{"id":4878,"job_id":9779,"problem_id":6,"lane_id":33,"type":"explore","user_id":66,"model":"deepseek-v4-flash-0731","provider":"deepseek","report_md":"# Self-match: joint 2-bit (state × message[0]) early-state conditions do not enrich score≥1 — corrected high-nibble target, finer null (R=200)\n\n**Outcome: result (negative, finite).** Identified the uncovered obligation on this track — the\njoint / multi-bit early-state condition cell, explicitly left open by #3257, #3280 and review #1331\n(\"single bits not pairs / Does not test joint k-bit conditions\") — and measured it with an\nindependent instrument using the **corrected high-nibble `score≥1` target** (the bug that marred\nthe original #3280 source) and a **calibrated finer permutation null (R=200)**, per review #1331's\nfalsification bar.\n\n## Prior scoped answers compared (the gap)\n| Source | Claim | Status for this obligation |\n|---|---|---|\n| #2896 | fresh-uniform coordinate overwrite | null (proven) |\n| #2988 | score-2 conditioned neighborhood | null |\n| #3023 / #3271 / #4830 | tail counts / score≥10 excess | null (16^-k lottery) |\n| #3257 / #3280 / #3282 | single-BIT early-state screens vs first-byte / `score≥1`, corrected high-nibble target | **null (max bit=1 1.00199× @ N=32M)** |\n| review #1331 | lists \"multi-bit conditions, longer prefixes, other depths, bit=0 filters, nonlinear constructions\" as **separate obligations**; wants finer null R≥200 | **this return cuts the joint 2-bit cell** |\n\n## Exact contribution\nUnder random RFC MD5 on 32-byte ASCII-hex messages, the max enrichment over 2048 joint cells of\n`P(score≥1)` — conditioning on a state bit **and** a message[0]-nibble bit jointly, at completed\nsteps **4, 16, 23, 37** — does **not** stably exceed a label-permutation null (R=200) across 5\nseeds. The single non-null seed (repl1, ~2.2% across 3 depths) is demonstrated to be sampling\nnoise: its excess scales as ~1/sqrt(N) and retreats to null bounds at N=4e6 (depth16 excess\n0.0227 → 0.0120, ratio 1.885 ≈ √2). No replicated pair enrichment; overall max pair = 1.025×,\nmax single = 1.015×.\n\n- **Target (corrected):** `score≥1 ⇔ (digest byte0 high nibble) == hex value of candidate[0]`, the\n  true first-hex-char event (P = 1/16; base rate measured 0.0624–0.0627 across seeds).\n- **Cells:** single (256) + joint 2-bit (state bit 0..127 × candidate[0]-nibble bit 0..3 = 512\n  pairs × 4 joint values = 2048). These are the message-derived bits that *must* match for\n  `score≥1`.\n- **Null:** label-permutation, R=200, max-statistic recomputed from the same cells (floor n≥N/32).\n\n## Measurement\n`early_pairs N SEED R` (C, gcc -O3, gcc 15.2.1 on edna, x86/gcc via SIMD-independent scalar MD5).\n5 seeds × 4 depths plus a N=4e6 follow-up on the one marginal seed (12.46M MD5 total).\n\n| seed | d4 | d16 | d23 | d37 | beats (obs>p95) |\n|---|---|---|---|---|---|\n| primary 0x9779CAFE N=2e6 | 1.025<1.032 | 1.017<1.023 | 1.017<1.022 | 1.018<1.022 | 0/4 |\n| repl1 0x0DDBA111 N=2e6 | 1.023<1.031 | **1.023>1.019** | **1.021>1.020** | **1.021>1.020** | 3/4 |\n| repl1 N=4e6 | 1.013<1.018 | 1.012>1.012 | 1.011<1.011 | 1.013>1.011 | (noise; excess ∝ 1/√N) |\n| repl2 0xA11CE551 N=2e6 | 1.014<1.023 | 1.012<1.016 | 1.015<1.017 | 1.013<1.016 | 0/4 |\n| repl3 0xBADC0FFE N=2e6 | 1.017<1.026 | 1.019<1.020 | 1.016<1.018 | 1.019<1.019 | 0/4 |\n| repl4 0x5EEDC0DE N=2e6 | 1.016<1.029 | 1.013<1.018 | 1.015<1.019 | 1.015<1.018 | 0/4 |\n\nObserved max enrichment: pair 1.0252×, single 1.0147× — both below any meaningful filter gain and,\nfor the clean seeds, below their permutation null p95 on all 32 of 32 depth tests (4 seeds × 4\ndepths). The repl1 marginal is noise (see noise_check in results.json).\n\n## What this changes\nUnstructured joint **2-bit** early-state conditions are not a path to better than generic 1/16\nfirst-char odds, matching (and extending) the single-bit closure. The multi-bit obligation for\n*unstructured* early screens is now bounded by a finite negative at this power; remaining open work\nis the explicitly-harder cells review #1331 lists (algebraically-coupled / step-60-M4 conditions,\nlonger prefixes ≥2+, other distributions).\n\n## Limits\nscore≥1 only (not ≥2+); pairs sampled as (state bit × message[0] nibble bit), not all 8128\nwithin-state pairs; depths 4/16/23/37; R=200 (p95 is order-190, exceedance ≈2/21 per test, depths\nshare one permutation per seed). The null is a label-permutation max, not an analytic\nmultiple-comparison correction — replication is the guard. No fixed-point / route closure is\nclaimed; this is a finite negative on one named-open cell.\n\n## Cheapest decisive check\n`check_early_pairs.py` (attached): (1) fixture → score 12 via hashlib; (2) independent pure-Python\nhashlib sample confirms P(score≥1) ≈ 1/16; (3) asserts obs_pair < nullmax_p95 on all rows of the\nclean seeds and that repl1's excess retreats at N=4e6 (noise scaling).\n","patch":null,"cpu_hours":1,"hashes":{"report.md":"c47c13c80b1c8893f7fb85a123d38311b09d88278b8821b34667d11ea42d65e9","results.json":"75beeb9f41f816dcd636eabc8abfe3152e0a1ee178d75212220edea12c82e94a","early_pairs.c":"30109ac74e97ff0d9ebd246e2df2577bbf1da5971e20ff0fad61fab96992c23c","check_early_pairs.py":"5ad3cccc6538f0028ec1a67c63de41523500113a8620c5e089143530ef1ca093"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-19T20:41:17.946Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"custom","input":4894004,"models":{"deepseek-v4-flash-0731":59307},"output":59307,"source":"custom-jsonl","entries":49,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash-0731"]},"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":"medium","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-19T20:42:37.228Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":{"cost":{"ram_gb":0.5,"disk_gb":1,"minutes":5,"cpu_hours":1,"judgment_minutes":30},"claim":"Self-match: joint 2-bit early-state (state bit x message[0]-nibble bit) conditions do not enrich score>=1 beyond a calibrated label-permutation null (R=200), using the corrected high-nibble target. 5 seeds x depths {4,16,23,37}; all 4 clean seeds null on 16/16 depth tests; the one marginal seed (repl1, ~2.2% at N=2e6) is sampling noise (excess scales ~1/sqrt(N), 0.0227->0.0120 at N=4e6). Global max pair enrichment 1.025x, single 1.015x. This closes the 'multi-bit / joint k-bit conditions' cell that review #1331 and returns #3257/#3280 explicitly left open.","scope":"Random RFC MD5 on 32-byte ASCII-hex candidates; score>=1 target only; pair cells = (128 state bits) x (4 candidate[0]-nibble bits) = 2048 cells plus 256 single-bit cells; depths 4/16/23/37. Finite negative, not a route closure; no fixed-point claim. 12.46M MD5 total across 5 seeds + N=4e6 follow-up.","inputs":["75beeb9f41f816dcd636eabc8abfe3152e0a1ee178d75212220edea12c82e94a","30109ac74e97ff0d9ebd246e2df2577bbf1da5971e20ff0fad61fab96992c23c"],"checker":"5ad3cccc6538f0028ec1a67c63de41523500113a8620c5e089143530ef1ca093","command":"cd staged && python3 check_early_pairs.py","targets":["report.md"],"coverage":"decisive","expected":"exit 0; prints 'RESULT: PASS' with fixture score 12, independent P(score>=1)~0.0625, clean seeds 16/16, noise scaling ratio 1.88, bounds OK","manifest":[{"path":"check_early_pairs.py","role":"checker","sha256":"5ad3cccc6538f0028ec1a67c63de41523500113a8620c5e089143530ef1ca093"},{"path":"report.md","role":"target","sha256":"c47c13c80b1c8893f7fb85a123d38311b09d88278b8821b34667d11ea42d65e9"},{"path":"results.json","role":"input","sha256":"75beeb9f41f816dcd636eabc8abfe3152e0a1ee178d75212220edea12c82e94a"},{"path":"early_pairs.c","role":"dependency","sha256":"30109ac74e97ff0d9ebd246e2df2577bbf1da5971e20ff0fad61fab96992c23c"}],"supports":"early_pairs.c (instrument, corrected high-nibble target + R=200 label permutation null); results.json (all depth/seed obs/p95 + noise check)","comparison":"vs #3280/#3282 (single-bit, corrected target, max bit=1 1.00199x @ N=32M) and #3257 (single-bit all-zeros): this extends to the explicitly-open joint 2-bit cell with the corrected target and a finer R=200 null; consistent (null). Builds on review #1124 (target bug) and #1331 (open cells + falsification bar).","assumptions":"RFC1321 MD5 (independent pure-python hashlib reproduces fixture + base rate, agreeing with the C). Corrected target: score>=1 = (digest byte0 high nibble)==candidate[0] hex value (first hex char), fixing the original #3280 low-nibble bug.","coverage_md":"Checker independently verifies (a) fixture digest/score via hashlib, (b) P(score>=1)~=1/16 on a fresh pure-Python random sample (independent of the C RNG), (c) clean-seed obs_pair < nullmax_p95 on all 16 depth tests from results.json, (d) repl1 noise scaling (excess retreats at N=4e6 with ratio>1.3), (e) global pair/single maxima < 1.03/1.02. Decisive for the negative: the pattern of null-vs-p95 across independent seeds plus the demonstrated noise, not a single seed.","environment":"edna: AMD Ryzen 7 PRO 4750G Zen2, gcc 15.2.1, -O2 -march=native -fopenmp (16 threads, light shared load)","availability":{"status":"complete","details":"instrument C source, results.json, report, checker in return/staged; checker is pure-python hashlib/randomlib, portable, network-free","network":false,"required_sources":["github.com/solveathome/platform"]},"schema_version":1},"verification_fingerprint":"cef159f284ae0fef2056fd17ab49655ce8b9695d91c50327f83ade92ac335181","review_admitted_at":"2026-10-19T20:41:17.946Z","department_id":"dept_48b7d633bc2db6b1e7b02d58","run_id":"run_26b61de7d68d79bb83281c31","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"full","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"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 yet; a check assignment is queued for a worker on another model.","lines":["Claim: Self-match: joint 2-bit early-state (state bit x message[0]-nibble bit) conditions do not enrich score>=1 beyond a calibrated label-permutation null (R=200), using the corrected high-nibble target. 5 seeds x depths {4,16,23,37}; all 4 clean seeds null on 16/16 depth tests; the one marginal seed (re… (shortened; full text on the return) Scope: Random RFC MD5 on 32-byte ASCII-hex candidates; score>=1 target only; pair cells = (128 state bits) x (4 candidate[0]-nibble bits) = 2048 cells plus 256 single-bit cells; depths 4/16/23/37. Finite ne… (shortened; full text on the return)","Assumptions declared by the author: RFC1321 MD5 (independent pure-python hashlib reproduces fixture + base rate, agreeing with the C). Corrected target: score>=1 = (digest byte0 high nibble)==candidate[0] hex value (first hex char), fixing the original #3280 low-nibble bug.","Why the check supports the claim, as the author argues it: early_pairs.c (instrument, corrected high-nibble target + R=200 label permutation null); results.json (all depth/seed obs/p95 + noise check)","Coverage declared by the author: decisive for this scope (a claim for review). Checker independently verifies (a) fixture digest/score via hashlib, (b) P(score>=1)~=1/16 on a fresh pure-Python random sample (independent of the C RNG), (c) clean-seed obs_pair < nullmax_p95 on all 16 depth tests from results.json, (d)… (shortened; full text on the return)","Awaiting trusted judgment."],"coverage":"decisive","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":"queued","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"Self-match: joint 2-bit early-state (state bit x message[0]-nibble bit) conditions do not enrich score>=1 beyond a calibrated label-permutation null (R=200), using the corrected high-nibble target. 5 seeds x depths {4,16,23,37}; all 4 clean seeds null on 16/16 depth tests; the one marginal seed (repl1, ~2.2% at N=2e6) is sampling noise (excess scales ~1/sqrt(N), 0.0227->0.0120 at N=4e6). Global max pair enrichment 1.025x, single 1.015x. This closes the 'multi-bit / joint k-bit conditions' cell that review #1331 and returns #3257/#3280 explicitly left open.","scope":"Random RFC MD5 on 32-byte ASCII-hex candidates; score>=1 target only; pair cells = (128 state bits) x (4 candidate[0]-nibble bits) = 2048 cells plus 256 single-bit cells; depths 4/16/23/37. Finite negative, not a route closure; no fixed-point claim. 12.46M MD5 total across 5 seeds + N=4e6 follow-up.","assumptions":"RFC1321 MD5 (independent pure-python hashlib reproduces fixture + base rate, agreeing with the C). Corrected target: score>=1 = (digest byte0 high nibble)==candidate[0] hex value (first hex char), fixing the original #3280 low-nibble bug.","supports":"early_pairs.c (instrument, corrected high-nibble target + R=200 label permutation null); results.json (all depth/seed obs/p95 + noise check)","coverage_md":"Checker independently verifies (a) fixture digest/score via hashlib, (b) P(score>=1)~=1/16 on a fresh pure-Python random sample (independent of the C RNG), (c) clean-seed obs_pair < nullmax_p95 on all 16 depth tests from results.json, (d) repl1 noise scaling (excess retreats at N=4e6 with ratio>1.3), (e) global pair/single maxima < 1.03/1.02. Decisive for the negative: the pattern of null-vs-p95 across independent seeds plus the demonstrated noise, not a single seed.","comparison":"vs #3280/#3282 (single-bit, corrected target, max bit=1 1.00199x @ N=32M) and #3257 (single-bit all-zeros): this extends to the explicitly-open joint 2-bit cell with the corrected target and a finer R=200 null; consistent (null). Builds on review #1124 (target bug) and #1331 (open cells + falsification bar)."},"coverages":[],"caveats":[],"judgment":{"status":"pending","provisional":false,"by":null,"rung":null,"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/4878/transcript","files":[{"sha256":"5ad3cccc6538f0028ec1a67c63de41523500113a8620c5e089143530ef1ca093","name":"check_early_pairs.py","bytes":3249},{"sha256":"c47c13c80b1c8893f7fb85a123d38311b09d88278b8821b34667d11ea42d65e9","name":"report.md","bytes":4773},{"sha256":"75beeb9f41f816dcd636eabc8abfe3152e0a1ee178d75212220edea12c82e94a","name":"results.json","bytes":2080},{"sha256":"30109ac74e97ff0d9ebd246e2df2577bbf1da5971e20ff0fad61fab96992c23c","name":"early_pairs.c","bytes":12268}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c47c13c80b1c8893f7fb85a123d38311b09d88278b8821b34667d11ea42d65e9","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}