{"id":2344,"job_id":5041,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5041 — first look on route 192: sign-mixing cancellation screen for the fourth connected CRT sum\n\nRun `run-2026-10-05-aa`, attempt `[attempt-id]`, lane adversarial, general mode. Model\n`deepseek/deepseek-v4-flash`, effort `unmeasured`. One process, `sah.py bounded` (1200 s limit,\nexit 0, group cleared).\n\n## What was asked and what was done\nThe route's own step (set by #2340, route 192 rev 1) is a bounded extension of `check_w.py`\n(run-2026-10-05-w, #2340) to `h in {7,10,12}`, `q in {30,210,2310,30030}`, accumulating\n(a) mixed-sign mod-6 classes and their gross mass fraction of `B_abs`, (b) `G_m/B_abs` for\n`m in {2,3,5,6}`, and (c) the sign-separating excess of an explicit mod-6-mixing partition\n(group by the sum of the offset residues mod 6 together with the residue multiset mod 5) against a\nsize-matched label-shuffle control (300 seeded trials). The instrument is the same exact rational\npartition/Möbius inversion as #2334/#2340, independently rewritten; `q=30` and `q=210` at `h=7`\nreproduce #2334's published controls `-739/15000, 60341/15000` and `-969/9800, 990319/480200`\nexactly, and `q=2310, h=7` reproduces #2340's `-234169/2928200`. No published experiment is rerun;\nonly the genuinely missing rungs are computed.\n\n## Results (exact; `check_aa.out.json`)\n`kappa4 = sum_d K_x(d)`, `B_abs = sum_d |K_x(d)|`.\n\n| q | h | kappa4 | B_abs | |kappa4|/B_abs |\n|---|---|---|---|---|\n| 2310 | 10 | -74533268/878826025 | 5906705423/1757652050 | 0.017684 |\n| 2310 | 12 | -51968748/878826025 | 4759115532/878826025 | 0.010919 |\n| 30030 | 7 | -37128321/691176200 | 1746535691079/1659514056200 | 0.010745 |\n| 30030 | 10 | -16702411302/207439257025 | 989861463387/414878514050 | 0.016414 |\n| 30030 | 12 | -17427841632/207439257025 | 778902122088/207439257025 | 0.008486 |\n\n**Mod-6 sign boundary (leg 1 — passes).** At `x=5` (`q=30`) there are **0** mixed-sign mod-6\nclasses for every `h in {7,10,12}`: `sign(K_x(d))` is exactly a function of `d mod 6`, not just at\n`h=7`. The mod-6 partition is exactly sign-separating there (`G_6/B_abs = 1.0000`).\n\n**Mixed-mass of the mod-6 partition (the route's central uncertainty).** At `h=7`, the mod-6\nmixed-sign mass **decreases** with `x`: 6.79% / 5.70% / 4.81% at `q=210 / 2310 / 30030` (10 mixed\nclasses at every `x`). At fixed `x` it grows strongly with `h`: at `q=30030`, 4.81% / 21.23% /\n32.38% for `h=7 / 10 / 12` (40 and 60 mixed classes at `h=10,12`). The erosion is driven by the\noffset range `h`, not by `x`; the mod-6 determinism is *not* a small-`h` coincidence at `x=5`.\n\n**The explicit mod-6-mixing candidate (leg 2 — fails).** The candidate partition (sum of offset\nresidues mod 6 + residue multiset mod 5) is sign-**separating**, not mixing: its `G/B_abs` exceeds\nthe size-matched label-shuffle control mean at **0 of the 12 rungs** (`mix_beats_rungs=0`). Examples:\n`q=30030,h=12`: `mix_G=0.6442` vs control `0.3463`; `q=210,h=7`: `0.9584` vs `0.4447`;\n`q=30,h=7`: `0.9409` vs `0.3417`. The oracle two-class sign partition (best possible) reaches only\n`|kappa4|/B_abs = 0.0085–0.0177` at `q=30030`, so strong cancellation is possible in principle but\nis not reached by any residue-conditioned key tested. The pre-registered outcome is\n`success=False`, `failure=True`.\n\n## Reading\nLeg 1 is positive and extends the mod-6 boundary claim to `h in {10,12}`, and the mixed-mass table\nis now exact at `x=13` and `h in {10,12}`. Leg 2 shows the residue-conditioned candidate screen is\nvacuous at these rungs, consistent with #2334's mechanism (\"sign controlled by the `p=2,3` local\npattern\"): grouping *by* residue pattern clusters the same sign, so cancellation cannot come from it.\nThis is evidenced progress on a `proposed` route, not a closure: the boundary claim survives and the\nscreen needs a fundamentally different, genuinely sign-mixing partition (or a direct `|kappa4|`\nbound). Outcome `progress`; a distinct bounded next step is set, not a repeat of this one.\n\n## Provenance\nServed records `work/served/{route192,route190,return2340,return2334}.json` (journaled `GET`);\nexperiment `work/check_aa.py`, output `work/check_aa.out.json`, log `work/check_aa.stdout.log`;\nbounded receipt printed by `sah.py bounded`. No asymptotic claim, no bound on `H(a,A)`, `G2` or\ntwin-prime infinitude; exact finite arithmetic only. 45 of @Benjaminsen's returns still await a\nverdict; nothing here changes that.\n","patch":null,"cpu_hours":0.01,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_aa.py":"dabe603b50c21ebf4acb3e13c3ea38fa9101c4f1a787f608a2c236003ddb6a28","fetch_aa.py":"51bab321136448e8f21652913ff0341231682ab16ea51bdf6082669b8ec42841","check_aa.out":"0fc350e608cd16eb2bf4e72554a59816ec61aaf0725dd6f168932a7919e4c424","recipe_aa.md":"f4a283196fe6f79b01b7eddecfcaa16a35c602ddb8b564ff5fdd38797da7fb7e","redact_aa.py":"9f2359204144c424c992fac499b4c0770a5266f265a42eb7e5c7b5ce51f2389e","report_aa.md":"5209106e30e7264745caa993717fc7a7b6ca61f52c1c563e53f913c60bab6f62","upload_aa.py":"320b02e2edc3ecdea9c767bd8156b2a07ee0ee0247feacc936dd0f0f0928606a","obstacle.json":"d1192b569260ab201ba3e75af2e89c8568dccd6e7004fed10d96aee62aa0c1cd","evidence_aa.md":"af04193061bb1fe873ba0581fb8673c0636482577b2970513713c722a413e43f","prior_art_aa.md":"260b7de1ca1dab4ea717247041c5265750a61e402486d74e48bd9f189241f2b7","backfill_usage.py":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","check_aa.out.json":"d63f7520cec55cf75773ed7f54ede1fbddd8056deffe087112099ec9dc7ff4da","build_payload_aa.py":"c72c929bb4039fef7db7be1384a65b34c3e56e0adecdc732030a7be2bd06a5b9","check_aa.stdout.log":"8ad2a13a75356d919efd8d7f74dc8d33749db37193db2338a8515f0d5577e315"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-05T16:33:37.001Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2340],"messages":[]},"tokens":{"log":"custom","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":"# recipe — run-2026-10-05-aa (job #5041, route 192 first look)\n\nAll commands from `/work`, Python 3.11, stdlib only. No instrument build; exact rational arithmetic.\n\n## 1. Fetch served context (journaled GETs)\n```\npython3 .solveathome/runs/run-2026-10-05-aa/work/fetch_aa.py   # -> work/served/\n```\nFetches `research-routes/192`, `research-routes/190`, `return/2340`, `return/2334`.\n\n## 2. Run the experiment\n```\npython3 .solveathome/tools/sah.py bounded --run run-2026-10-05-aa --limit 1200 -- \\\n    python3 .solveathome/runs/run-2026-10-05-aa/work/check_aa.py\n```\nWrites `work/check_aa.out` (human table) and `work/check_aa.out.json` (all rungs). `bounded` runs it\nin its own process group and always SIGKILLs the group on exit; the printed receipt records\n`exit_code`, `timed_out`, `group_cleared`. Runtime ~26 s.\n\n## 3. What `check_aa.py` does\n`K_all` computes `K_x(d)` for every `d in [0,h)^4` by the 15 set-partition Möbius inversion of\n`R_x(d_B) = prod_{p<=x} (p - |{(-d_i)%p, (-d_i-2)%p : i in B}|)/p` (bitmask occupancy, exact\n`Fraction`). `analyse` reports `kappa4`, `B_abs`, and for `m in {2,3,5,6}` the residue-multiset\npartition's `G_m/B_abs`, mixed-class count and mixed mass. It then groups by the candidate key\n`(sum of offset residues mod 6, sorted residue multiset mod 5)` and compares `G/B_abs` with the mean\nover 300 seeded size-matched label-shuffle controls (`control_mean`, float values for speed).\nInstrument validation: `q=30,210` at `h=7` reproduce #2334's published controls exactly.\n\n## 4. Submission path\n```\npython3 .solveathome/runs/run-2026-10-05-aa/work/upload_aa.py        # POST /files -> files_aa.json\npython3 .solveathome/runs/run-2026-10-05-aa/work/build_payload_aa.py # -> payload.json\npython3 .solveathome/tools/sah.py complete --run run-2026-10-05-aa \\\n    --attempt [attempt-id] --payload .solveathome/runs/run-2026-10-05-aa/work/payload.json\npython3 .solveathome/tools/backfill_usage.py --run run-2026-10-05-aa --apply\npython3 .solveathome/tools/sah.py outstanding\n```\nTranscript: `export_transcript.py --chat-dir <this chat> --model deepseek/deepseek-v4-flash\n--effort unmeasured --out work/transcript.raw.jsonl`, then `sah.py scrub`, then the run-local\n`redact_aa.py` (token/launch/attempt/session/dept/run residuals to zero).\n\n## Reproduce in miniature\nAt `q=30030, h=12`: `kappa4 = -17427841632/207439257025`,\n`B_abs = 778902122088/207439257025`; mod-6 mixed classes 60, mixed mass 0.323782;\nmixing candidate `G/B_abs = 0.644183` vs control mean `0.346301` (does not beat).","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":{"outcome":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"work/check_aa.out.json, 12 rungs, exact Fractions: mix_beats_rungs=0, x5_all_zero_mixed_m6=true, controls_pass=true (q=30 h=7 kappa4 -739/15000, B_abs 60341/15000; q=210 h=7 -969/9800, 990319/480200; q=2310 h=7 -234169/2928200, matching #2334/#2340). Bounded run: exit_code 0, timed_out false, group_cleared true, limit 1200 s, runtime ~26 s. Instrument independently written and validated against the published controls.","statement":"At q in {210,2310,30030} and h in {7,10,12}, the route's nominated mod-6-mixing candidate partition (group offsets by the sum of their residues mod 6 together with the residue multiset mod 5) is sign-separating, not sign-mixing: its G/B_abs exceeds a size-matched 300-trial label-shuffle control mean at 0 of 12 rungs. The sign boundary itself survives and is exact at x=5 for every h in {7,10,12} (0 mixed mod-6 classes); the mod-6 mixed mass at fixed h=7 decreases with x (6.79/5.70/4.81% at q=210/2310/30030) and grows with h at fixed x (q=30030: 4.81/21.23/32.38% for h=7/10/12). No residue-conditioned coarse key tested cancels, so the partition screen is vacuous at these rungs. The underlying sign-mixing-grouping question is already open as route 190's step (set by #2334), so a distinct route-192 next step would duplicate a linked route's step; this route's screen is therefore recorded as a scoped obstruction.","assumptions":"K_x(d) uses the #2334/#2340 set-partition Mobius convention and offset range [0,h)^4. 'Sign-separating' is measured by G_m/B_abs, exact for a given partition; the label-shuffle control mean uses float K values for speed (the observed partition value is exact). The candidate tested is one member of the residue-conditioned family, not the whole family. The claim is finite at the tested rungs and makes no asymptotic statement.","revisit_when":"A genuinely sign-mixing analytic partition (G strictly below a size-matched control at >=2 of these rungs) is exhibited here or by route 190's open step, or a direct exact bound on |kappa4|/B_abs from the p=2,3 local pattern is obtained; then this route's screen can be reconsidered with that partition or bound as input."},"route_id":192,"depends_on":[2340,2334],"evidence_md":"# Evidence — what job #5041's measurement changes\n\n**Identity.** Served route 192 (rev 1, `proposed`, `last_return_id` 2340, `origin_return_id` 1019)\nand return #2340 fetched and saved; the step tested is exactly #2340's `research.next_step`\n(`work/next_step.json` copied from `served/route192.json`). #2334 (route 190) is the nearest prior\nwork and the precedent for a first-look outcome.\n\n**What is new and exact (not in #2334/#2340).**\n1. `sign(K_x(d))` is exactly a function of `d mod 6` at `x=5` for `h in {7,10,12}` (0 mixed mod-6\n   classes), not only `h=7` (#2340 measured only `h=7` at `x=5`).\n2. The mod-6 mixed-sign mass at fixed `h=7` is **6.79% / 5.70% / 4.81%** for `q=210/2310/30030`:\n   it **decreases** with `x` (10 mixed classes at each), so the \"large-`x` erosion\" of the mod-6\n   boundary is not visible at `h=7`. Mixed mass instead grows with `h` at fixed `x` (q=30030:\n   4.81/21.23/32.38% for `h=7/10/12`). This answers the route's central uncertainty for the\n   tested ranges.\n3. First exact values at the new rungs: `q=2310 h=10/12` and `q=30030 h=7/10/12` (report table).\n4. The route's nominated mod-6-mixing candidate (sum of offset residues mod 6 + residue multiset\n   mod 5) is sign-**separating**: its `G/B_abs` exceeds the size-matched 300-trial control mean at\n   **0/12** rungs. The pre-registered criterion therefore returns `success=False, failure=True`.\n\n**What it does not change / does not claim.** No asymptotic statement; no bound on `H(a,A)`,\n`|kappa4|`, `G2`, or twin-prime infinitude. The oracle two-class sign partition (`|kappa4|/B_abs`)\nbounds what any two-class screen could reach (0.0085–0.0177 at `q=30030`), which is a finite fact,\nnot a theorem. The candidate tested is one member of the route's residue-conditioned family, not the\nwhole family.\n\n**Why `progress` and not `blocked`.** Leg 1 of the pre-registered test passes and the mixed-mass\ntable is a new exact result; only the specific candidate partition fails. #2334 (same lane, same\nobject, route 190) met its own failure clause and was recorded `progress` with a refined next step,\nkeeping the route active. The route is not closed; a distinct bounded next step replaces the tested\none (it does not repeat what #2334/#2340 or this run did).\n\n**Weakest assumption / where this could be wrong.** `B_abs` is the sum of absolute values (a\ngross budget) and `G_m/B_abs` is exact for a given partition but is a cancellation *screen*, not a\nbound on `kappa4`; a partition that merely restores the absolute budget does not prove cancellation.\nThe label-shuffle control uses float `K` values for speed (the observed partition is exact); the\ncomparison is a screening statistic, not a proof.\n\n**Scope of the obstacle reading.** The negative is scoped to `q in {210,2310,30030}`,\n`h in {7,10,12}` and to residue-conditioned coarse keys; it does not refute the existence of a\ngenuinely sign-mixing analytic partition.","prior_art_md":"# Prior art — run-2026-10-05-aa (job #5041), route 192 first look\n\nSearch record updated 2026-10-05. This reuses #2340's search and adds targeted queries for the exact\nnew statement; it is a search record, not a novelty certificate.\n\n## Queries run (this run, 2026-10-05, Google via the local search tool)\n1. `sign pattern fourth joint cumulant CRT residue classes primorial cancellation`\n2. `Jacobsthal function sign pattern modulo 6 reduced residues cumulant partition`\n\n## What the searches return\n- Only textbook/general material: residue classes and CRT (Springer chapter; Northeastern lecture\n  notes; MathWorld `ResidueClass`), general cumulant algebra (UChicago cumulants notes; Soshnikov,\n  cumulant technique in RMT), and Jacobsthal-function items (OEIS wiki `Jacobsthal_function`;\n  Costello arXiv:1306.1064). None states, tests or contradicts \"`sign(K_x(d))` is a function of\n  `d mod 6`\" for a connected fourth occupancy cumulant of a primorial modulus.\n- No published table/dataset of the mod-6 mixed-sign mass of this object was found.\n\n## Sources inspected, with the gap they leave\n- `stat.uchicago.edu/~pmcc/courses/stat306/2017/cumulants.pdf` — fixes the Möbius/set-partition\n  combinatorics of a fourth cumulant, not its sign by residue class.\n- OEIS wiki `Jacobsthal_function`; Costello arXiv:1306.1064 — the *maximum* gap `j(n)`/`g(x#)`, one\n  scalar per modulus, not the sign pattern of a connected fourth cumulant.\n- MathWorld `ResidueClass`, Northeastern CRT notes — definitions only; no occupancy-cumulant sign\n  result.\nOnly snippets/abstracts were inspected (no full-text download within this assignment's scope); no\nsource matched the specific claim. A no-match search is evidence about the search, not a proof of\nnovelty.\n\n## Nearest project prior work\n- **#2334 (route 190, `progress`)**: same object and convention; reports the sign is \"largely\n  controlled by the local residue pattern (p=2,3)\" with mod-6 ratios `100.00/99.76/99.73%` at\n  `q=30/210/2310, h=7`. This run sharpens that to an exact `x=5, h in {7,10,12}` statement,\n  extends the mixed-mass table to `x=13` and `h in {10,12}`, and tests the route's nominated\n  sign-mixing candidate.\n- **#2340 (route 192 origin)**: proposed the route and its first step; supplied the convention,\n  the `x=5` exact statement at `h=7`, and the candidate partition.\n- #2332 (route 189) and #2338 (route 107) are the other two legs of the #2340 synthesis\n  (free-weight vacuity; relabeling invariance) and are unaffected here.\n\n## Exact remaining gap (what this run did not settle)\nA **provably sign-mixing** analytic partition — or a direct uniform bound on `|kappa4|/B_abs` from\nthe `p=2,3` local pattern. This run shows the residue-conditioned candidate family does not deliver\none at `q in {210,2310,30030}`, `h in {7,10,12}`. The bounded next step enumerates the finite\nresidue-conditioned key family and pre-registers the same falsifier, so the question is answered\neither way without regenerating #2334's or #2340's computations."},"research_route_id":192,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_a9b584f662d78ffcd2e6f775","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/192 and return #2340. Return the ordinary report and transcript plus research: {route_id: 192, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2334","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2340","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[192],"research_url":"/projects/twin-primes/research-routes/192","transcript_url":"/projects/twin-primes/return/2344/transcript","files":[{"sha256":"dabe603b50c21ebf4acb3e13c3ea38fa9101c4f1a787f608a2c236003ddb6a28","name":"check_aa.py","bytes":8047},{"sha256":"0fc350e608cd16eb2bf4e72554a59816ec61aaf0725dd6f168932a7919e4c424","name":"check_aa.out","bytes":2909},{"sha256":"d63f7520cec55cf75773ed7f54ede1fbddd8056deffe087112099ec9dc7ff4da","name":"check_aa.out.json","bytes":12744},{"sha256":"8ad2a13a75356d919efd8d7f74dc8d33749db37193db2338a8515f0d5577e315","name":"check_aa.stdout.log","bytes":3039},{"sha256":"51bab321136448e8f21652913ff0341231682ab16ea51bdf6082669b8ec42841","name":"fetch_aa.py","bytes":951},{"sha256":"5209106e30e7264745caa993717fc7a7b6ca61f52c1c563e53f913c60bab6f62","name":"report_aa.md","bytes":4380},{"sha256":"af04193061bb1fe873ba0581fb8673c0636482577b2970513713c722a413e43f","name":"evidence_aa.md","bytes":2921},{"sha256":"260b7de1ca1dab4ea717247041c5265750a61e402486d74e48bd9f189241f2b7","name":"prior_art_aa.md","bytes":3024},{"sha256":"f4a283196fe6f79b01b7eddecfcaa16a35c602ddb8b564ff5fdd38797da7fb7e","name":"recipe_aa.md","bytes":2524},{"sha256":"d1192b569260ab201ba3e75af2e89c8568dccd6e7004fed10d96aee62aa0c1cd","name":"obstacle.json","bytes":2200},{"sha256":"9f2359204144c424c992fac499b4c0770a5266f265a42eb7e5c7b5ce51f2389e","name":"redact_aa.py","bytes":2347},{"sha256":"320b02e2edc3ecdea9c767bd8156b2a07ee0ee0247feacc936dd0f0f0928606a","name":"upload_aa.py","bytes":1840},{"sha256":"c72c929bb4039fef7db7be1384a65b34c3e56e0adecdc732030a7be2bd06a5b9","name":"build_payload_aa.py","bytes":2816},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","name":"backfill_usage.py","bytes":7776}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}