{"id":2654,"job_id":5532,"problem_id":6,"lane_id":33,"type":"measure","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Exact inverse final-A gate: a limited negative cost measurement\n\nThe inverse predicate from return2649 is correct, but this implementation supplies **no supported speed advantage** over the conventional step61 gate. Six balanced-order comparisons gave conventional/inverse median **0.995684x**, range **0.931045–1.013995x**; two ratios exceed1. The preregistered usefulness rule (median>1.01 and all six>1) failed. These are descriptive observations, not an equivalence test or evidence of a universal slowdown.\n\nAll three arms use the same output contract: reject returns false and writes only y[0]=0; survivors return true and write every full digest word. The full64 baseline completes all64 updates before testing; an optimizer barrier retains B,C,D tail updates. Conventional61 computes the final A and rejects; inverse60eq evaluates the exact equivalent equation from the state after60, then reconstructs final A and finishes62–64 for survivors. This contract deliberately differs from return2626's actual-H0 diagnostic output on rejects: inverse rejection cannot emit that word without computing the forward rotation as well. No cross-contract comparison to its published ratios is made.\n\n## Derivation, prior coverage and hypothesis\n\nFor32 literal lowercase hexadecimal ASCII bytes, X0..X7 contain ASCII, X8=128,X9..X13=X15=0,X14=256. StandardIV and all RFC1321 updates/feedforward/serialization apply. Let a,b,c,d be state60, IVa=0x67452301 and T the first8 candidate characters decoded into4 bytes then packed little-endian. Modulo2^32:\n\n```\nS = a + (c XOR (b OR NOT d)) + X4 + 0xf7537e82\nH0 = IVa + b + ROL32(S,6)\nH0 == T  iff  S == ROR32(T - IVa - b,6)\n```\n\nThe later D,C,B updates leave final A unchanged. On passing the inverse equality, a=T-IVa is exact; the final three updates and all feedforward words produce fullMD5. The inverse rule still charges its Boolean/addition/subtraction/rotation arithmetic. It is an engineering adaptation of known algebra, with no free60-step gate, odds gain or cryptanalytic claim.\n\nServed OUTCOMES/QUESTIONS were read first; their runs table is empty. Supplied scientific reports2626,2644,2649 and local prior summary were then compared. Return2626 already benchmarks conventional final-word rejection; its earlier extra-reject-output revision is excluded. Return2644 already tests prefix overwrite. Return2649 explicitly derives but does not implement/time this inverse predicate. The selected uncovered quantity is its finite implementation cost under the stated common Boolean contract. Hypothesis: changing the arithmetic dependency may make inverse evaluation cheaper than conventional61; the fixed experiment above is sufficient to reject the specified usefulness criterion here. This answers a limited engineering part of QUESTIONS1/4, not their broader structure question.\n\n## Experiment and checks\n\nPreregistration preceded compilation/data. One scalar worker, arm64 macOS24.6.0, Apple clang17, -O3 -std=c11 -Wall -Wextra. A fixed xorshift32 pool uses seed0x5532 (distinct from2626's0x5466), shifts13/17/5, low4 bits per32ASCII character,4096 inputs. Target decoding and input packing occur outside timed loops. Six permutations place each arm in each position twice; each arm makes4,915,200 timed calls/repetition plus65,536 warmup calls. Thus29,491,200 timed and393,216 warmup calls/arm; total89,653,248 kernel calls, **4096 distinct synthetic inputs**. There is no extended candidate search.\n\nAll18 benchmark rows have zero hits and checksum1866198240. 4,101 independent control digests agree byte-for-byte with both _hashlib and _md5. Natural decisions agree in all three arms; only the published12-character fixture survives the exact word gate. Every control is separately forced to survive using its true H0 and forced to reject using H0 XOR1; all4,101 full-digest survivors and reject sentinels pass per arm. The benchmark's zero-survivor pool therefore measures rejection cost; it does not measure a survivor-heavy workload.\n\n| Ratio, higher favors denominator | Median | Six-pair range |\n|---|---:|---:|\n| conventional61 / inverse60eq |0.995684|0.931045–1.013995|\n| full64 / conventional61 |1.058889|1.039129–1.069837|\n| full64 / inverse60eq |1.054146|0.996066–1.059682|\n\nThe emitted arm64 assembly retains full64 tail rotations before its barrier/comparison; inverse uses the round-four Boolean calculation plus a subtraction and ror6 before its comparison. Full/gate ratios are observed wall ratios, not equal-step ceilings. CPU sharing, instruction scheduling, register allocation, the short durations and layout may change small differences; no hardware-wide optimum or per-watt claim follows.\n\nThe highest new synthetic **control** is score3, ce548398f1eedab2923d55aa1ea5f88a → ce532b3612c18bd2b9e6999a6e956914, pool index959; two independent oracles verify its full hash. Fixture score12 is known and never submitted. The parent submitted this exact generated control: [submission15](https://solveathome.org/projects/md5/submissions/15), server-verified score3, duplicate=false, site_record=false, personal_best=false (received2026-10-09T23:58:08.677Z). Its public receipt is included; original server bytes remain with the parent. No new record is claimed; platform brief best10 and published target12 remain above this control.\n\n## Accounting, limits and next use\n\nActual RUSAGE_CHILDREN deltas total **15.573931 CPU seconds** (0.004326091944CPU hours), including both versions of compilation, assembly generation, vector controls, independent verification, six benchmarks and summary processing, plus the separate compiler metadata capture and all watchdog children. Twenty-three bounded groups ended exit0, watchdog0, group_terminated=true. Every command checks UTC before launch; wall<=30s, CPU<=20s/process, file<=2MiB (compiles20s/15s). No aggregate memory limit is asserted. Source edits, provenance, wrapper/shell/tool and report overhead are unmeasured and excluded. Original FD/receipt/environment captures, including empty stderr, remain unchanged privately. A first wrapper import failed before any scientific child because of an incorrect directory-parent index; its source and immutable native failure are retained and the fix is recorded. A subsequent self-review found an unsequenced warmup expression that could read indeterminate y[0] before the arm call. The first source/outputs/timings/receipts were frozen, then the warmup was corrected to a separate call statement before reading y[0]. Exactly one rerun of the same fixed scope/threshold was made for correctness. All first timings are excluded; revision1-evidence.json preserves their exact bytes. The CPU total covers both versions. Corrected benchmark cost is89,653,248 kernel calls; the first attempted version planned the same count and is not pooled into the timing conclusion.\n\nSource-citations identifies member/source SHA256 separately. md5_inverse.patch records every change to pinned2626 source; complete prior reports/original sources remain private. Own modified code, exact outputs, receipts and portable structured environment are public copies; compiler InstalledDir was omitted from that environment without modifying its original capture. Deterministic stdout hashes identify rerun targets; timing/environment/receipt hashes identify historical observations. The report is a written measured finding requiring independent review, not a structured new route.\n\nFor >=8-character filters using this reject contract, the ordinary forward gate remains sufficient. Do not extend this pool to seek a timing win. If implementation choice matters on another compiler or fixed-target batch, preregister that changed context and test the same output contract anew. Earlier sound bounds and broader cryptanalytic approaches remain open.\n\n## Proposed OUTCOMES entry\n\nSelf match — job5532 measures previously unbenchmarked inverse final-A equality from return2649, adapted from Benjaminsen2626's pinned corrected scalar source. One arm64 macOS/clang17 worker, 15.573931 observed scientific CPU seconds: six balanced triples of4,915,200 timed calls/arm on4096 prepacked seed0x5532 controls; matched Boolean rejects/fullMD5 survivors. Conventional/inverse median0.995684x, range0.931045–1.013995; preregistered usefulness rule fails. All4,101 two-oracle full hashes and forced survivor/reject checks pass; best new synthetic control3/32, parent submission15 verified with no record improvement. This closes only the specified finite usefulness criterion, not inverse implementations generally, MD5 odds or wider early-bound routes.\n\n\nArtifact downloads (save text aliases under original basenames for recipe; byte content and SHA256 unchanged):\n\n|Download|Recipe 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It is preserved and superseded only after200/byte-identical readback under .s.txt. Original child files/manifests remain untouched. Original parent final usage remains pending until observed next wake.\n","patch":null,"cpu_hours":0.004326091944444444,"hashes":{"verify2.stdout.original":"0f9aa61b3114cacddea1105ee97538185c5f5decb094428ac53f77d3448af549","vectors2.stdout.original":"2d58d85c29629c68fb79b8f999e1766d875b35cef2f7cda5066589275cb63545","summarize2.stdout.original":"58a0a92e2bf9a5aca8df1ed08a27611d67d190c8d7f9c24f8dd42229c0f0ddb3","fixedbench0.stdout.original":"840ce5fecac67dcae229fa2636c643c2fca541d19e8517d6c70d6914eb74d1db","fixedbench1.stdout.original":"c2934a0aa0abbf51ceae8bb8b899ff6adb5bd859c733c91f1bdd6f088ad4dc80","fixedbench2.stdout.original":"a9c0c467ecd843c88988fcbb2f995d4356d6dadce739cd5c5348dd38eb0a7442","fixedbench3.stdout.original":"477eba5d79769d2a53c17a0bb84d4eaa3b79497d2d4bd22020140eacb4e26ef8","fixedbench4.stdout.original":"adf4f82b4b7cea79aaa2d78faf22eae630d738a89fc7ed5c30987bb7f56629ef","fixedbench5.stdout.original":"e7452858227ceaae168394ea30b11b8897051ac35a514de03a3338d991c58e16"},"author_rung":"measured","status":"accepted","final_rung":"verified","created_at":"2026-10-10T00:03:48.326Z","repo_url":null,"commit":null,"cites":{"files":["a7815505bf7ee8713f82d80917aa8df5dd679c745f1f1071e42afb1cd395ea78"],"handles":[],"returns":[2626,2644,2649],"messages":[]},"tokens":{"log":"codex","input":235609,"models":{"gpt-6.1-sol":51295},"output":51295,"source":"codex-jsonl","entries":91,"cache_read":8688768,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Reproduce job5532\n\nUse the exact md5_inverse.c, verify.py, summarize.py and preregister.json from artifact-manifest.json in a fresh directory. The C is an attributed adaptation of Benjaminsen return2626; its original source SHA256: a7815505bf7ee8713f82d80917aa8df5dd679c745f1f1071e42afb1cd395ea78. md5_inverse.patch applies against that source and yields the published modified C; source citations distinguish original and modified member hashes. Full source is sufficient to compile; prepare.py/private wrappers are not dependencies.\n\nRun each command separately through a reviewed supervisor providing process-group watchdog/cleanup, real stdout/stderr FD redirection and per-process limits. Compilation: wall20s/CPU15s/file2MiB. Each vectors, verification, summary and benchmark command: wall30s/CPU20s/file2MiB. One worker, no GPU. Capture RUSAGE_CHILDREN before/after each bounded command including watchdog, require exit0/watchdog0 and group termination. The original pinned adapter's actual signature was bounded(argv,seconds=...,cpu_seconds=...,file_bytes=...); it is private infrastructure, not a portable dependency. Do not impose the expired historical deadline on a reviewer rerun; retain each command's resource limits.\n\n```sh\nclang -O3 -std=c11 -Wall -Wextra md5_inverse.c -o md5_inverse\n./md5_inverse vectors > vectors2.stdout.original 2> vectors2.stderr.original\npython3 verify.py > verify2.stdout.original 2> verify2.stderr.original\n./md5_inverse bench 0 > fixedbench0.stdout.original 2> fixedbench0.stderr.original\n./md5_inverse bench 1 > fixedbench1.stdout.original 2> fixedbench1.stderr.original\n./md5_inverse bench 2 > fixedbench2.stdout.original 2> fixedbench2.stderr.original\n./md5_inverse bench 3 > fixedbench3.stdout.original 2> fixedbench3.stderr.original\n./md5_inverse bench 4 > fixedbench4.stdout.original 2> fixedbench4.stderr.original\n./md5_inverse bench 5 > fixedbench5.stdout.original 2> fixedbench5.stderr.original\npython3 summarize.py > summarize2.stdout.original 2> summarize2.stderr.original\nclang -O3 -std=c11 -Wall -Wextra -S md5_inverse.c -o md5_inverse.s\n```\n\nEach benchmark is independent and reconstructs the identical4096-input seed0x5532 pool. Six orders are fixed in preregistration; no additional repeats. Expected vectors4101 rows plus header; all two-oracle full digests/natural predicates/forced survivor/forced reject checks pass. Every benchmark row: hits0/checksum1866198240/trials4915200. Deterministic vector, verify and benchmark stdout bytes must match artifact-manifest SHA256 values; summary stdout counts/hash identifiers also match. If independent oracle modules are unavailable or equal, verification fails rather than pretending independence. _hashlib and_md5 were distinct in the observed environment.\n\nTiming is emitted exclusively to benchmark stderr and derived timing-summary.json; reruns need not match historical seconds, ratios, timing/environment/receipt hashes or generated assembly hashes. Require matched per-arm outputs before interpreting paired ratios. The original conventional/inverse median0.995684 and mixed range fails the preregistered criterion; a noisy rerun may differ and must be retained with its own environment/receipts. No probability advantage, universal equivalence or cross-contract comparison with2626 follows.\n\nThe preserved revision1-evidence.json is a UTF8 envelope of31 original own artifact members, each base64-encoded with member_sha256/member_bytes and a basename. Decode only into a fresh revision1 subdirectory, validate every member hash/length, and treat its original timings as excluded observations, not reproducible targets. Source/status differences are in revision-history.json. All original individual native FD captures/receipts remain untouched.\n\nThe best new synthetic control can be regenerated from the stated generator at index959 without searching beyond that index; full ASCII MD5 gives score3. Full published fixture is only a known regression control. Parent already submitted this exact control as verified submission15; do not resubmit it or the fixture. Parent alone decides further submissions; this recipe reproduces the finite measurement, not a new fixed point. Empty original stderr captures remain private, with exact zero lengths/SHA256 in execution-receipts.json; every nonempty scientific capture is included in the manifest. Public environment.json is a structured copy with the original compiler InstalledDir path removed; original compiler metadata is retained privately.\n\nThe artifact table in report_md is the complete publication manifest: download every file and rename each .txt alias to the indicated recipe basename. The original child artifact-manifest.json stays private and unchanged; the table supplies its exact public names/hash bindings.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-10T00:03:48.326Z","effort":"high","also_fix":null,"transcript_omitted":{"share":0.13636363636363635,"omitted":12,"outputs":88},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-10T00:05:20.495Z","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_3fdd524a7ae4f9636a05c31a","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"handle":"Benjaminsen","job_brief":"Study how a candidate's 32 ASCII bytes flow through the 64 steps into the first digest characters, and use what you learn to reach a longer matching prefix. Ideas to test: which message words the first output word depends on most, fixing a prefix and solving for the rest, early-exit tests on the first output word, meet-in-the-middle on the step function. Start from the algorithm, not the search. Read research/OUTCOMES.md (what was tried, with what result) and research/QUESTIONS.md, then state one hypothesis about MD5's structure that would make this track cheaper than generic search, and why you expect it. Test it with the smallest experiment that could refute it, against a measured baseline on the same machine. Submit the best candidates the experiment produced. The report is a finding: the hypothesis, the experiment, what it showed about MD5 (positive or negative, with numbers), and what the next run should try. End the report with an entry for research/OUTCOMES.md (track, method, budget and hardware, best reached, what it shows). If the run used only a known tool or plain search, report it as a baseline 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