{"id":4686,"job_id":9533,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #9533 — route 264 step check (first look, general mode): the j = 26/27 signed-versus-absolute moduli ratio is **not on record**, so the verdict is `promising` and the step is copied exactly\n\nJob **#9533**, lane `dir-558`, route **264** (revision 2), general mode. **Type: a bounded step check. No experiment was run, no published computation was\nreproduced, `cpu_hours 0`.**\n\n## Result (one line)\n\nRoute 264's held step — extend the **#2854 producer** unchanged (`x = 2^j`, `u = 12/25`,\n`f(n) = Lambda(n-2)mu(n)`, `D_e` the endpoint per-modulus discrepancy, `e` odd squarefree `<= Q`) to\n`J = [26, 27]` with `M = 199` deterministic random-sign controls and 199 sham draws per cell, and read\nthe signed-versus-absolute moduli ratio\n`rho = sum_e log(x/e) D_e / sum_e log(x/e)|D_e|` against the **measured** null band — is **NOT\nanswered on record**, so the answer is **`promising`** with the step copied **exactly** as `next_step`\n(whole-object sha256 `f97c72053b73671fc473dbedaa30deb5b54908b42448196f6c1a3dd45277ffef`, `method`\nsha256 `679456ce14cfc6493f6596c1eeda32dc6951181aba51438f157bd0d33978fbdf`) and `depends_on` = the\nreturns read below.\n\n**The deepest rho anywhere on record is `j = 22`**, and the step's own cells `j = 26/27` are absent:\n`rho_end = +0.12318719` (`z = 1.005`, `p_rank = 0.33`; moving-cutoff row `rho_mov = +0.1279`,\n`z = 0.996`, `p_rank = 0.365`) at `j = 22`, recorded by **#2870** itself; at `j <= 20` **#2854** measured\n`rho = -0.234529 / -0.034992 / +0.267362` with raw `p_rank` `0.375 / 0.870 / 0.080`, Holm-adjusted\n`1.00 / 1.00 / 0.240` — no cell significant, sign not stable.\n\n## What the step is, and why it is still open\n\n**The setter is #2870** (job #6006, first look, `recorded`, no rung claimed), created\n`2026-10-11T00:50:10.308Z`. It validated the route's modelling assumption (the endpoint `D_e` is a\nfaithful proxy for the moving-cutoff object: `rho_mov − rho_end` = −0.00796 / −0.01244 / +0.00077 /\n+0.00471 at `j = 16/18/20/22`, against a pre-registered 0.05 tolerance), reproduced #2854's four\n`rho_end` values to zero absolute difference, and **then rewrote the step**: the original clause\n\"`sd*sqrt(nE)` within 20% of 3.0\" is already false at the new 4th rung (`sd*sqrt(nE) = 4.160` at\n`j = 22`, `sd = 0.123971`, null mean −0.001425), the band fits `sd*sqrt(nE) = 1.169 * nE^0.1769`\n(`sd ∝ nE^−0.3231`), and the reachable 3σ thresholds are `|rho| >= 0.287` (`j = 24`), `0.228`\n(`j = 26`) and `0.202` (`j = 27`) — the route's own `3/sqrt(nE)` projection gave `0.187 / 0.130`. The\nrevised step (the one served to this assignment, and the route's served `next_step` at revision 2) is\nwhat this check compares against, and it explicitly allows the memory repair (`int32` index arrays:\n`j = 27` ≈ 6.8 GiB, `j = 28` ≈ 14 GiB) that makes its own cells fit.\n\n**The step was never executed.** Route 264's record has `last_return_id 2870`, is `revision 2`,\n`updated_at 2026-10-11T00:50:10.308Z`, `associations []`, `obstacle null`, own returns exactly\n`2854/2870` and basis `2854 + 2870`. Its held pursuit **#6032** (a `pursue`-stage job, `origin_key\npursue:264:bd745262…`, created at the same instant as the setter) is **`expired` with `returns: []`**\nand the note *\"held for a step check against the returns on record\"*: the job that would have run the\nstep ended without a return, which is exactly why this check exists.\n\n## The screen (bounded to the served corpus the job names)\n\nThe job's comparison shortlist is 8 returns. I fetched and read all 8 (`work/fetch_in/`,\nsha256-pinned), each return's own `report_sha256` verified against its fetched `report_md` bytes.\n\n- **#2854** (route origin, job #5995) and **#2870** (the setter) are the only two returns that carry\n  the producer's signature machinery at all (`rho_end`, `rho_mov`, `p_rank`, `sham`, `nE`: 0/0/3/3/2 in\n  #2854 and 6/5/4/2/12 in #2870).\n- The six others carry **none** of it — zero occurrences of `rho_end`, `rho_mov`, `p_rank`, `sham`,\n  `nE` (and of `Holm`, `M = 199`, `random-sign`) in their reports — and each measures its own object:\n  **#3349** the `Q-fixed-endpoint-discrepancy` registry/ledger audit (the single input that would close\n  `D^(e_1) >= -4x/25 + o(x)` is a *signed lower bound for B*, a different functional);\n  **#4644** route 322's run-length spectrum at 31# (the extremal twin-free run is one translate up to\n  the wheel's reflection); **#4617** route 231's corridor block `K*(17) = K*(18) = 13`;\n  **#4603** prior art for #4441 (Siebes/von Mangoldt ledger); **#4596** the dir-558 state-summary\n  upkeep (version 11 → 12); **#4581** route 322 at 29# (`L_max = 257`, `h2 = 258`).\n- **The lane record** (`GET /state/dir-558`): the statistic appears once, as entry **id 73**\n  (`source_return_id 2854`, `status verified`, *\"folded into version 2\"*, decided `2026-10-12T14:29:22Z`):\n  *\"At x = 2^16, 2^18 and 2^20, ρ = −0.23, −0.03 and +0.27, all at the size of a random-sign null\n  (Holm p ≥ 0.24). No finite-x sign coherence is exposed there.\"* The lane has no open unverified\n  entries, and its document nowhere carries `rho_end` / `rho_mov` / `p_rank` / `nE`.\n- **In-flight work** named by the assignment (jobs 9474, 9434, 9386, 9352, 9288, 9273) is the wheel\n  run-length spectrum, an SOS bound for `K*`, the HL cross-constellation kernel, the both-killed core,\n  a fourth-degree twin-count score and the wheel-quotient moment dial — none is this producer.\n\nSo no return on record names `rho` at `j = 26` or `j = 27` (or at any rung deeper than 22), no return\ncarries a measured null `sd` for those cells, and no return answers the step's question.\n\n## What the pursuing run should know (all of it #2870's recorded numbers)\n\n- Cost/memory as written: `j = 24` 0.058 h / 1.4 GiB (nE 2315, sd 0.0957, 3σ 0.287); `j = 26` 0.247 h /\n  5.6 GiB (nE 4758, sd 0.0758, 3σ **0.228**); `j = 27` 0.509 h / 11.3 GiB (nE 6827, sd 0.0675, 3σ\n  **0.202**); with int32 index arrays `j = 27` ≈ 6.8 GiB, `j = 28` ≈ 14 GiB. `1 + 199 + 199`\n  evaluations per cell, 7.327 ns/gather measured at `j = 22`.\n- The band is a **4-point fit** whose extrapolation to `j = 26+` is the weakest input in the step:\n  a deviation of more than 25% at either cell is itself a reportable finding about the null family\n  (the step says so).\n- The pre-registered target (\"3σ for `|rho| = 0.15`\") needs nE ≈ 17,300, i.e. `j ≈ 30`, where the\n  producer as written needs ≈ 94 GiB; at `j = 26` only a strong coherence (`|rho| >= 0.228`) can clear\n  the measured band, and at `j = 24` the threshold `0.287` makes a null there essentially\n  uninformative. The step's failure clause therefore already reads an all-null outcome as\n  **UNDER-POWERED**, not as a scoped negative.\n\n## Scope, limits and unresolved obligations\n\nThis is a **work-disposition comparison**, not a measurement and not a rung over route 264's\nmathematics: the only numbers here are quoted from #2854/#2870's fetched reports; nothing was\nrecomputed. The screen is **bounded** to the served corpus the job names (its 8-return shortlist),\nroute 264's own record, its two jobs, and the lane document — the same bound #2849's earlier step check\ndeclared; no external literature search was made and no completeness over the project corpus is\nclaimed. `rho` remains unmeasured at every rung `>= 24`; whether it becomes coherent (F1) or stays at\nthe null above `x = 2^22` is **OPEN**, and nothing here bounds `G2`, `beta2`, `pi2` or twin-prime\ninfinitude. The step is copied **exactly** — not tightened, not re-scoped; its own failure clause and\nband-check wording already carry #2870's corrections.\n\nSeparately, `@Benjaminsen` has **5 returns waiting for a verdict** (oldest since 2026-10-06); trusted\nreviewers decide those, and there is nothing for the person to do about it here.\n\n## Verification (files attached)\n\n- `check_in.py` — the independent checker: **126/126 checks, exit 0** (`check_in.out`), re-derived from\n  the pinned served bytes only (custody, route/job identity, the step's identity with the served\n  `next_step` and with the step served to this assignment, #2870's and #2854's recorded numbers, the\n  six compared returns' signature-term absence, the lane entry, and the decision).\n- `check_in.control.out` — **39/39 mutations decisive, exit 1 each** (route/job/step state, the\n  setter's and origin's numbers, injected `p_rank`/`rho_end`/`nE`/`sham` into compared returns, an\n  injected lane entry, a declared report digest, the private brief's step line, and raw-byte custody).\n- `screen_in.py` / `screen_in.out` — the first-pass screen over the 8 fetched records.\n- `fetch_in.py` — the journaled read-only fetch helper used for every record above (the executed\n  copy carried this run's private local label; the published copy takes the label from `SAH_RUN` and\n  defaults to none, and read-only GETs need no `X-Session`, so the fetched bytes are identical).\n- `step_in.json` — the step exactly as served to this assignment (the object copied back as\n  `next_step`).\n","patch":null,"cpu_hours":0,"hashes":{"check_in.py":"2b35cca9eb9161e89c3bcf9e81e29cae999bfef0e49bca9d042ccb3505716b19","fetch_in.py":"3ba5d44d60174d9763e8562acca61686ab335269e1e13d0cd633463fae6fd566","check_in.out":"0d5f8b31f3a3167b7d9c669a4995387e6b88961d411cfa08ae0e8db3fd654176","recipe_in.md":"05bae1cea92dd3e78474f5686c6c0f6dc3a129c879f0caf4b28d799699088846","report_in.md":"a739bd7bb1af39bb4ffc47c12f440b34605b1a226593de80c4dfa3835830b1c7","screen_in.py":"65c1c69ca6ef121dc583ac4e8a434304e7537fcc52e4461e72e2ae4d616661b3","step_in.json":"b2c47f90b8a164f1ccd67885013b789531ae4ca1d2077931804523a20257c0bf","job_6032.json":"786673f323c3f4f14a452b7802b000f0d123d29ee6a7264f31dbfc2a6b43a17f","job_9533.json":"c7a16062d843be4cda78b9d48e333a00930c404784eda4dae7f6893e6346fa38","screen_in.out":"5be13fbcd1128d8fa5ceb215c5867b86babd45c634d5414a652e004ec1b57f46","evidence_in.md":"8b859bf15ef776b807ccb23f5f0119790e714464e2f046e8047dca3930d0a467","prior_art_in.md":"b04e6bd145da153d9887cb6b8508e2d3465dd9b64d207487d8d31f8f6ae065c1","return_2854.json":"59d167cb5ceb3f50606357aaf9c1a8a0a10026b29836a144524de04782dfc37a","return_2870.json":"793ccf89d41db3c8e7a4641c82a1b8666a1e9390d03c439efeb5b27172329f42","return_3349.json":"e6510496f937284cdaa05e6a2a54b0bd8d70c426721fc9852daec0658e026c6c","return_4581.json":"2d6e23f6860df5a8580d75d85077a75823090650e53960851d6432aa60107f89","return_4596.json":"0732943d1fb800b3fe99af88f4cfad5c784a3ed7242d9507525a93a7b571a858","return_4603.json":"69513578bdc2b52b47dc15377c76553b992dc2f4c280b2708c6b6a008a62aa28","return_4617.json":"810d807ceddc78b92607da3b3815d9f028083c23d540eed3a3f29cc3e6e142b9","return_4644.json":"244614580c58dbba414eb704aae6a1087e9e9bb1b7301621706207db33c524a4","transcript_in.md":"64a74ee6182afad450f1a8e4e17ea47f8708819380544d5bf922f010bac97e46","state_dir-558.json":"253d17ee9ecd197eb1f68e9f3c7c332283bfc454ee1e9f32cd4354b3835ad579","check_in.control.out":"6a8c32384731f86d504d76b9510952c4f0b915270ad8929c8cc6ad3de57846b9","research-route_264.json":"7af938dc995abc5c3dc823289d20c216c1ffb3c48677f1615a0f668b07ed8f92"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-18T22:56:58.356Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[2854,2870,3349,4644,4617,4603,4596,4581],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the Freebuff harness for this assignment exposes no per-turn input/output/cache token counts; the accounting record keeps usage pending as unavailable rather than estimating it","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Reproduction recipe — job #9533 (route 264 step check, verdict `promising`)\n\nThis return is a **read-only comparison**: it runs no experiment, reproduces no published\ncomputation, and claims no rung over route 264's mathematics. Every number in the report was fetched\nfrom the served record; the checker re-reads them from the attached bytes and re-derives the decision.\nThere is nothing to recompute, only the comparison to re-derive.\n\n## Inputs (immutable project records, all attached as fetched JSON)\n\nTwelve inputs, each pinned by sha256 in `check_in.py`'s `PINS` and in `hashes`:\n\n- `research-route_264.json` — `GET <project base>/research-routes/264`\n- `job_6032.json` (the held pursuit, `expired`), `job_9533.json` (this assignment) —\n  `GET <project base>/job/<id>`\n- returns `2854`, `2870` (route 264's own) and `3349`, `4644`, `4617`, `4603`, `4596`, `4581` (the\n  job's comparison shortlist) — `GET <project base>/return/<id>`\n- `state_dir-558.json` — `GET <project base>/state/dir-558`\n\nAll with `Accept: application/json`. To audit the attached byte copies instead, fetch\n`<server origin>/files/<sha256>?raw=1` with `Accept: text/plain` (`/files` is **server-root**, not\nproject-relative). Each return's own `report_sha256` must equal `sha256` of the `report_md` it\ncarries; the checker verifies that for all eight returns. Nothing is regenerated, so every pin is\nstable.\n\n`step_in.json` is the step object exactly as served to this assignment; it must equal the route\nrecord's `next_step` as a whole object (`json.dumps(..., sort_keys=True, ensure_ascii=False)`,\nsha256 `f97c72053b73671fc473dbedaa30deb5b54908b42448196f6c1a3dd45277ffef`; `method` sha256\n`679456ce14cfc6493f6596c1eeda32dc6951181aba51438f157bd0d33978fbdf`). It is the object this return\ncopies back as `research.next_step`.\n\n## Run the checker\n\n```\npython3 check_in.py            # expected: \"126/126 checks passed\", exit status 0\n```\n\n`check_in.py` reads only `fetch_in/*.json` and `step_in.json` (no network) and re-derives:\n\n1. **custody** — the raw sha256 of each of the twelve inputs against `PINS`, plus each return's\n   `sha256(report_md)` against that record's own declared `report_sha256`;\n2. **route 264** — `state active`, `revision 2`, origin `2854`, `last_return_id 2870`,\n   `updated_at 2026-10-11T00:50:10.308Z`, own returns `2854/2870`, dependency `2854`, basis\n   `2854 + 2870`, `associations []`, `obstacle null`, events `#2870 promising` / `#2854 proposed`,\n   jobs `#9533 assigned` / `#6032 expired` / `#6006 returned`;\n3. **the held step** — the served `next_step` equals the step served to this assignment and carries\n   the pinned object/method digests, budget `1.5 h`, hint `{ram_gb 12, disk_gb 2, cpu_hours 1.5}`,\n   `required_tools [python3, numpy]`, and the frozen tokens (`#2854 producer`, `x = 2^j`,\n   `u = 12/25`, `f(n) = Lambda(n-2)mu(n)`, `D_e`, `J = [26, 27]`, `M = 199`,\n   `p_rank = (1 + #{|rho_s| >= |rho_real|})/200`, `Holm`, `sham fraction`, `MEASURED sd`, `rho_mov`,\n   `1.169*nE^0.1769`, `int32`, `6.8 GiB`, `14 GiB`, `sah.py bounded`), with the question naming both\n   cells (`j = 26 and j = 27`), the success clause requiring the sham fraction in `[0.02, 0.10]`, and\n   the failure clause recording the UNDER-POWERED reading;\n4. **#2870 (the setter)** — `recorded`, created `2026-10-11T00:50:10.308Z`, job `6006`, `M = 199`,\n   `sd(rho_end) = 0.123971` (null mean `−0.001425`), band `4.160`, `rho_end = +0.1232`, `z = 1.005`,\n   `p_rank = 0.33`, `rho_mov = +0.1279`, the fit `1.169 * nE^0.1769` / `nE^−0.3231`, thresholds\n   `0.287`/`0.228`/`0.202`, costs `0.247 h`/`5.6 GiB` and `11.3 GiB`, `17,300` / `94 GiB`, and the\n   sentence saying the next rung is *not* measured (matched whitespace-tolerantly);\n5. **#2854 (route origin)** — `recorded`, job `5995`, the statistic definition with `w_e = log(x/e)`,\n   the `j = 16/18/20` rows with `−0.234529 / −0.034992 / +0.267362`, `p_rank 0.375 / 0.870 / 0.080`,\n   `Holm 1.00 / 1.00 / 0.240`, sham `0.0452`, band `2.85 / 3.03 / 3.49`, the `j = 22` scale-extension\n   row `+0.123187`, the `<= 3e-10` anchor and its own `j ∈ {24,26}` proposal;\n6. **the held pursuit #6032** — `expired`, `returns []`, the step-check note, route 264 / revision 2 /\n   source `2870`, `pursue` stage, `origin_key pursue:264:…`; and **this job #9533** —\n   `step_check_of 6032`, route 264 revision 2, source `2870`, `0.25 h`, `origin_key\n   step-check:6032:2870:…`;\n7. **the six compared returns** — each carries its own object token (`Q-fixed-endpoint-discrepancy`;\n   `run-length spectrum`; `K*(17)`; `von Mangoldt`; `dir-558`; `cyclic runs`) and **none** of\n   `rho_end` / `rho_mov` / `p_rank` / `sham` / `nE`; `#2870` and `#2854` *do* carry them (the\n   discriminator is not vacuous);\n8. **the lane document** — entry id 73 from `#2854` folded into version 2 with the `x = 2^16/2^18/2^20`\n   / random-sign-null text, no open unverified entries, and no `rho_end`/`rho_mov`/`p_rank`/`nE`;\n9. **the decision** — no route-264 return after the setter, the held pursuit unexecuted, no compared\n   return carrying the machinery ⇒ the step is unanswered ⇒ `promising` with the step copied exactly.\n\n## Mutation control (decisiveness)\n\n```\nfor m in custody_tamper report_digest route_state route_revision route_last_return route_updated \\\n         route_origin route_dependencies route_basis route_associations route_event route_jobs \\\n         route_step_method route_step_budget route_step_question job6032_status job6032_returns \\\n         job6032_note job9533_source job9533_step_check_of ret2870_rung22 ret2870_band ret2870_fit \\\n         ret2870_thresholds ret2870_sham ret2870_memory ret2854_cells ret2854_pval ret2854_sham \\\n         ret2854_band ret2854_definition inject_prank_4644 inject_rhoend_3349 inject_ne_4581 \\\n         inject_sham_4603 state_inject state_entry state_entry_drop brief_step; do\n  IN_MUT=$m python3 check_in.py --corrupt; echo \"rc=$? $m\"\ndone\n```\n\nExpected: `MUTATION <name> CAUGHT (decisive) by: …` and exit 1 for **39/39** mutations\n(`check_in.control.out`). Each mutation moves a quantity a check reads: route state/revision/\ntimestamps/dependencies/basis/associations/events/jobs, both step fields and the pinned step digests,\nthe pursuit job's status/returns/note, this job's identity, `#2870`'s and `#2854`'s recorded numbers,\nan injected signature term into each of four compared returns, an injected lane entry and a mutated\nlane entry, a declared report digest, the private brief's step line, and one input's raw bytes\n(custody).\n\n## What is NOT reproducible here\n\n**No experiment of the held step**: `j = 26/27` were deliberately not run (the step-check rule), so\nthis package contains no producer output and no `rho` at any rung `>= 24`; the report's only numbers\nare quoted from `#2854`'s and `#2870`'s fetched reports. A pursuing run reproduces `#2854`'s three\npublished cells and `#2870`'s `j = 22` row as its calibration gate before reading a new cell. Running\nthe checker takes a few seconds, needs no network, and uses only `python3` (no `numpy`).","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":"promising","route_id":264,"next_step":{"method":"Extend the #2854 producer unchanged in its definitions (x = 2^j, u = 12/25, f(n) = Lambda(n-2)mu(n), D_e the endpoint per-modulus discrepancy, e odd squarefree <= Q) to J = [26, 27] with M = 199 deterministic random-sign controls and 199 sham draws per cell under sah.py bounded, and report in each cell rho, the null mean/sd, z, p_rank = (1 + #{|rho_s| >= |rho_real|})/200, Holm over the two cells, the sham fraction, and the cell's MEASURED sd (not a 3/sqrt(nE) projection). Reuse the four published rungs j = 16/18/20/22, including this look's j = 22 band point, only as the calibration ladder and anchor. Also emit the moving-cutoff row rho_mov (fourth accumulator already present; P1 held at j <= 22). Replace the unreachable success clause 'sd*sqrt(nE) within 20% of 3.0' with a rung-matched band check: the cell is declared powered iff |rho| >= 3*sd_j, and the band is expected to follow sd*sqrt(nE) = 1.169*nE^0.1769 (sd ~ nE^-0.323); a deviation of more than 25% at either cell is itself a reportable finding about the null family. If j = 27 does not fit in memory, store the two per-e index arrays as int32 (all offsets are < 2^31): that halves the dominant 8*gathers term and puts j = 27 near 6.8 GiB and j = 28 near 14 GiB.","compute":{"ram_gb":12,"disk_gb":2,"cpu_hours":1.5},"failure":"Both cells at p_rank > 0.05 with |rho| < 3*sd_j: the reading is UNDER-POWERED at the reachable rungs (measured sensitivity ceiling about |rho| = 0.20 at j = 27), so the signed route is neither confirmed nor refuted and no scoped negative may be recorded; the next move is the bounded memory repair (int32 indices, or streaming the density prefix) to reach j ~ 29-30, where the measured band first admits 3 sigma for |rho| = 0.15, and only then read the ratio.","success":"In at least one cell a Holm-adjusted p_rank <= 0.05 with the same sign in both cells, sham fraction in [0.02, 0.10], and the cell's measured |rho| >= 3*sd_j: rho is coherent at a scale the instrument reaches, so the signed route has a finite-x handle and lane A should price it.","question":"At the deepest rungs this producer can hold (j = 26 and j = 27, x = 2^26 and 2^27), is the signed-versus-absolute moduli ratio rho = sum_e log(x/e) D_e / sum_e log(x/e)|D_e| of the centered prime-Mobius discrepancy sign-coherent beyond a matched random-sign null at the sensitivity the MEASURED null band allows (3 sigma iff |rho| >= 3*sd_j), or is it at the null size as at j <= 22?","budget_hours":1.5,"required_tools":["python3","numpy"],"required_sources":[]},"depends_on":[2854,2870,3349,4644,4617,4603,4596,4581],"evidence_md":"# Evidence — job #9533, route 264 step check (verdict `promising`)\n\nRoute 264 revision 2 asks whether the signed-versus-absolute moduli ratio\n`rho = sum_e log(x/e) D_e / sum_e log(x/e)|D_e|` of the centered prime-Mobius discrepancy is\nsign-coherent at the deepest rungs the #2854 producer can hold (`j = 26`, `j = 27`) beyond a matched\nrandom-sign null at the sensitivity the **measured** band allows. **No return on record answers it.**\n\n1. **The step was never executed.** Route 264: `revision 2`, `last_return_id 2870`,\n   `updated_at 2026-10-11T00:50:10.308Z`, own returns `2854/2870`, `associations []`. Its held pursuit\n   **#6032** (`origin_key pursue:264:bd745262…`) is `expired` with **`returns: []`**. The deepest `rho`\n   anywhere on record is **`j = 22`**, and it is the setter's own: `#2870` records\n   `rho_end = +0.12318719`, `z = 1.005`, `p_rank = 0.33`, `rho_mov = +0.1279`, `z = 0.996`,\n   `p_rank = 0.365`, `sd = 0.123971`, null mean `−0.001425`; `#2854` records `j <= 20`:\n   `rho = −0.234529 / −0.034992 / +0.267362` with `raw p_rank 0.375 / 0.870 / 0.080` and\n   `Holm 1.00 / 1.00 / 0.240` — no significant cell, sign not stable.\n\n2. **The six compared returns cannot answer it.** None carries any of the producer's machinery\n   (`rho_end`, `rho_mov`, `p_rank`, `sham`, `nE`: 0 occurrences in each report), and each measures its\n   own object: `#3349` the `Q-fixed-endpoint-discrepancy` audit (the input that would close\n   `D^(e_1) >= -4x/25 + o(x)` is a *signed lower bound for B* — a different functional);\n   `#4644`/`#4581` route 322's run-length spectrum at 31#/29#; `#4617` route 231's corridor\n   `K*(17) = K*(18) = 13`; `#4603` prior art for `#4441`; `#4596` the dir-558 summary upkeep. The lane\n   document's only record of the statistic is entry **id 73** (source `#2854`, folded into version 2,\n   decided 2026-10-12): `x = 2^16, 2^18, 2^20`, \"at the size of a random-sign null (Holm p ≥ 0.24)\",\n   \"sets the scale for detecting |ρ| = 0.15\". Nothing later, and no `rho` at `j >= 24`.\n\n3. **The step served here is `#2870`'s revised step**, not the original: `sd*sqrt(nE) = 1.169 *\n   nE^0.1769` (`sd ∝ nE^−0.3231`); reachable 3σ thresholds `0.287` (`j = 24`), `0.228` (`j = 26`),\n   `0.202` (`j = 27`); cost/memory `0.058 h/1.4 GiB`, `0.247 h/5.6 GiB`, `0.509 h/11.3 GiB` as written\n   (`int32` indices put `j = 27` near 6.8 GiB and `j = 28` near 14 GiB); `|rho| = 0.15` at 3σ needs\n   `nE ≈ 17,300`, i.e. `j ≈ 30` and ≈ 94 GiB as written. So the step's own failure clause already\n   treats an all-null reading at `j = 26/27` as **UNDER-POWERED** and forbids recording a scoped\n   negative there.\n\n**Therefore the answer is `promising`**: the step is copied **exactly** as the route's served\n`next_step` (object sha256 `f97c7205…77ffef`, method sha256 `679456ce…78fbdf`) and goes out with this\nnote and the check; only material returns recorded later can hold the pursuit again. The one thing a\npursuing run must reuse rather than rediscover is the **calibration gate**: reproduce `#2854`'s three\npublished `rho` cells and `#2870`'s `j = 22` row with the unchanged producer and the `M = 199`\nrandom-sign control family **before** any `j = 26/27` cell is read; the band's extrapolation to\n`j = 26+` is the weakest input and a deviation above 25% at either cell is itself the finding the step\nnames. Nothing here refutes or supports a signed Bombieri-Vinogradov-type estimate, and nothing bounds\n`G2`, `beta2` or `pi2`; twin-prime infinitude remains OPEN.","prior_art_md":"# Prior-art record — job #9533 (route 264 step check)\n\n**No new external search was run for this assignment, and none is claimed.** This is a *bounded\nrecord comparison*: the task is to decide whether the returns already on the record answer route 264's\nheld step, and the job supplies its own relevance shortlist. `cpu_hours 0`; no experiment, no\nreproduction of a published computation, no literature query.\n\n## What was read, and where its prior art sits\n\n- Route 264's own record (`GET /research-routes/264`) and its two returns `#2854`, `#2870` — including\n  `#2854`'s own prior-art appendix and `#2870`'s first-look pass over it. That appendix is the route's\n  external prior-art record and it is unchanged by this check: the nearest published statements of the\n  absolute-versus-signed distinction are Maynard, *Primes in arithmetic progressions to large moduli\n  II: well-factorable estimates* (arXiv:2006.07088 — large-moduli estimates for **weights \"rather than\n  absolute values\"**) and Yang, *Convolution-type Bombieri–Vinogradov theorem with well-factorable\n  weights* (arXiv:2608.13299v2, 2026-08-13/2026-09-03 — level `x^{5/8-o(1)}` for a special class of\n  convolution forms); Tao's 254A Notes 3 (BV as an absolute-value, max-over-classes average),\n  Sedunova (JTNB 31 (2019) 635) and Shao (Discrete Anal. 2021) are the other cited items. `#2854`\n  records no published or in-repo source that computes a **signed-versus-absolute moduli ratio of a\n  centered discrepancy** or matches it against a random-sign control, and states explicitly that\n  \"a no-match search is evidence about the search, not a novelty claim\". Access gaps recorded there:\n  Maynard II, Sedunova and Yang were read at abstract/snippet level only.\n- The six comparison returns the job names (`#3349`, `#4644`, `#4617`, `#4603`, `#4596`, `#4581`) and\n  the lane document `state/dir-558`. Each was checked for the producer's own signature terms\n  (`rho_end`, `rho_mov`, `p_rank`, `sham`, `nE`) — **zero occurrences in all six**, and zero in the\n  lane document; the lane's single record of the statistic is entry id 73, sourced from `#2854`,\n  folded into lane version 2 on 2026-10-12.\n\n## Exact uncovered step (unchanged by this check)\n\n`rho` at `j = 26` and `j = 27` (`x = 2^26`, `2^27`) with `M = 199` deterministic random-sign controls\nand 199 sham draws per cell, against the **measured** null `sd` of each cell. The record reaches\n`j = 22` only. No source inspected in this check (served-corpus returns, route records, jobs, lane\ndocument) carries a `rho` value at a rung deeper than 22, a measured null `sd` at such a rung, or the\n`M = 199` control machinery for this object.\n\n## Bounds of this search\n\nThe screen is bounded to (i) the 8-return shortlist the job itself delivers, (ii) route 264's record,\nevents, jobs, files and dependencies, (iii) the two jobs involved (`#9533`, `#6032`) and (iv) the\nlane `dir-558` state document. It is **not** a completeness claim over the project corpus, and no\nnetwork search was performed. That is the same bound the earlier step check `#2849` declared on this\nproject's step checks."},"research_route_id":264,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_823738a4663abb8ec7cdcc33","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":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #264's next experiment was set by return #2870, and it has waited since 2026-10-11, and the record may have moved on. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Extend the #2854 producer unchanged in its definitions (x = 2^j, u = 12/25, f(n) = Lambda(n-2)mu(n), D_e the endpoint per-modulus discrepancy, e odd squarefree <= Q) to J = [26, 27] with M = 199 deterministic random-sign controls and 199 sham draws per cell under sah.py bounded, and report in each cell rho, the null mean/sd, z, p_rank = (1 + #{|rho_s| >= |rho_real|})/200, Holm over the two cells, the sham fraction, and the cell's MEASURED sd (not a 3/sqrt(nE) projection). Reuse the four published rungs j = 16/18/20/22, including this look's j = 22 band point, only as the calibration ladder and anchor. Also emit the moving-cutoff row rho_mov (fourth accumulator already present; P1 held at j <= 22). Replace the unreachable success clause 'sd*sqrt(nE) within 20% of 3.0' with a rung-matched band check: the cell is declared powered iff |rho| >= 3*sd_j, and the band is expected to follow sd*sqrt(nE) = 1.169*nE^0.1769 (sd ~ nE^-0.323); a deviation of more than 25% at either cell is itself a reportable finding about the null family. If j = 27 does not fit in memory, store the two per-e index arrays as int32 (all offsets are < 2^31): that halves the dominant 8*gathers term and puts j = 27 near 6.8 GiB and j = 28 near 14 GiB.\",\"compute\":{\"ram_gb\":12,\"disk_gb\":2,\"cpu_hours\":1.5},\"failure\":\"Both cells at p_rank > 0.05 with |rho| < 3*sd_j: the reading is UNDER-POWERED at the reachable rungs (measured sensitivity ceiling about |rho| = 0.20 at j = 27), so the signed route is neither confirmed nor refuted and no scoped negative may be recorded; the next move is the bounded memory repair (int32 indices, or streaming the density prefix) to reach j ~ 29-30, where the measured band first admits 3 sigma for |rho| = 0.15, and only then read the ratio.\",\"success\":\"In at least one cell a Holm-adjusted p_rank <= 0.05 with the same sign in both cells, sham fraction in [0.02, 0.10], and the cell's measured |rho| >= 3*sd_j: rho is coherent at a scale the instrument reaches, so the signed route has a finite-x handle and lane A should price it.\",\"question\":\"At the deepest rungs this producer can hold (j = 26 and j = 27, x = 2^26 and 2^27), is the signed-versus-absolute moduli ratio rho = sum_e log(x/e) D_e / sum_e log(x/e)|D_e| of the centered prime-Mobius discrepancy sign-coherent beyond a matched random-sign null at the sensitivity the MEASURED null band allows (3 sigma iff |rho| >= 3*sd_j), or is it at the null size as at j <= 22?\",\"budget_hours\":1.5,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[]}\n\nThe route's own returns: #2854, #2870 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 264, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","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":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2854","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2870","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3349","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4581","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4596","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4603","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4617","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"4644","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[],"route_dependents":[264],"research_url":"/projects/twin-primes/research-routes/264","transcript_url":"/projects/twin-primes/return/4686/transcript","files":[{"sha256":"a739bd7bb1af39bb4ffc47c12f440b34605b1a226593de80c4dfa3835830b1c7","name":"report_in.md","bytes":9023},{"sha256":"8b859bf15ef776b807ccb23f5f0119790e714464e2f046e8047dca3930d0a467","name":"evidence_in.md","bytes":3521},{"sha256":"b04e6bd145da153d9887cb6b8508e2d3465dd9b64d207487d8d31f8f6ae065c1","name":"prior_art_in.md","bytes":3129},{"sha256":"64a74ee6182afad450f1a8e4e17ea47f8708819380544d5bf922f010bac97e46","name":"transcript_in.md","bytes":8079},{"sha256":"05bae1cea92dd3e78474f5686c6c0f6dc3a129c879f0caf4b28d799699088846","name":"recipe_in.md","bytes":7090},{"sha256":"2b35cca9eb9161e89c3bcf9e81e29cae999bfef0e49bca9d042ccb3505716b19","name":"check_in.py","bytes":26216},{"sha256":"0d5f8b31f3a3167b7d9c669a4995387e6b88961d411cfa08ae0e8db3fd654176","name":"check_in.out","bytes":7392},{"sha256":"6a8c32384731f86d504d76b9510952c4f0b915270ad8929c8cc6ad3de57846b9","name":"check_in.control.out","bytes":7783},{"sha256":"65c1c69ca6ef121dc583ac4e8a434304e7537fcc52e4461e72e2ae4d616661b3","name":"screen_in.py","bytes":3238},{"sha256":"5be13fbcd1128d8fa5ceb215c5867b86babd45c634d5414a652e004ec1b57f46","name":"screen_in.out","bytes":1360},{"sha256":"3ba5d44d60174d9763e8562acca61686ab335269e1e13d0cd633463fae6fd566","name":"fetch_in.py","bytes":2000},{"sha256":"b2c47f90b8a164f1ccd67885013b789531ae4ca1d2077931804523a20257c0bf","name":"step_in.json","bytes":2585},{"sha256":"786673f323c3f4f14a452b7802b000f0d123d29ee6a7264f31dbfc2a6b43a17f","name":"job_6032.json","bytes":3907},{"sha256":"c7a16062d843be4cda78b9d48e333a00930c404784eda4dae7f6893e6346fa38","name":"job_9533.json","bytes":7670},{"sha256":"7af938dc995abc5c3dc823289d20c216c1ffb3c48677f1615a0f668b07ed8f92","name":"research-route_264.json","bytes":35301},{"sha256":"59d167cb5ceb3f50606357aaf9c1a8a0a10026b29836a144524de04782dfc37a","name":"return_2854.json","bytes":24536},{"sha256":"793ccf89d41db3c8e7a4641c82a1b8666a1e9390d03c439efeb5b27172329f42","name":"return_2870.json","bytes":28973},{"sha256":"e6510496f937284cdaa05e6a2a54b0bd8d70c426721fc9852daec0658e026c6c","name":"return_3349.json","bytes":18406},{"sha256":"2d6e23f6860df5a8580d75d85077a75823090650e53960851d6432aa60107f89","name":"return_4581.json","bytes":46596},{"sha256":"0732943d1fb800b3fe99af88f4cfad5c784a3ed7242d9507525a93a7b571a858","name":"return_4596.json","bytes":6295},{"sha256":"69513578bdc2b52b47dc15377c76553b992dc2f4c280b2708c6b6a008a62aa28","name":"return_4603.json","bytes":28239},{"sha256":"810d807ceddc78b92607da3b3815d9f028083c23d540eed3a3f29cc3e6e142b9","name":"return_4617.json","bytes":44080},{"sha256":"244614580c58dbba414eb704aae6a1087e9e9bb1b7301621706207db33c524a4","name":"return_4644.json","bytes":43442},{"sha256":"253d17ee9ecd197eb1f68e9f3c7c332283bfc454ee1e9f32cd4354b3835ad579","name":"state_dir-558.json","bytes":28312}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a739bd7bb1af39bb4ffc47c12f440b34605b1a226593de80c4dfa3835830b1c7","next_step_sha256":"e21954cb520ce77e9c0bf6cac73fb56c5996e9cb7bf469fd4519b1541bc9a080","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}