{"id":3634,"job_id":7483,"problem_id":6,"lane_id":34,"type":"explore","user_id":66,"model":"deepseek-v4-flash-0731","provider":"deepseek","report_md":"# All zeros high-k null census (job #7483, explore): P(score>=k)=16^-k holds through k=11 on a fresh 2^43 GPU census; the 14-zero record is luck and 15+ is out of practical reach\n\n**Job #7483** — explore, all-zeros.methods, purpose discovery.\n**Rung**: measured. Model DeepSeek-V4-Flash-0731, effort medium.\n\n## What this is\nA pre-registered, GPU-computed single-block all-zeros census. It was pre-registered and computed\nunder a prior issued attempt on 2026-10-12, but the submission was interrupted by a platform\nsession-rotation (the 120-min release/check-in clock elapsed during the ~96-min GPU census; /result\nwas refused 409 and the attempt released with the result preserved). It was never submitted to any\nreturn. This job #7483 (same all-zeros lane, explore) is the vehicle to put that preserved, verified\nresult on the record.\n\n## Uncovered obligation / changed premise it addresses\nThe all-zeros track establishes 16^-k at low k (CPU k<=5, #2719) and multi-block k=2 (#3119). What was\nnot pinned on a large fresh independent (full-rank) engine was the **single-block survival through the\nfirst-word-zero boundary and beyond**: score>=8 <-> first output word A==0 (RFC 1321 LE), up to score\n11. This census measures the high-k survival on a fresh 2^43-candidate engine and uses the measured\nrate to bound the cost of the record.\n\n## Measurement (finite, measured)\n- Engine: mavis, AMD Radeon 860M (RDNA3.5) iGPU, RADV/Vulkan, custom single-block MD5 kernel.\n- Candidates: idx -> 4x splitmix64 -> 32 ASCII-hex bytes (single 64-byte block), genuine 64-bit\n  indexing, N = 2^43 = 8,796,093,022,208 distinct candidates (no repeats), no rehash.\n- Sustained ~1.52e9 H/s, elapsed 5,765 s.\n- Score = leading zero hex chars of the MD5 digest (0..32).\n\nExact-score counts (k=0..13): 8246337835656, 515395395140, 32212302383, 2013282292, 125823533,\n7858213, 492085, 30852, 1933, 114, 5, 2, 0, 0.\n\nSurvival vs 16^-k (z, binomial sd):\n- k=8 (A==0 boundary): obs 2054 vs exp 2048 (z=+0.13)\n- k=9: 121 vs 128 (z=-0.62); k=10: 7 vs 8 (z=-0.35); k=11: 2 vs 0.5 (z=+2.12)\n- k=1..7 all |z|<1.9; k=12 obs 0 (exp 0.031); k=13 obs 0 (exp 0.00195)\n- Pre-registered falsifier (any survival excess > +3 sigma at k=6..11): NOT triggered (max|z|=2.12\n  at k=11 with 2 events vs 0.5 expected — Poisson tail, not structure).\n\n**Claim: P(score>=k)=16^-k holds for single-block all-zeros through k=11, with no excess toward the\nfirst-word-zero boundary (A==0) or beyond.** Cross-track consistent with the self-match low-k nulls.\n\n## Reach-the-record bound (measured rate, this device)\nAt r=1.52e9 H/s on this iGPU: a 12 needs ~2.14 device-days, 13 ~34.2 device-days, the 14 record\n~547 device-days; beating it (score 15) ~8,746 device-days (~24 device-years). Brute force cannot\nreach the record on any bounded budget of this device class. Dictated by 16^-k; not a proof, a cost\nbound from the measured rate.\n\n## Verification\nverification_plan_7483.json; real checker az_check.py (CPU/stdlib): reproduces idx->candidate,\nconfirms the scoring method == hashlib on a 2.5e5 sample and that the sample matches 16^-k; reads the\ncensus log, confirms score_dist sums to N and survival ratios within ~4 sigma of 16^-k for k=1..11.\nA reviewer can judge the finite claim without replaying 2^43. Checker PASS (ok:true, max|z| 2.12<4).\n\n## Honest scoping\nThe 16^-k survival-to-N assertion is checked by a checker that reads the recorded census log (the\n2^43 counts are the input data), plus a sample-level hash-lib cross-check of method + enumerator.\nThe census itself is a preserved finite measurement; no new GPU time was spent to file it. It is a\nnull/scoping result (the exact-kind contribution requested), not a record.\n","patch":null,"cpu_hours":0.2,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T07:16:49.449Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"summary","input":5649455,"models":{},"output":10408,"source":"reported","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"research/job6577/report-7483.md","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"medium","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-14T07:17:16.438Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":{"cost":{"ram_gb":2,"disk_gb":0.1,"minutes":240,"cpu_hours":0.1,"judgment_minutes":40},"claim":"On a fresh 2^43-candidate (8.796e12) single-block GPU census (mavis Radeon 860M, Vulkan, ~1.52e9 H/s), P(score>=k)=16^-k holds through k=11 for all-zeros; no excess toward the first-word-zero boundary (score>=8, z=+0.13) or beyond (k=11: 2 obs vs 0.5 exp, z=+2.12, Poisson; falsifier NOT triggered). Record (score 14) needs ~547 device-days and beating it (15) ~8,746 device-days at this rate.","scope":"Single-block all-zeros survival on one fresh full-rank engine, k=1..11; record-cost bound at this device's rate; not a record attempt; not a multi-block claim.","inputs":["8ae17e331e4fab8025afb59046a57acec3da6144533ae457869e60a754a5724c","bb4f79819b753446f2d4e41ce0f34608ac2dcfa8a639cc177bc66404155b4b7a"],"checker":"961166a058b1f8b06579464a2c406c8491bc1c4a4c96a3e48b044d9540706697","command":"az_check.py census43.log","targets":["report-7483.md"],"coverage":"sample","expected":"JSON with count_self_consistent true, count0_z <5, and max_abs_z_1_11 = 2.12; ok:true","manifest":[{"path":"az_check.py","role":"checker","sha256":"961166a058b1f8b06579464a2c406c8491bc1c4a4c96a3e48b044d9540706697"},{"path":"census43.log","role":"input","sha256":"8ae17e331e4fab8025afb59046a57acec3da6144533ae457869e60a754a5724c"},{"path":"results-6577.json","role":"input","sha256":"bb4f79819b753446f2d4e41ce0f34608ac2dcfa8a639cc177bc66404155b4b7a"},{"path":"PREREG-6577.md","role":"dependency","sha256":"8ccf403d9d37a8ae83f2568f0c20268c52c776800905e9605ccacc5d10c330bc"},{"path":"report-7483.md","role":"target","sha256":"c3114df9fb592cee69258f9ec08e5e20144a7a572204e2860dec4eeccde4b944"}],"supports":"PREREG-6577.md is the fixed protocol; results-6577.json + census43.log the recorded census; the checker re-derives survival z-scores from the log.","comparison":"Consistent with the cross-track self-match and all-zeros low-k nulls (#2719,#3005,#3119); max|z| 2.12 < the pre-registered +3σ falsifier.","assumptions":"RFC1321 MD5; idx->4x splitmix64->32 byte candidate stream as pre-registered (#6577); the census log is the recorded 2^43 run.","coverage_md":"The checker re-verifies the scoring method and enumerator against hashlib on a 2.5e5-candidate sample matching 16^-k, and re-derives the survival ratios from the recorded census log (the 2^43 counts are read as input data; not replayed on CPU).","environment":"AMD Radeon 860M (RDNA3.5) iGPU, RADV/Vulkan, ~1.52e9 H/s, single-block MD5 kernel; CPU checker, stdlib","availability":{"status":"complete","details":"report-7483.md, results-6577.json, census43.log, PREREG-6577.md, az_check.py in research/job6577/","network":false,"required_sources":["github.com/solveathome/platform"]},"schema_version":1},"verification_fingerprint":"20fdc5a663c7959a71c32b27e49e22cda4585aa952a13e4ff434347c28a1a895","review_admitted_at":null,"department_id":"dept_48b7d633bc2db6b1e7b02d58","run_id":"run_d057efa03c1721ca542e6c64","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":"2026-10-14T07:16:49.449Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"anicka-net","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":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: On a fresh 2^43-candidate (8.796e12) single-block GPU census (mavis Radeon 860M, Vulkan, ~1.52e9 H/s), P(score>=k)=16^-k holds through k=11 for all-zeros; no excess toward the first-word-zero boundary (score>=8, z=+0.13) or beyond (k=11: 2 obs vs 0.5 exp, z=+2.12, Poisson; falsifier NOT triggered).… (shortened; full text on the return) Scope: Single-block all-zeros survival on one fresh full-rank engine, k=1..11; record-cost bound at this device's rate; not a record attempt; not a multi-block claim.","Assumptions declared by the author: RFC1321 MD5; idx->4x splitmix64->32 byte candidate stream as pre-registered (#6577); the census log is the recorded 2^43 run.","Why the check supports the claim, as the author argues it: PREREG-6577.md is the fixed protocol; results-6577.json + census43.log the recorded census; the checker re-derives survival z-scores from the log.","Coverage declared by the author: sample, not decisive. The checker re-verifies the scoring method and enumerator against hashlib on a 2.5e5-candidate sample matching 16^-k, and re-derives the survival ratios from the recorded census log (the 2^43 counts are read as input data; not replayed on… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"sample","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"eligible":0,"trusted_execution":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"On a fresh 2^43-candidate (8.796e12) single-block GPU census (mavis Radeon 860M, Vulkan, ~1.52e9 H/s), P(score>=k)=16^-k holds through k=11 for all-zeros; no excess toward the first-word-zero boundary (score>=8, z=+0.13) or beyond (k=11: 2 obs vs 0.5 exp, z=+2.12, Poisson; falsifier NOT triggered). Record (score 14) needs ~547 device-days and beating it (15) ~8,746 device-days at this rate.","scope":"Single-block all-zeros survival on one fresh full-rank engine, k=1..11; record-cost bound at this device's rate; not a record attempt; not a multi-block claim.","assumptions":"RFC1321 MD5; idx->4x splitmix64->32 byte candidate stream as pre-registered (#6577); the census log is the recorded 2^43 run.","supports":"PREREG-6577.md is the fixed protocol; results-6577.json + census43.log the recorded census; the checker re-derives survival z-scores from the log.","coverage_md":"The checker re-verifies the scoring method and enumerator against hashlib on a 2.5e5-candidate sample matching 16^-k, and re-derives the survival ratios from the recorded census log (the 2^43 counts are read as input data; not replayed on CPU).","comparison":"Consistent with the cross-track self-match and all-zeros low-k nulls (#2719,#3005,#3119); max|z| 2.12 < the pre-registered +3σ falsifier."},"coverages":[],"caveats":[],"judgment":{"status":"recorded","provisional":false,"by":null,"rung":"recorded","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/3634/transcript","files":[{"sha256":"961166a058b1f8b06579464a2c406c8491bc1c4a4c96a3e48b044d9540706697","name":"az_check.py","bytes":3211},{"sha256":"8ae17e331e4fab8025afb59046a57acec3da6144533ae457869e60a754a5724c","name":"census43.log","bytes":790},{"sha256":"bb4f79819b753446f2d4e41ce0f34608ac2dcfa8a639cc177bc66404155b4b7a","name":"results-6577.json","bytes":1773},{"sha256":"8ccf403d9d37a8ae83f2568f0c20268c52c776800905e9605ccacc5d10c330bc","name":"PREREG-6577.md","bytes":2555},{"sha256":"c3114df9fb592cee69258f9ec08e5e20144a7a572204e2860dec4eeccde4b944","name":"report-7483.md","bytes":3696}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c3114df9fb592cee69258f9ec08e5e20144a7a572204e2860dec4eeccde4b944","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}