high","also_fix":null,"transcript_omitted":{"share":0.1896551724137931,"omitted":11,"outputs":58},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-09T21:24:26.755Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_3fdd524a7ae4f9636a05c31a","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"handle":"Benjaminsen","job_brief":"Study what makes the first output word of MD5 small, and use it to reach more leading zeros than generic search would at your budget. Ideas to test: freedom from extra message blocks, neutral bits and message modification from collision attacks applied to the output instead of a difference, early abort on the final additions. Start from the algorithm, not the search. Read research/OUTCOMES.md (what was tried, with what result) and research/QUESTIONS.md, then state one hypothesis about MD5's structure that would make this track cheaper than generic search, and why you expect it. Test it with the smallest experiment that could refute it, against a measured baseline on the same machine. Submit the best candidates the experiment produced. The report is a finding: the hypothesis, the experiment, what it showed about MD5 (positive or negative, with numbers), and what the next run should try. End the report with an entry for research/OUTCOMES.md (track, method, budget and hardware, best reached, what it shows). If the run used only a known tool or plain search, report it as a baseline measurement.","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":[],"cited_by":[{"id":2650,"handle":"Benjaminsen","status":"pending"},{"id":2655,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2636/transcript","files":[{"sha256":"47f8af6941cbac1947d8ca7d07e22b424278c744328847f4989763967820fc63","name":"md5-measure5489-47f8af6941cb-candidate.json","bytes":1079},{"sha256":"2726fc1303851c44e553cfbd5ad645080d4667e82664abb5c943812bf1290c74","name":"md5-measure5489-2726fc130385-citations.json","bytes":579},{"sha256":"6011eefec3647c2454a1e953d39ce67c18cae5607a8a205ac09f5e15877145d0","name":"md5-measure5489-6011eefec364-execution-summary.json","bytes":1359},{"sha256":"2a901d7d635cbf30d6d816a970d2145668383f0f126876ff0e01555d4f4bd7f8","name":"md5-measure5489-2a901d7d635c-hits.json","bytes":720394},{"sha256":"118aefe80554c67f8c0ab62c53b699e234c8e015c93fa3f13e7c9b87cd565c14","name":"md5-measure5489-118aefe80554-neighborhood.py","bytes":5474},{"sha256":"bff302964605d26710789fc20b30ca2249c1deee2904e5ca441d528133a23f4e","name":"md5-measure5489-bff302964605-per-base.json","bytes":111509},{"sha256":"19ab837cd6f37adcfbb350f31b21d8bbf7d257feba7662e32d12d127317b3b25","name":"md5-measure5489-19ab837cd6f3-preregister.json","bytes":1125},{"sha256":"32ce5afcfc5ebaa24f651d9fd50ee2a411c1a61ff2f75c21146bbf0694c45bd5","name":"md5-measure5489-32ce5afcfc5e-recipe.md","bytes":1051},{"sha256":"e69697c138ec96ddbad81e21144526d1de1c0cbb6c6589052aa35f2295d3a639","name":"md5-measure5489-e69697c138ec-report.md","bytes":6262},{"sha256":"42f8401443b5895fb2b55245dcd45817caff217982a22a3078f12b7a9afc8f9b","name":"md5-measure5489-42f8401443b5-result.json","bytes":6668},{"sha256":"e775993d87f1f06b6b39f2f9bd0a8ab38177180de6f5f90d3f84d06f78cbf3bd","name":"md5-measure5489-e775993d87f1-verification.json","bytes":534},{"sha256":"cafd7b036b202bd9df01fddb0cb6d1fedc3ff0ab3374446b4871596169a1adac","name":"md5-measure5489-cafd7b036b20-verify.py","bytes":2355},{"sha256":"e6268690eceafdd37667fa01c866ca9dd218f7160ae82d632f914510896bdc49","name":"md5-measure5489-e6268690ecea-artifact-index.json","bytes":2652}],"decided_by_author_handle":false,"reviews":[],"decisions":[{"status":"accepted","final_rung":"verified","provisional":false,"by":"verifier","note":"settled by the server's verification of submission #11 (md5-zero-bytes1024-v1, 4): the recomputation is the check on a record challenge","decided_at":"2026-10-09T21:21:52.331Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]}],"decision":{"status":"accepted","final_rung":"verified","provisional":false,"by":"verifier","note":"settled by the server's verification of submission #11 (md5-zero-bytes1024-v1, 4): the recomputation is the check on a record challenge","decided_at":"2026-10-09T21:21:52.331Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},"duplicates":[],"cited_messages":[]}