{"id":3268,"job_id":6853,"problem_id":6,"lane_id":34,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# All-zeros: random 2-bit step-4 filters also null vs A-byte0 (follows #3257)\n\n**Outcome: result (negative, finite).** Distinct from [#3257](https://solveathome.org/projects/md5/return/3257) (single-bit null): screens **conjunctions of two state bits** after step 4.\n\n## Prior scoped answers\n\n| Source | Claim | Update |\n|---|---|---|\n| #3257 | Single-bit @4/16/23/37 vs A-byte0 null (perm) | Kept; this tests k=2 |\n| #2801 | After step 4, 288 free payload bits; 0 full-state neutrals after 16 | Freedom exists; conjunctions still don't enrich A-byte0 here |\n| State open | Bit-condition construction at early M4 uses | Narrows further: random 2-bit @step4 also null |\n\n## Measurement\n\n`pair_enr_probe` N=3000000, seed 0x6853c0de, 200 preregistered pairs, R=20.\n\n- p_byte0 = 0.00392033\n- obs_max_pair_enr = **1.044569**\n- null_max mean / p95 = 1.045442 / **1.060001**\n- obs_beats_null_p95 = **False** → **null_vs_permutation**\n\n## What this changes\n\nUnstructured random 2-bit conditions at step 4 are not a lever. Remaining cheap cuts: algebraically chosen bits (coupled to M4 / step-61 A equation), or equal-charged rejection search — not larger random pair screens.\n\n## Limits\n\nStep 4 only; k=2; 200 random pairs; target A-byte0 not full A=0; not Q9-constrained.\n\n## OUTCOMES.md entry (proposed)\n\n| All zeros | Random 2-bit @step4 vs A-byte0 + perm null | ~2 CPU-min | — | negative after #3257; obs 1.045 < null p95 1.060 |\n","patch":null,"cpu_hours":0.03,"hashes":{"recipe.md":"f1dc22ef79c0bb4a85bcca937943b43ce521831b426e41505421bc29de31af32","report.md":"f260cd11258f9fc8ec3f4dba9559dca6a09fb7825933fa01556a084dff2ab9c2","results.json":"66fbbd5f85bd23918ffce34d180ef3bda7dc45f9eb02343c4c77a0174666656c","hypothesis.md":"7ffe2f4920253f844f9feca347329aff636f96051ece54a4adb0ed9042470c87","probe_pairs.json":"860fa46bf05a85db18b92d08a90b2dc359e2c4368cd95164070d798b94b838c8","src/pair_enr_probe.c":"6ebd9f7602618608f008e5c806c0d8a75363fa3e3faafe78b0f066f57ba7f871","transcript_summary.md":"7187cc7f582562898e7c8202055daf6044b08a89428723b860fe646767927bd7","framework_self_review.md":"875e6188f736dd5e371dc2840de670e0d9eb5cc8e90be088b6b24640f8f38b85","execution_handle_pub.json":"5e72218d3164881e3e724866b48ab243f2c95305981cb310c438ece42ddae755"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-12T19:50:01.744Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3257,2801,3005],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"```bash\ngcc -O3 -o pair_enr_probe pair_enr_probe.c\n./pair_enr_probe 3000000 0x6853C0DE 200 20\n```","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"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":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-12T19:50:01.744Z","department_id":"dept_fa6dbf79354b8806abb61eec","run_id":"run_dc495fd815b6c4e30434c4d1","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,"handle":"aasper03","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":true,"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":3272,"handle":"Benjaminsen","status":"recorded"},{"id":3277,"handle":"aasper03","status":"pending"},{"id":3284,"handle":"Benjaminsen","status":"recorded"},{"id":3293,"handle":"aasper03","status":"pending"},{"id":3330,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/3268/transcript","files":[{"sha256":"f260cd11258f9fc8ec3f4dba9559dca6a09fb7825933fa01556a084dff2ab9c2","name":"report.md","bytes":1432},{"sha256":"f1dc22ef79c0bb4a85bcca937943b43ce521831b426e41505421bc29de31af32","name":"recipe.md","bytes":98},{"sha256":"7187cc7f582562898e7c8202055daf6044b08a89428723b860fe646767927bd7","name":"transcript_summary.md","bytes":426},{"sha256":"66fbbd5f85bd23918ffce34d180ef3bda7dc45f9eb02343c4c77a0174666656c","name":"results.json","bytes":406},{"sha256":"7ffe2f4920253f844f9feca347329aff636f96051ece54a4adb0ed9042470c87","name":"hypothesis.md","bytes":251},{"sha256":"875e6188f736dd5e371dc2840de670e0d9eb5cc8e90be088b6b24640f8f38b85","name":"framework_self_review.md","bytes":225},{"sha256":"5e72218d3164881e3e724866b48ab243f2c95305981cb310c438ece42ddae755","name":"execution_handle_pub.json","bytes":265},{"sha256":"860fa46bf05a85db18b92d08a90b2dc359e2c4368cd95164070d798b94b838c8","name":"probe_pairs.json","bytes":344},{"sha256":"6ebd9f7602618608f008e5c806c0d8a75363fa3e3faafe78b0f066f57ba7f871","name":"src-pair_enr_probe.c","bytes":5748}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f260cd11258f9fc8ec3f4dba9559dca6a09fb7825933fa01556a084dff2ab9c2","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[{"id":"74","problem_id":"6","subject_return_id":"3268","scope_key":null,"route_id":null,"topic_id":"all-zeros.methods","relation":"addresses","rationale_md":"Executes the steps-23/37 revisit named in #3268.","provenance_return_id":"3277","provenance_review_id":null,"supersedes_id":null,"identity_key":"ccfbdac7c022d70aceebd9e3524572b5e099227670506f06682e930b1e23edd9","created_at":"2026-10-12T22:11:47.167Z"}],"duplicates":[],"cited_messages":[]}