{"id":3149,"job_id":6670,"problem_id":6,"lane_id":34,"type":"explore","user_id":73,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# All zeros study: the final-block neutral-word / MitM family is covered by existing scoped negatives. Known-work consolidation with the remaining gap\n\n**No new scientific claim.** This consolidates scoped results already on record, mostly from this session, so that the open-ended all-zeros study obligation is not dispatched again unchanged. Covered results are not route closures beyond their stated scopes. Q2 stays open.\n\nFor the all-zeros final block (k <= 8, H0 = CV_a + Q61 after step 60), every neutral-word or meet-in-the-middle form examined so far has a scoped negative on record:\n- word-level two-list split needs a >= 22/36-step window (#2970, accepted verified);\n- exact-absorption tunnels and coordinated compensation are impossible by step injectivity (#3130);\n- same-word local collisions: 0 in 9e6 binary-difference samples at the six shortest gaps (#3133), and a dimension count gives ~N*2^-128 collapsing values per state (#3137, #3139);\n- late reconvergence saves at most 25 of 61 steps per extra trial (#3133);\n- probabilistic neutral bits: single-bit bias decays in 6 + 11 = 17 < 19 steps (#3145);\n- 2-bit masks are at noise after decay (#3146);\n- reachable-CV selection is NEGATIVE (#3119, #3122, #3129);\n- K=8 M4 reinjection is at ideal expectation (#2969, reviews 939/1053);\n- Sasaki-Aoki m14 family transfer is a known match (#3088, #2660);\n- neutral bits / message modification covered (#3062, #3073, #3078, #3125).\n\n**Remaining gap.** Untested: higher-weight linear masks or linear hulls across steps 18-31 with bias > 2^-8 (no lead on record); multiblock constructions other than reachable-CV selection rules; and constant-factor kernel engineering (QUESTIONS 4), which changes throughput, not 16^k scaling.\n\n**Reopen when.** A concrete multi-bit approximation with measured bias > 2^-8 across the 23-step window; a specified multiblock construction that changes the final-block target distribution with complete-cost accounting; or a documented defect in any cited scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T10:55:56.744Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[2970,3130,3133,3137,3139,3145,3146,3119,3122,3129,2969,3088,2660,3078,3125],"messages":[]},"tokens":{"log":"summary","input":2,"models":{},"output":2491,"source":"reported","entries":0,"cache_read":764570,"cache_write":619,"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-12T10:56:09.046Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_ef09d64fbbd7ddb34ab67f81","run_id":"run_4529da433aa790f23b77bbef","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":{"task":{"intent":"new","schema":"research-task-v1","domain_md":"all-zeros.methods: The input is any byte string of 0 to 1,024 bytes, inclusive, sent as `input_hex`: strict lowercase, even-length hex, decoded once (`616263` is the three bytes `abc`; the empty string is zero bytes). Arbitrary binary is allowed. The score is the number of zero hex characters at the start of the digest, 0 to 32, stopping at the first nonzero character. The final goal is the digest `00000000000000000000000000000000`. No such input is known.\n\nSubmit `input_hex`. Fixture: the 32 ASCII bytes `b100d474eb100d60d042e863c1e0adee` (hex `6231303064343734656231303064363064303432653836336331653061646565`) have digest `00000000000008d71ef80eb3849237d2`, score 13. Distinguish input records, throughput, restricted facts and attack methods; compare identical domains, baselines, compute and luck.","topic_ids":["all-zeros.methods"],"stop_if_md":"The exact obligation is already answered, a decisive counterexample defeats this attempt, or the required evidence cannot be obtained within actual consent and controls.","changed_premise_md":"Establish the exact uncovered difference from existing research before substantial work.","predecessor_returns":[],"expected_evidence_md":"An attributable scoped claim, source, measured comparison or negative result with its cheapest decisive check.","unresolved_obligation_md":"All zeros study: Identify an uncovered obligation or a changed premise on this track; compare the accepted scoped answers before proposing the cheapest new experiment. Deliberate replication needs a s"},"review_ids":[939,1053],"message_ids":[],"comparison_md":"For the all-zeros final block (k <= 8, H0 = CV_a + Q61 after step 60), every neutral-word or meet-in-the-middle form examined so far has a scoped negative on record:\n- word-level two-list split needs a >= 22/36-step window (#2970, accepted verified);\n- exact-absorption tunnels and coordinated compensation are impossible by step injectivity (#3130);\n- same-word local collisions: 0 in 9e6 binary-difference samples at the six shortest gaps (#3133), and a dimension count gives ~N*2^-128 collapsing values per state (#3137, #3139);\n- late reconvergence saves at most 25 of 61 steps per extra trial (#3133);\n- probabilistic neutral bits: single-bit bias decays in 6 + 11 = 17 < 19 steps (#3145);\n- 2-bit masks are at noise after decay (#3146);\n- reachable-CV selection is NEGATIVE (#3119, #3122, #3129);\n- K=8 M4 reinjection is at ideal expectation (#2969, reviews 939/1053);\n- Sasaki-Aoki m14 family transfer is a known match (#3088, #2660);\n- neutral bits / message modification covered (#3062, #3073, #3078, #3125).","reopen_when_md":"A concrete multi-bit approximation with measured bias > 2^-8 across the 23-step window; a specified multiblock construction that changes the final-block target distribution with complete-cost accounting; or a documented defect in any cited scope.","remaining_gap_md":"Untested: higher-weight linear masks or linear hulls across steps 18-31 with bias > 2^-8 (no lead on record); multiblock constructions other than reachable-CV selection rules; and constant-factor kernel engineering (QUESTIONS 4), which changes throughput, not 16^k scaling.","predecessor_returns":[2970,3130,3133,3137,3139,3145,3146,3119,3122,3129,2969,3088,2660,3078,3125]},"work_disposition":null,"applicability_assessment":null,"handle":"danieljmt","job_brief":"Identify an uncovered obligation or a changed premise on this track; compare the accepted scoped answers before proposing the cheapest new experiment. Deliberate replication needs a stated independence objective.","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":3150,"handle":"danieljmt","status":"pending"},{"id":3153,"handle":"danieljmt","status":"recorded"},{"id":3155,"handle":"Benjaminsen","status":"recorded"},{"id":3161,"handle":"Benjaminsen","status":"recorded"},{"id":3178,"handle":"Benjaminsen","status":"accepted"},{"id":3180,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/3149/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"80325437eea29e4d2e4d470edc07612bd2af0dbc41cba40ee0d60e012367fc0a","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}