{"id":4649,"job_id":9467,"problem_id":6,"lane_id":35,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Padding assignment comparison: covered\n\nThis reaffirms return #2987 for the unchanged conceptual obligation. It is a management decision about duplicate investment, not a new scientific verdict, route closure, document edit, construction or record claim. Management judgment rung: heuristic; the reused source conclusions retain their own accepted grades.\n\n## Material evidence delta\n\nThe issued delta comprises returns #2629/#2634 and their new gpt-6.1-sol reviews. Current served records show #2629 accepted/verified with review #1667 and #2634 accepted/proven with review #1673. Earlier #2987 described both as pending. The new reviews preserve the substantive answer and its limitations rather than overturning it. Complete older reviews #704/#767 and #706/#770 were read beside the newer reviews; their execution claims remain attributable historical evidence, not executions in this assignment.\n\n## Exact coverage and remaining gap\n\nReturn #2634 already establishes nonconstructively that some full-MD5 pair has both members at most 16 bytes and total at most 32: 2^128 sixteen-byte strings plus the empty string exceed the 128-bit output space. It also guarantees equal-length 17+17 existence. The finite-output countermodel shows only that cardinality alone forces neither total at most 31 nor an unequal-length pair among individual lengths 0..1024. Unbounded unequal-length existence is outside this bounded domain. No concrete short pair follows from these arguments.\n\nRFC byte padding is injective, but that does not make full MD5 injective. One-padded-block lengths 0..55 fix m14=8L and m15=0; unequal lengths force nonzero delta m14 in [-440,440]. Raw lengths 56..63 require two padded blocks. Preserve review #706's restriction, reiterated by #1673: identical terminal padding from equal length residues is a block-aligned construction argument; unaligned terminal blocks may also contain data. The historical report's total-1024 wording is not the current rule: each member may independently contain 0..1024 bytes. Its countermodel covers that full individual-length domain, as #1673 explicitly checks.\n\nReturn #2629 covers only its specified 13-member two-word family: 40,768 ordered one-block length/family cases, no unequal-length feasible case, 126 equal one-block and 86 equal first-block embeddings. Its 212 selected deterministic witnesses fail entry and full-digest equality. These are inherited finite results, not a general short-collision impossibility. Review #1667 also distinguishes #767's copied witness-count fields from actual independent replay evidence in the earlier reviews. Failed zero-filled embeddings do not exclude message modification or other differential paths.\n\nThe supplied current lane snapshot reports a server-verified 126-byte record; this supersedes historical frontier figures without changing the counting/padding answer. Its provenance and attack performance are not revalidated here, and it supplies no unequal-length conclusion in this comparison.\n\nDecision: covered for the unchanged conceptual question. Concrete bounded unequal-length construction, sharper MD5-specific bounds and new short-pair methods remain separate scientific obligations. No distinct next task is invented and no replication is requested or performed: this assignment has no new independence objective. Reopen this scheduling comparison for a specific defect in the scoped answer, a changed obligation or source requiring distinct analysis, or an explicitly assigned replication with its independence objective. A new witness may justify a distinct construction/provenance task without requiring these elementary arguments to be repeated.\n\n## Work and limitations\n\nRead-only source inspection and small evidence parsing only; no scientific compute invocation, solver, hash search, candidate, patch or new verification package. Scientific CPU: 0 seconds, cpu_hours=0; source-reading overhead is unmeasured. Three initial scoped API reads failed with DNS error [Errno 8]; the same authorized reads succeeded with network-enabled execution. No source blocker remains. No new mathematical test was executed. 117 returns await a verdict according to the issued brief; this comparison creates no additional scientific review request.\n\n## Sources\n\n- Project return #2987, report and effective covered disposition: /projects/md5/return/2987, report SHA-256 cf69170c970a84bd6c7de29a96aad84f4c100c8cbe26aac3a959cf89a9d08056.\n- Project return #2629, accepted/verified, report, complete reviews #704/#767/#1667 and file metadata: /projects/md5/return/2629. Served report SHA-256 f1267adac4733774715e30877289f6de1d56ac8ff05611c918ac8e1b3b1823be.\n- Project return #2634, accepted/proven, report, complete reviews #706/#770/#1673 and file metadata: /projects/md5/return/2634. Current served report SHA-256 5f61aad864744464723fdb157d94a32ed56a83f4ad43b4bed7e989c4345c510c. This is a served report hash, not a claim of byte identity with its historical uploaded manuscript.\n- Latest available local collision-padding topic summary, summaries/collision-padding.json, initial counting/padding synthesis and scope; local-only navigation evidence, with current public returns taking precedence over its historical pending statuses.\n- Issued job #9467, complete task-specific comparison brief and supplied smallest-collision state v42, including the current frontier line; cached department protocol scientific evidence/publication/files sections. RFC and cryptanalysis papers are cited by the source returns but were not freshly inspected here.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T20:20:55.881Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2987,2629,2634],"messages":[]},"tokens":{"log":"summary","input":87157,"models":{"gpt-6.1-sol":7485},"output":7485,"source":"reported","entries":0,"cache_read":849920,"cache_write":0,"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":"2026-10-18T20:21:00.875Z","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_b39d6ffa10f132d30a9250af","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":{"task":{"intent":"consolidation","schema":"research-task-v1","domain_md":"smallest-collision.methods: Inputs `a_hex` and `b_hex` are arbitrary byte strings of 0 to 1,024 bytes each, with the same strict hex transport as All zeros. They must differ, and **all 128 digest bits** must match: there is no partial score. The pair is unordered (swapping is a duplicate), unequal lengths and an empty member are allowed. Lower total bytes is better; an equal total is a tie and the earlier receipt keeps the record. The 128-byte reference is not a proven minimum: by counting, some pair with both members at most 16 bytes must collide, but that argument finds no pair.\n\nSubmit `a_hex` and `b_hex`. Fixture: Marc Stevens' 64-byte single-block pair, digest `008ee33a9d58b51cfeb425b0959121c9`, 64 + 64 = 128 bytes. Distinguish input records, throughput, restricted facts and attack methods; compare identical domains, baselines, compute and luck.\nsmallest-collision.study-2: Inputs `a_hex` and `b_hex` are arbitrary byte strings of 0 to 1,024 bytes each, with the same strict hex transport as All zeros. They must differ, and **all 128 digest bits** must match: there is no partial score. The pair is unordered (swapping is a duplicate), unequal lengths and an empty member are allowed. Lower total bytes is better; an equal total is a tie and the earlier receipt keeps the record. The 128-byte reference is not a proven minimum: by counting, some pair with both members at most 16 bytes must collide, but that argument finds no pair.\n\nSubmit `a_hex` and `b_hex`. Fixture: Marc Stevens' 64-byte single-block pair, digest `008ee33a9d58b51cfeb425b0959121c9`, 64 + 64 = 128 bytes. Full 64-step MD5, RFC IV, exact padding; reductions or different IVs are separate scopes. Negative evidence closes only its tested method and scope.","topic_ids":["smallest-collision.methods","smallest-collision.study-2"],"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":"Can two inputs of unequal length, or a member shorter than one block, collide under full MD5 padding? What does the padding force?"},"review_ids":[704,767,1667,706,770,1673],"message_ids":[],"comparison_md":"The only nominated material changes are accepted source status and new read reviews #1667/#1673. They preserve the counting/padding answer, correct terminal-block and per-member-domain scope explicitly, and retain the exact two-word-family restrictions. The conceptual obligation remains covered by #2634/#2629 and prior decision #2987; construction remains separate. No replication is requested or performed, and no new independence objective was issued.","reopen_when_md":"A specific material defect in the counting, padding or scoped family answer; a changed obligation or relevant source requiring distinct analysis; or an explicitly assigned replication with a named independence objective. A short-pair witness may warrant distinct construction/provenance work, not automatic repetition of the conceptual answer.","remaining_gap_md":"No concrete bounded unequal-length construction, sharper MD5-specific minimum, general unequal-length impossibility, or universal short-path exclusion follows. Source #2629 is family/length scoped; source #2634 is nonconstructive. New pair provenance or method validation would be distinct work.","predecessor_returns":[2987,2629,2634]},"work_disposition":{"task":{"intent":"consolidation","schema":"research-task-v1","domain_md":"smallest-collision.methods: Inputs `a_hex` and `b_hex` are arbitrary byte strings of 0 to 1,024 bytes each, with the same strict hex transport as All zeros. They must differ, and **all 128 digest bits** must match: there is no partial score. The pair is unordered (swapping is a duplicate), unequal lengths and an empty member are allowed. Lower total bytes is better; an equal total is a tie and the earlier receipt keeps the record. The 128-byte reference is not a proven minimum: by counting, some pair with both members at most 16 bytes must collide, but that argument finds no pair.\n\nSubmit `a_hex` and `b_hex`. Fixture: Marc Stevens' 64-byte single-block pair, digest `008ee33a9d58b51cfeb425b0959121c9`, 64 + 64 = 128 bytes. Distinguish input records, throughput, restricted facts and attack methods; compare identical domains, baselines, compute and luck.\nsmallest-collision.study-2: Inputs `a_hex` and `b_hex` are arbitrary byte strings of 0 to 1,024 bytes each, with the same strict hex transport as All zeros. They must differ, and **all 128 digest bits** must match: there is no partial score. The pair is unordered (swapping is a duplicate), unequal lengths and an empty member are allowed. Lower total bytes is better; an equal total is a tie and the earlier receipt keeps the record. The 128-byte reference is not a proven minimum: by counting, some pair with both members at most 16 bytes must collide, but that argument finds no pair.\n\nSubmit `a_hex` and `b_hex`. Fixture: Marc Stevens' 64-byte single-block pair, digest `008ee33a9d58b51cfeb425b0959121c9`, 64 + 64 = 128 bytes. Full 64-step MD5, RFC IV, exact padding; reductions or different IVs are separate scopes. Negative evidence closes only its tested method and scope.","topic_ids":["smallest-collision.methods","smallest-collision.study-2"],"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":"Can two inputs of unequal length, or a member shorter than one block, collide under full MD5 padding? What does the padding force?"},"schema":"work-disposition-v3","sources":{"topic_ids":["smallest-collision.methods","smallest-collision.study-2"],"review_ids":[706,770,704,767],"message_ids":[],"predecessor_returns":[2629,2634]},"trusted":true,"decision":"covered","effective":true,"input_sha256":"ba6a1b46c80f8b326c76583c9cb41351ae29079cfd55d07b532fdf3978aa4d55","rationale_md":"The only nominated material changes are accepted source status and new read reviews #1667/#1673. They preserve the counting/padding answer, correct terminal-block and per-member-domain scope explicitly, and retain the exact two-word-family restrictions. The conceptual obligation remains covered by #2634/#2629 and prior decision #2987; construction remains separate. No replication is requested or performed, and no new independence objective was issued.","scope_sha256":"ac662d7e9c4af2e42eff002299a238d7bb80d18757effb65da39fd3b3399890c","allow_covered":true,"input_version":"material-evidence-v1","reopen_when_md":"A specific material defect in the counting, padding or scoped family answer; a changed obligation or relevant source requiring distinct analysis; or an explicitly assigned replication with a named independence objective. A short-pair witness may warrant distinct construction/provenance work, not automatic repetition of the conceptual answer.","material_evidence":{"sha256":"ba6a1b46c80f8b326c76583c9cb41351ae29079cfd55d07b532fdf3978aa4d55","entries":{"return:2629":"a498686e073cec04cdc969b5f5042d200fcd4bc66fa5877586acd1fe70ee9915","return:2634":"b4ca2593ce8eca2f1e16bb28841179b93b21c258ee89e18c3626d20134219c3f","finding:66756":"43c165c6da19094675440011ea67169fd821cb689c2ef17488052133fc2a2e79","review:2629:1:gpt-6.1-sol":"2f63d79f5686fb6722587dcaa9d7338df0b6859f24f2cdc82c9abc3eedcf9b1f","review:2634:1:gpt-6.1-sol":"6290260770d6f6a6f675ac84f464d834277006d32e89078af3a9074800f58750","review:2629:1:claude-opus-5-5":"4eb5461fded0e8f34c28d8559538191f7d28c594915ce5b171563f55ae41802f","review:2634:1:claude-opus-5-5":"8a53467719ca1427768e39dd63ddbfc7e724e22f70fc39530e9852293170c779","review:2629:73:claude-opus-5-5":"8c6344109afe47a90ed73d9806ca295f2016191cbb59fc0b640a15a6c4d74597","review:2634:73:claude-opus-5-5":"7af88208eac0a3eb170448b50135a93309e908efa5ba89eef567c06a8525ad2d","artifact:2629:07df8d985af07e72001618f324b2331356980d3808f884de85201bb35b828a82":"07df8d985af07e72001618f324b2331356980d3808f884de85201bb35b828a82","artifact:2629:34a65c58a66f9add2194f23805e01fbe9df22fe80871b9c87313de25c338346e":"34a65c58a66f9add2194f23805e01fbe9df22fe80871b9c87313de25c338346e","artifact:2629:4c9147127ea26d0be06ac73077ab05eca383684e5a202e69e8e43ad9b3b65c81":"4c9147127ea26d0be06ac73077ab05eca383684e5a202e69e8e43ad9b3b65c81","artifact:2629:68913b49abada08755919dd96553788386c8bd828d9c0da50463b4c3b94e28bf":"68913b49abada08755919dd96553788386c8bd828d9c0da50463b4c3b94e28bf","artifact:2629:6cf2f5a767d1b14ec5b3388adc133608e897fc8971e31ac41c26d843eaf7c167":"6cf2f5a767d1b14ec5b3388adc133608e897fc8971e31ac41c26d843eaf7c167","artifact:2629:856766664c263280ec1088ade88d9822d40ed345ee8b60375d71ebb718d7b764":"856766664c263280ec1088ade88d9822d40ed345ee8b60375d71ebb718d7b764","artifact:2629:cffe2e68ac63188701c3f41ee84722ef7ca4392e53225058e0bc54d108d47b8d":"cffe2e68ac63188701c3f41ee84722ef7ca4392e53225058e0bc54d108d47b8d","artifact:2629:e963ec56e5851a638267394e53ab1bf9f2b3884d24003ace64895f02d1fa4e1b":"e963ec56e5851a638267394e53ab1bf9f2b3884d24003ace64895f02d1fa4e1b","artifact:2629:e9bde85b23a8109bdda2fc3229934e6dfae9d2688d4b577f4b51f22e530824f6":"e9bde85b23a8109bdda2fc3229934e6dfae9d2688d4b577f4b51f22e530824f6","artifact:2629:f1267adac4733774715e30877289f6de1d56ac8ff05611c918ac8e1b3b1823be":"f1267adac4733774715e30877289f6de1d56ac8ff05611c918ac8e1b3b1823be","artifact:2629:fdf266a96423331f5d74276e844d6e0f4862bfe11e9c7365df2ff0339b38af40":"fdf266a96423331f5d74276e844d6e0f4862bfe11e9c7365df2ff0339b38af40","artifact:2634:148e8e88e3004ce1e54af0af826dd0f654c05b120293055c42571f84afe928dd":"148e8e88e3004ce1e54af0af826dd0f654c05b120293055c42571f84afe928dd","artifact:2634:20d139c7d60ce8d65a5f8c639d33eef8f88ffb06345b0c3ec131525d8128bae3":"20d139c7d60ce8d65a5f8c639d33eef8f88ffb06345b0c3ec131525d8128bae3","artifact:2634:237e0bfbd0d85bad44463b6b35a2ddd31457e4af692f1a3c354e4de289938b59":"237e0bfbd0d85bad44463b6b35a2ddd31457e4af692f1a3c354e4de289938b59","artifact:2634:3452ca60abf8a195503ab629b1ba7825a2bf91cc3eb7a7bd61913c6cbb4c170d":"3452ca60abf8a195503ab629b1ba7825a2bf91cc3eb7a7bd61913c6cbb4c170d","artifact:2634:5ac2291660cdfbb94d3994abc5cd9014a10c1fb73bb5635e9663dc3fbaed4bdd":"5ac2291660cdfbb94d3994abc5cd9014a10c1fb73bb5635e9663dc3fbaed4bdd","artifact:2634:84234d0d4de9e61f33c3f57a16dbd6e0f22d986b553cd5afe1a3b7d1b156112b":"84234d0d4de9e61f33c3f57a16dbd6e0f22d986b553cd5afe1a3b7d1b156112b","artifact:2634:9a8a4e966f6e7e91c6d996829ead6bebbc19fba723527cffd4b2389e3a1622e2":"9a8a4e966f6e7e91c6d996829ead6bebbc19fba723527cffd4b2389e3a1622e2","artifact:2634:a470b836b9ebfb24d99385b955a36a209bf231635538a77cee4bafbb1f13b788":"a470b836b9ebfb24d99385b955a36a209bf231635538a77cee4bafbb1f13b788","artifact:2634:d8837f9e2b2716a2790d98fe2f2f3b1acdc310c5ff9ab4e66fba824f46c4bb13":"d8837f9e2b2716a2790d98fe2f2f3b1acdc310c5ff9ab4e66fba824f46c4bb13","artifact:2634:fab409d44f89f8fc39f700cbf2bb3ca41377c41330a65319b82e64bf4e8d582e":"fab409d44f89f8fc39f700cbf2bb3ca41377c41330a65319b82e64bf4e8d582e"},"version":"material-evidence-v1","complete":true},"work_check_job_id":9467,"base_decision_return_id":2987},"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Material evidence delta from the prior decision: return:2629, return:2634, review:2629:1:gpt-6.1-sol, review:2634:1:gpt-6.1-sol. Read only these changes and the prior rationale first. If unchanged, a short reaffirmation suffices; do not re-prove identities or regenerate coverage artifacts.\n\nCompare this exact assignment with its predecessors and corrections before further investment. This is an assignment decision, not scientific acceptance. Read the cited messages and the lane's current claims; chat is evidence only.  Nomination: return #2987, message #none, review #none. Use existing packages and the cheapest source check; do not repeat large experiments.\n\nQuestion: Can two inputs of unequal length, or a member shorter than one block, collide under full MD5 padding? What does the padding force?\nDomain: smallest-collision.methods: Inputs `a_hex` and `b_hex` are arbitrary byte strings of 0 to 1,024 bytes each, with the same strict hex transport as All zeros. They must differ, and **all 128 digest bits** must match: there is no partial score. The pair is unordered (swapping is a duplicate), unequal lengths and an empty member are allowed. Lower total bytes is better; an equal total is a tie and the earlier receipt keeps the record. The 128-byte reference is not a proven minimum: by counting, some pair with both members at most 16 bytes must collide, but that argument finds no pair.\n\nSubmit `a_hex` and `b_hex`. Fixture: Marc Stevens' 64-byte single-block pair, digest `008ee33a9d58b51cfeb425b0959121c9`, 64 + 64 = 128 bytes. Distinguish input records, throughput, restricted facts and attack methods; compare identical domains, baselines, compute and luck.\nsmallest-collision.study-2: Inputs `a_hex` and `b_hex` are arbitrary byte strings of 0 to 1,024 bytes each, with the same strict hex transport as All zeros. They must differ, and **all 128 digest bits** must match: there is no partial score. The pair is unordered (swapping is a duplicate), unequal lengths and an empty member are allowed. Lower total bytes is better; an equal total is a tie and the earlier receipt keeps the record. The 128-byte reference is not a proven minimum: by counting, some pair with both members at most 16 bytes must collide, but that argument finds no pair.\n\nSubmit `a_hex` and `b_hex`. Fixture: Marc Stevens' 64-byte single-block pair, digest `008ee33a9d58b51cfeb425b0959121c9`, 64 + 64 = 128 bytes. Full 64-step MD5, RFC IV, exact padding; reductions or different IVs are separate scopes. Negative evidence closes only its tested method and scope.\nPremise: Establish the exact uncovered difference from existing research before substantial work.\nReturns: 2629, 2634; reviews: 706, 770, 704, 767; messages: none nominated.\n\nCovered means only this unchanged obligation need not be dispatched again.\nReturn work_disposition:{decision:\"covered|open\",scope_sha256:\"ac662d7e9c4af2e42eff002299a238d7bb80d18757effb65da39fd3b3399890c\",input_sha256:\"ba6a1b46c80f8b326c76583c9cb41351ae29079cfd55d07b532fdf3978aa4d55\",rationale_md,reopen_when_md,next_task?:<research-task-v1>}. Name replication explicitly. Only a fresh trusted open decision explicitly reopens this exact scope. Changed evidence or chat requests reconsideration and never removes prior suppression. A changed source snapshot or superseded base decision makes this response ineffective; it grants no scientific authority.","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":4675,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/4649/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"813b6098d799a5f7feaffb3199ebecc86e22d98c3822e7bce92a53fd6c527409","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}