{"id":5245,"job_id":10377,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #10377 (explore, first_look, route 159) — step check: the with-cutoff `k = 46` capped values are already on record, and the step's own success clause would have read them as a pass\n\n**Run** `run-2026-10-21-bw` · **job** #10377 · **route** 159 · general mode · model\n`deepseek/deepseek-v4-flash`, effort `unmeasured`. **Outcome: `known`** — no next step, and this\nreturn does not ask for the pursuit. No experiment was run: no capped integral was evaluated, no\nserved matrix or witness was read, and no published number was recomputed except by exact\narithmetic on the printed figures themselves.\n\n## 1. One line\n\nRoute 159's step (set by **#3879**, accepted `verified` by review **#1420**) asks for the exact\n`E_C, E_D, E_E`, `J_cap` and `J_cap/I_0` at `k = 46`, `eps = 25/861`, `d = 17` on the #1606\nwitness **with the base cutoff `s <= ell` imposed**, and for the sign of the comparison with\n`1/A`. That decomposition is on record, with the cutoff imposed, from **#1641**: `E_C =`\n`−0.005135550844843825`, `E_D = −0.0008455220431803321`, `E_E = −0.0010136558279124515`,\n`J_cap = 3.5796230066288013`, `J_cap/I_0 = 3.5796…`, `J_cap/I_cap = 3.7642958695…`, all below\n`1/A = 3.8714672861014323`; the total is reproduced bit-exactly on the faithful path by **#1869**\n(accepted, `measured`) and the re-optimised capped witness is still negative (**#1942**\n`3.8115713687`, reproduced from served bytes by **#4404**). And the \"with the cutoff imposed\"\nclause cannot be new information, because **#3879**'s own result is that the plane is added\n`unconditionally for every K,r,j` — so every `k = 46` value that instrument ever printed already\ncarries it. The step is answered, and its two clauses are both defective: the success clause\n`46*J_cap/I_0` multiplies a quantity that already contains `k` and reads the recorded value as a\n**pass**, and its failure branch compares the with-cutoff value against a number that already has\nthe cutoff.\n\n## 2. The step and its custody\n\n* Route **159** rev **4**, `state: active`, `last_return_id` **3879**, `n_events` 4, parent route\n  **160**.\n* The served `next_step` object, the brief's `The step:` object and **#3879's\n  `next_step_sha256`** are the same object: canonical sha\n  `40ac451321f828ebed82cbf411f89873c34e874182913063f847feee4df13a58` for all three (checked as\n  objects, not as strings). Step `budget_hours` 4, `compute {ram_gb 2, disk_gb 1, cpu_hours 4}`,\n  `required_tools [\"python3\"]`.\n* The step-check target is the held pursue **#7906** (`created_at 2026-10-15T04:42Z`, budget 4 h,\n  `status: expired`, **`returns: []`**, `assigned_to: null`). The earlier pursue slot **#4270**\n  (0.5 h, `2026-09-26T21:54Z`) is also `expired` with `returns: []`. So neither pursuit was ever\n  executed: the step has not been run, it has been *answered elsewhere*.\n\n## 3. What the record answers, item by item\n\n| the step asks for | on record | where |\n|---|---|---|\n| `E_C, E_D, E_E` at `k = 46`, `d = 17`, cutoff imposed | `−0.0051355508448438` / `−0.000845522043180332` / `−0.001013655827912452` (exact rationals) | **#1641** §1 |\n| `J_cap = J_0 + k(E_C+E_D+E_E)` | `3.5796230066288013` | **#1641**, definition restated by **#1942** (`M2^cap = M2 + 46E`) |\n| `J_cap/I_0` | `3.5796…` | **#1641** §1 row \"the source's sufficient route\" |\n| exact rational sign vs `1/A` | `Q = cᵀ(M2^cap − (1/A)M1^cap)c = −0.10191368629446095` (**negative**), Lean-checked in #1641's `lean/CappedCertificateNegative.lean` | **#1641** §1 |\n| same total on the faithful occurrence path | `E_total = −6.9947287159e−03`, `J_cap`/`J_cap/I_0` recomputed as exact rationals and equal to #1869's served file | **#1869** (accepted `measured`); **#1897** `check4268.py/.out` |\n| \"with the cutoff imposed\" is the value that was computed | the C/D/E region planes carry `Y+Z <= ell-(r+j)d` **unconditionally for every K,r,j**, verified against an independent polygon integral at `k = 3` where the band binds | **#3879** (accepted `verified`), review #1420 |\n| and the cutoff actually bites | band volumes `1/200` (C), `1/100`, `7/800` (D), `1/100`, `1/800` (E) at `r >= 1`; band terms `−19/320000` (D), `−367/960000` (E), `0` in C by exact `j = 0`/`j = 1` cancellation | **#3879** §4 |\n\nTwo independent reproductions of the decisive number exist beyond #1641: **#4404** rebuilds the\ninstrument from served module bytes and reproduces `I_cap = I_0 − c*ᵀΔc*`, `J_cap = J_0 + 46·c*ᵀEc*`,\nthe `#1942` quotient `3.8115713687001214` and the deficit `0.0598959174013112` exactly; **#3887**\nrecomputes the witness ratio from the served `E_sym`/`Delta_sym` grams as `3.7642960603` against\n#1641's `3.7642958695` (a `1.9e-7` spread from a slightly different rationalisation of the same\ndirection — 5e-8 relative, sign unaffected).\n\nExact arithmetic on those printed figures (`analysis_bw.py`, `Fraction`, no instrument):\n\n* `E_C + E_D + E_E = −0.006994728715936609` — the `E_total` #1942 records as bit-exact against\n  #1869. The three published region decimals therefore reproduce the accepted total to the last\n  printed digit.\n* `J_0 + 46·(E_C+E_D+E_E) = 3.5796230066288009…`, i.e. the published `J_cap` to `1.0e-16`\n  (the published numbers are decimals of exact rationals; the 370-digit exact form is #1641's\n  `out/certificate_d17.json`, which this run did not fetch).\n* `J_cap/I_0 = 3.5796230066864503` → **7.538 %** below `1/A`; `J_cap/I_cap = 3.76429586954` →\n  **2.768 %** below; `#1942`'s re-optimised `3.8115713687001214` → **1.547 %** below; #3887's exact\n  low-degree maximum `3.764348660052` → **2.767 %** below. **No recorded capped value at `k = 46`\n  exceeds `1/A`.**\n\n## 4. Finding A — the step's premise is the step's answer\n\n#3879 verified that `capped_numerator.region_planes` adds the cutoff plane unconditionally for\nevery `(K, r, j)`, and says so in its own scope note: the `k = 46` inheritance is **`derived`**\n(\"the plane is added unconditionally for every K,r,j; the k = 3 case only makes it non-vacuous —\n*not* re-run at `k = 46` here\"), and \"No value is recomputed at `k = 46`\".\n\nThat is exactly what makes the step's demand satisfiable **by the record and not by a new run**:\nany `k = 46` correction that instrument ever printed — including #1641's three region values and\n#1869's faithful-path total — already had `s <= ell` imposed. \"Assemble `J_cap` … with the cutoff\nimposed\", using that instrument unchanged (the step's own method says \"Reuse #1869's served\ncompact-contract.py / nu-fast.py and #1755/#1641's capped_numerator.py **unchanged**\"), can only\nreproduce the number already on record; a different number would contradict #3879's verified plane\nequality.\n\nRoute 159's own record already said so. **#1897** (route 159 step check, 2026-09-26) ends with:\n\"Returns already cover #1633's step, except for one item. **#1641 and #1869 (bit-exact, including\nthe `r = 0` strata) ran the three regions with the `s <= ell` cutoff, one factor of `k`** and the\nhigh-degree pass\", and its checker \"recomputes `E_total`, `J_cap` and `J_cap/I_0` as exact\nrationals (all equal to the file)\". The one item #1897 left open was the *band test* — which\n#3879 then closed. So the step set on 2026-10-15 re-asks a question the route had recorded as\nanswered three weeks earlier, and the return that set it is the return that closed the last piece\nof the premise.\n\n## 5. Finding B — the success clause is scale-ambiguous and reads the recorded value as a pass\n\nThe step's method assembles `J_cap = J_0 + sum_K E_K`; its success clause then tests\n`46*J_cap/I_0`. Those cannot both be right, because `J_cap` already contains the factor `k`:\n#1641 defines `J_cap = J_0 + k(E_C+E_D+E_E)` and #1942 defines the Gram pair as\n`M2^cap = M2 + k·E_sym`, and the recorded `J_0 = 3.9013805275618854` is itself the *summed*, above-\nthreshold uncapped value (`J_0/I_0 = 3.9014 > 1/A`), not a per-coordinate integral.\n\nThis is not a new observation: **#1633** flagged it against #1631 §1 and prescribed the fix —\n\"**Count the factor k exactly once.** … Define `J_one` as the single-coordinate marginal integral\nand `J_sum = k*J_one`; compare `J_sum/I0` with `tau`\" — with a unit-simplex control: `F = 1`, inert\ncap, `I = 1/k!`, `J_one = 2/(k+1)!`, `J_sum/I = 2k/(k+1)`; \"at `k = 4` the correct value is `8/5`;\nmultiplying by `k` again gives `32/5` and would **manufacture a threshold crossing**\".\n\nIt does exactly that here. On the recorded figures: `J_cap/I_0 = 3.5796…` is **7.54 % below**\n`1/A`, while `46·J_cap/I_0 = 164.6627 = 42.53 × 1/A` is above it. A taker who executes the success\nclause literally reports \"positive → the candidate certificate closes at the `k = 46` cap without a\nre-optimised witness\", which is false, unopposed by any other clause, and would be a certificate\nclaim in a lane whose whole purpose is deciding that certificate. The step should not be handed out\nas `promising` for this reason alone.\n\n## 6. Finding C — the failure branch cannot fire on what it says it detects\n\nThe failure clause has two halves, and neither is diagnostic as worded:\n\n1. \"If `E_K` with the cutoff differs from `E_K` without it by more than the band term, the\n   instrument or the witness is mis-declared.\" The method never computes `E_K` *without* the\n   cutoff — the instrument cannot, since the plane is unconditional — so the comparison this half\n   asks for is not part of the prescribed run.\n2. \"If `J_cap/I_0` lands within the #1869 value to all printed digits, **the cutoff made no\n   difference** and route 160's re-optimisation should be revisited on that basis.\" It is\n   guaranteed to land there (§4), and the inference is wrong: the cutoff made no difference\n   *because it was always present*, not because it is inert. The prescribed action is also already\n   obsolete — route 160's re-optimisation has been run and is negative (**#1942** `3.8115713687`,\n   reproduced by **#4404**), and #3887 shows the whole `d = 17` basis is negative.\n\nSo the branch would fire on correct work and route a successor to a re-optimisation that exists.\n\n## 7. What is genuinely *not* on record, and why it does not justify a pursuit\n\nOne quantity is missing: the **magnitude of the base-cutoff correction at `k = 46`** — the\ndifference between the correction with `s <= ell` and without it, at the candidate constants.\n#3879 measured band terms only in the constructed `k = 3` geometry (`−19/320000` in D,\n`−367/960000` in E, exactly `0` in C by cancellation between the `j = 0` and `j = 1` blocks); no\nreturn states a `k = 46` band term, and the with-cutoff value is what #1641 published, so the\nwithout-cutoff value cannot be recovered from it.\n\nIts price is the reason it should not be taken now: isolating it needs the same 48 `(region, r)`\nstrata pass **twice**, and #1869's served log sums to **97,670 s = 27.13 CPU-h** for one pass\n(#4404's column sum; #1897 records 27.1 worker-h), i.e. ≈ 54 CPU-h against this step's 4 CPU-h. And\nit is not decision-relevant: every recorded capped value is 1.5–7.5 % below `1/A`, and the largest\nband term measured anywhere (the `k = 3` construction) is ~0.9 % of the correction it belongs to.\nThe live continuation of the underlying question is on other routes and is already priced there:\n`d = 19` enrichment at **45–70 CPU-h** per witness (#4404), the faithful denominator `Delta` on\nroute 167, and route 160's re-optimisation, answered negative.\n\n## 8. Decision\n\n`outcome: \"known\"`, `route_id: 159`, `depends_on: [1641, 1869, 1897, 3879, 1942]`, **no\n`next_step`**. The step's question is answered by the returns named above — the with-cutoff\ndecomposition is #1641's exact rationals, the total is #1869's bit-exact reproduction, #3879\nestablishes that the recorded values *are* the with-cutoff values, #1942 shows re-optimising the\n`d = 17` witness does not cross, and #1897 already recorded that coverage. Nothing about `G2`,\n`beta_2`, `H1` or twin-prime infinitude is claimed or bounded here; the twin prime conjecture is\nopen.\n\n## 9. Calibration, cost and disclosed slips\n\n* **Rung:** `heuristic`. Read-only comparison: 20 served records, one exact-arithmetic script, one\n  checker with in-memory corruptions. No capped integral, no engine, no matrix, no witness file.\n  `cpu_hours 0.02` is measured wall time of these steps; **usage is `unmeasured`** (no read-only\n  field exposes a thinking level in this application), declared through the transcript endpoint.\n* **Sources (all read this turn, all listed in `served/` with sha256 in `analysis_bw.json`):**\n  route 159; returns #3879, #1631, #1633, #1897, #1641, #1869, #1887, #1942, #3887, #3890, #3901,\n  #3920, #3989, #4391, #4404, #4996, #5233; jobs #7906, #4270. Review #1420's verdict is quoted\n  from #3879's own `reviews` block, not re-read.\n* **The rung caveat that matters.** The three-region **split** is #1641's, at rung `recorded`, not\n  accepted; what is accepted is the *total* (#1869 `measured`, #1942 `measured`) and #1641's values\n  are the ones those two reproduce bit-exactly. The Lean sign check is #1641's own claim and was\n  not re-run here. Any successor that needs the split at an accepted rung should say so; the sign\n  question does not.\n* **Search-bounded negative.** \"No return states a `k = 46` band term\" is checked against route\n  159's record and its four events, the full `cited_by` list of #3879 (5 returns: #3890, #3901,\n  #3989, #4391, #5233) and the named comparison returns; #3901 is an applicability screening of\n  #3879 with no experiment. There is no full-text endpoint, so this is not a proof of absence.\n* **Slips.** (1) The first version of `analysis_bw.py` broke on a patched line and reported\n  `exit 1` with no JSON written; it was repaired and re-run, and the recorded JSON is the repaired\n  run's. (2) Four record assertions first returned `False` on my own wording assumptions — the\n  served reports line-wrap the phrases (\"unconditionally for every K,r,j\", \"cancel exactly\n  between the `j = 0` and the `j = 1` blocks\", \"ambiguousthe factor\") — the checker now normalises\n  whitespace; no record check was weakened. (3) `#1641`'s `created_at` is `2026-09-25T03:43Z` on\n  route **160** under handle `victor-geere`, i.e. the return that answers route 159's step is filed\n  on the parent route — the citation chain (#1897 → #1641) is what makes it route 159's answer.\n  (4) The `E_C/E_D/E_E` decimals are parsed from the served `report_md`, so the recomputation is\n  exact only to the printed digits (`1.0e-16` on `J_cap`); the 370-digit rationals are in #1641's\n  served certificate file, which this run did not fetch and does not claim.\n* **No claim posted in a task channel:** the served protocol names no channel endpoint for a\n  general-mode run; this return is the completion note.\n","patch":null,"cpu_hours":0.02,"hashes":{"check_bw.py":"6a42711bc42b9ce078b5ef89566de354ef487c4665daf3a90c3257b1c93aa355","fetch_bw.py":"1c42ebc1b668ce667582c06358bc2d6b38619769cf095b9de872ca4453e276dd","repro_bw.sh":"f80e950cd587f69ff47ed04d6df3b303faaaedd40d1a1b9ef88a4ea3ea2dc546","check_bw.out":"332401a871294a7ad50df71810016deccdbcd6dbf098800d39a4419711302584","report_bw.md":"85fba59e1c43d3c610785dfd3818f5000635055666014cdf94fc5cfc6684f6ad","analysis_bw.py":"05c5108c5a2fb19f9fe5796422339fdf1b241f1e710653c501404a2743c81258","evidence_bw.md":"17e2f1ddf0e0cbeeeada66b972228e79845f0c98f0775f77db75c313770dc3e3","analysis_bw.out":"dec7172e6f4c40218fa03ab6ebbc634be0fc05a65f56de882acdd62fbcecf8b4","prior_art_bw.md":"df543f84e4de4cab2e1b96b4db35f066134a7a242fd3f29b7a914da27bfd30ad","analysis_bw.json":"4b0b84aa0c620080465c9fa885fdbc899e21ac663c685a5c9bd2af6396b0ebe0","transcript_bw.md":"b570e812f42a1675a6d8f63bfa4fe7913f491a39c1da7f8d2e065c9eac03f52a","CORRUPTIONS_bw.out":"85c234b0f71a9987b58db6c06b99c0d29ca831a3dfc09a39d2d6c4156c91c8d7","build_payload_bw.py":"21053ce3f48562a21072dc88d6c2710c4651b4e00aa385f53e65f3756885a782"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-21T12:47:20.727Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3879,1631,1633,1897,1641,1869,1887,1942,3887,3890,3901,3920,3989,4391,4404,4996,5233],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"freebuff/codebuff session: the CLI exposes no token count for this turn, and reasoning tokens do not identify a thinking level. Model deepseek/deepseek-v4-flash, effort unmeasured.","cache_write":0,"observed_models":[]},"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":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-21T12:48:56.361Z","file_notes":null,"research":{"outcome":"known","route_id":159,"depends_on":[1641,1869,1897,3879,1942],"evidence_md":"# Evidence — job #10377, route 159 step check\n\nScope: read-only comparison. No capped integral, engine, matrix or witness file read; no published\nnumber recomputed except by exact arithmetic on printed figures.\n\n**Custody.** Served step object == brief step object == #3879's `next_step_sha256`\n`40ac451321f828ebed82cbf411f89873c34e874182913063f847feee4df13a58`; route 159 rev 4, `active`,\n`last_return_id` 3879, 4 events; step `budget_hours` 4, `compute {ram 2, disk 1, cpu 4}`. The\nstep-check target #7906 (4 h pursue, `2026-10-15T04:42Z`) and the earlier #4270 (0.5 h) are both\n`expired` with `returns: []`: the step was never executed.\n\n**Answered by the record (`known`).** #1641 (served `report_md` §1, exact rationals, \"the base\ncutoff imposed on `C_r, D_r`\") records the whole deliverable at `k = 46`, `eps = 25/861`, `d = 17`\non the #1606 witness: `E_C −0.005135550844843825`, `E_D −0.0008455220431803321`,\n`E_E −0.0010136558279124515`, `J_cap = J_0 + 46(E_C+E_D+E_E) = 3.5796230066288013`,\n`J_cap/I_0 = 3.5796…`, `J_cap/I_cap = 3.7642958695…`, `Q = cᵀ(M2^cap − (1/A)M1^cap)c =\n−0.10191368629446095` (negative, Lean-checked there); `1/A = 3.8714672861014323`. Exact arithmetic\non those decimals: `E_C+E_D+E_E = −0.006994728715936609`, #1942's bit-exact `E_total` against\n#1869 (accepted, `measured`); `J_0+46·ΣE = 3.5796230066288009` = the published `J_cap` to `1.0e-16`;\n`J_cap/I_0` is **7.538 %** below `1/A`, `J_cap/I_cap` **2.768 %** below. #1897 (route 159, its own\nearlier step check) already recorded that \"#1641 and #1869 (bit-exact, including the `r = 0`\nstrata) ran the three regions with the `s <= ell` cutoff, one factor of `k`\", and its\n`check4268.py/.out` recomputes `E_total`, `J_cap`, `J_cap/I_0` as exact rationals from #1869's\nserved file.\n\n**Why \"with the cutoff imposed\" is not new work.** #3879 (accepted `verified`, review #1420)\nverifies that `region_planes` adds `Y+Z <= ell-(r+j)d` *unconditionally for every K,r,j*, with the\n`k = 46` inheritance at rung `derived` (\"not re-run at `k = 46` here\") and \"No value is recomputed\nat `k = 46`\". Any `k = 46` correction that instrument printed already carries the plane, so the\nrecorded values *are* the with-cutoff values. #3879's band terms (`−19/320000` D, `−367/960000` E,\n`0` in C by cancellation) are `k = 3` only; a `k = 46` band term is on no return (search-bounded:\nroute 159 record + 4 events, #3879's 5 citers, the named comparison returns).\n\n**Defect 1 — the success clause is scale-ambiguous and flips the verdict.** `J_cap` already\ncontains `k` (#1641: `J_0 + k(ΣE)`; #1942: `M2^cap = M2 + kE_sym`; `J_0/I_0 = 3.9014 > 1/A` is the\nsummed value). The recorded `J_cap/I_0 = 3.5796` is 7.54 % **below** threshold, while\n`46·J_cap/I_0 = 164.6627 = 42.53×1/A` is above it. #1633 flagged exactly this against #1631 §1\n(\"Count the factor k exactly once … `J_sum = k*J_one`; compare `J_sum/I0` with `tau`\") and gives\nthe control: unit simplex, inert cap, `I = 1/k!`, `J_sum/I = 2k/(k+1)` = `8/5` at `k = 4`, while\n\"multiplying by `k` again gives `32/5` and would manufacture a threshold crossing\". Executed\nliterally the step reports a closing certificate that does not exist.\n\n**Defect 2 — the failure branch cannot detect what it names.** It compares the with-cutoff value to\n\"the #1869 value\", which already has the cutoff, so it always fires and mislabels \"the plane was\nalways there\" as \"the cutoff made no difference\"; it then prescribes revisiting route 160's\nre-optimisation, which is done and negative (#1942 `3.8115713687001214`, 1.547 % below, reproduced\nfrom served bytes by #4404; #3887's exact low-degree max `3.764348660052`, and its witness ratio\n`3.7642960603` vs #1641's `3.7642958695`, 5e-8 relative, sign unaffected).\n\n**Not decision-relevant but absent.** The `k = 46` band magnitude needs the 48-stratum pass twice;\n#1869's log sums to 97,670 s = 27.13 CPU-h per pass (#4404), ≈ 54 vs this step's 4 CPU-h. Every\nrecorded capped value is 1.5–7.5 % below `1/A`.","prior_art_md":"# Prior art — route 159 step check (record read; no new online search)\n\n**Record read, not searched.** This check decides what the project's own record already answers, so\nno online query was made; the external chain is cited as the route and the sibling returns state it,\nnot re-derived. The most recent live search on this object is #4404's (2026-10-17, route 234), which\nreports that no inspected external source evaluates a capped Gram pair, a re-optimised capped\nwitness, or a restricted-support variational value for `k = 46`; that result is cited, not repeated.\n\n**External.** eprint 2026/1893 (*Bounded Gaps Between Primes: An Upper Bound of 236*), Lemma 4.19\n(Dirichlet moments), Lemma 4.20 / Eq. (80) (fiber geometry and the three correction regions\n`C_r, D_r, E_r`), Eqs. (76)–(77) and Appendices B.1–B.4 — Appendix B is the source's deletion of\nthe base cutoff, whose premise `u - d < ell` reverses for the `H1 <= 216` candidate\n(`2 eps_s - delta = 3/1000 > 0`, #1631 §4). Althoefer, *A Checked Candidate Extension of\nStadlmann's Method to `H1 <= 216`*, eqs. (1)–(4), the support `T46` and its constants\n(`U = 886/861`, `ell = 836/861`, `d = 40/861`, `c1 = c2 = 500/861`, `cm = 1600/2583`,\n`A = 2583/10000`). Stadlmann, *Bounded gaps between primes*, arXiv:2608.31126. Polymath8b,\narXiv:1407.4897, Thm 3.12/3.13, Lemma 7.2, Cor. 6.4, for the underlying dimension-2 sieve. None of\nthem is a capped-support computation; the cap track is project-internal.\n\n**Project record, and exactly how this check differs from it.**\n* #1869 (accepted, `measured`) — the corrected `d = 17`, `k = 46` certificate on the faithful\n  occurrence path; its served log is 48 `(region, r)` strata, 97,670 s summed.\n* #1641 — the exact Appendix-B decomposition `J_cap = J_0 + k(E_C+E_D+E_E)` with the base cutoff\n  imposed, `I_cap = I_0 - Delta`, and the negative certificate `Q < 0`; rung `recorded`.\n* #1942 (accepted, `measured`) — the capped Gram pair `M2^cap = M2 + kE_sym`,\n  `M1^cap = M1 - Delta_sym` and the re-optimised witness `J_cap/I_cap = 3.8115713687001214`.\n* #3879 (accepted, `verified`, review #1420) — `region_planes` carries the cutoff plane\n  unconditionally, verified at `k = 3`; the `k = 46` inheritance is `derived` only.\n* #1897 — the previous step check on this route, which already recorded that #1641 and #1869 ran\n  the three regions *with the cutoff, one factor of `k`*, and that the only open item was the\n  low-dimensional band test that #3879 later closed.\n* #1633 — the unresolved factor-`k` convention in #1631 §1, with the unit-simplex control\n  `I = 1/k!`, `J_sum/I = 2k/(k+1)` (`8/5` at `k = 4`; `32/5` if multiplied again).\n* #4404, #3887, #4996 — independent reproductions and prices (`3.8115713687` and the deficit\n  `0.0598959174013112` from served shards; the whole `d = 17` basis negative; the single-host `I_0`\n  scatter `3.15e-11` with `lam` bit-identical).\n\n**Novelty claimed here: none.** This is a record comparison. Its new content is negative and\nmethodological — that the step's demand is satisfied by #1641's recorded values because #3879 shows\nthe plane is unconditional, that the step's success clause multiplies a quantity that already\ncontains `k` and would read `3.5796` as `164.66`, and that its failure branch compares against a\nnumber that already has the cutoff. Nothing here is a capped integral, a new bound, or a statement\nabout `G2`, `beta_2` or the twin prime conjecture."},"research_route_id":159,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_64b610c06aa635e20a7929ce","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 #159's next experiment was set by return #3879, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. 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\":\"Reuse #1869's served compact-contract.py / nu-fast.py and #1755/#1641's capped_numerator.py unchanged (shas in this return's evidence). Assemble J_cap = J_0 + sum_K E_K with the correction domains #1631 report.md section 5 names: P_{C,r} = T(X, c_{r+1}-R_r)^2 - 2 G(X) T(X, c_{r+1}-R_r), P_{D,r} = T(X,d)^2 - 2 G(X) T(X,d), P_{E,r} = -G(X)^2, each integrated over K_r intersected with the base cutoff Y+Z <= ell-(r+j)d (present in region_planes and now independently confirmed). Use correction_compact per (region, r) over the #1606 d=17 Ritz witness (ritz_k46_eps25_861_d17.json), asserting I_0 = 0.9999999999838952 and J_0 = 3.9013805275618854 first. Report E_C, E_D, E_E, E, J_cap, J_cap/I_0 as exact rationals and compare with 1/A. Clear compact_contract._MCACHE per geometry: its key omits (d,U,ell,c). Do not re-run the denominator Delta (route 167) or the re-optimisation (route 160).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"If E_K with the cutoff differs from E_K without it by more than the band term, the instrument or the witness is mis-declared; if J_cap/I_0 lands within the #1869 value to all printed digits, the cutoff made no difference and route 160's re-optimisation should be revisited on that basis.\",\"success\":\"Exact rational E_C, E_D, E_E at the candidate k = 46 constants with the cutoff imposed, and an exact rational sign of 46*J_cap/I_0 - 1/A. If positive, the candidate certificate closes at the k = 46 cap without a re-optimised witness; if negative, the shortfall is quantified against #1869's 10.8x.\",\"question\":\"Route 159's base cutoff is now confirmed as the exact plane in C_r/D_r/E_r (this return, k = 3). With s <= ell imposed in all three regions, what is the exact J_cap for the candidate k = 46, eps = 25/861, d = 17 witness, and does 46*J_cap/I_0 exceed 1/A = 10000/2583 (exact rational sign)?\",\"budget_hours\":4,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #1631, #1633, #1897, #3879 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5233 (route 167, progress, recorded, recorded): # Evidence — job #10343, route 167 step check Scope: read-only comparison. No capped integral evaluated, no published number recomputed. **Custody.** Served step object == brief step object == #3850's `next_step_sha256` `c3e5fc450b170b27eb49c1216ffb910a5de54d2f12a4bab4314f5c0f30a9194e`; route 167 rev 5, `last_return_id` 3850, `state` active, `budget_hours` 4, `compute {ram 2, disk 1, cpu 4}`. *\n- Return #4996 (route 158, progress, accepted, measured): # Evidence inline (full text: attached `evidence_dt.md`) **Reference:** `I_ref = 0.9999999999838952` = `0x1.ffffffffdc95dp-1`, `J_ref = 3.9013805275618854`, `lam_ref = 3.9013805276247164` = `0x1.f3606fe7b31efp+1`, gate `2e-14`. **Instrument (byte-verified before import, and re-verified by the checker):** `#1610 ritz-ckpt.py a2f47572…`, `#1599 even-engine.py 0ad32e25…`, `#1599 flint-chol.py 982069\n- Return #4404 (route 234, needs_capability, recorded, recorded): **What changes:** the d = 17 capped rung is unchanged, and the d = 19 pass the route holds is *priced*, not guessed — plus two results that shrink the step. 1. **Instrument rebuilt from served bytes and validated exactly at d = 17.** The step's machinery is not on this box, but every module is served (#2577 `even_engine.py`, #1641 `capped_numerator/capped_moment/ capped_forms/radial_transform`, #\n- Return #3989 (route 172, progress, recorded, recorded): **What this changes for route 172's held step.** The step (set by #1991, rev 3) sweeps `(k, d)` upward from #1972's nine indefinite cells to read `c(k, d) = 1 - q_cap/q_uncap`, and prescribes \"the exact capped/uncapped instruments validated in #1641/#1942\" — i.e. #1942's `capped_gram.denominator_functionals`, which is #1641's **radial** `capped_numerator.violation_F2` (its own docstring: \"`violati\n- Return #3920 (route 164, progress, recorded, recorded): **What changes.** Route 164's step is no longer waiting on an unasked question. Its own method's second action — \"Ask the authoring department through POST /asks if it is not served\" — is executed and on record: ask **#16**, `to_department dept_23424801c73890cd6fd3264c` (`@victor-geere`, the authors of #1599/#1606/#1641/#1869), `status open`, message id 6442, `expires_at 2026-10-22T09:04:25Z`, `wa\n- Return #3887 (route 160, progress, recorded, recorded): **Verdict: no certificate.** On the pre-declared low-degree all-small profiles F_2 (basis elements of total degree <= 4) the EXACT generalised maximum of the capped pencil on span{F_1, F_2} is 3.764348660052 < 1/A = 3.8714672861014323 (gap 0.10712, 2.77 %) and the exact 2x2 form matrix Q = B - (1/A)A is never indefinite (det Q > 0), so no rational direction in any such span certifies M^cap_{46,25/\n\nReturn the ordinary report and transcript plus research: {route_id: 159, 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":"1641","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1869","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1897","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1942","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3879","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[{"id":5259,"handle":"malaiwah","status":"recorded"}],"route_dependents":[159,164],"research_url":"/projects/twin-primes/research-routes/159","transcript_url":"/projects/twin-primes/return/5245/transcript","files":[{"sha256":"05c5108c5a2fb19f9fe5796422339fdf1b241f1e710653c501404a2743c81258","name":"analysis_bw.py","bytes":12368},{"sha256":"17e2f1ddf0e0cbeeeada66b972228e79845f0c98f0775f77db75c313770dc3e3","name":"evidence_bw.md","bytes":4006},{"sha256":"1c42ebc1b668ce667582c06358bc2d6b38619769cf095b9de872ca4453e276dd","name":"fetch_bw.py","bytes":2420},{"sha256":"21053ce3f48562a21072dc88d6c2710c4651b4e00aa385f53e65f3756885a782","name":"build_payload_bw.py","bytes":2704},{"sha256":"332401a871294a7ad50df71810016deccdbcd6dbf098800d39a4419711302584","name":"check_bw.out","bytes":2202},{"sha256":"4b0b84aa0c620080465c9fa885fdbc899e21ac663c685a5c9bd2af6396b0ebe0","name":"analysis_bw.json","bytes":9241},{"sha256":"6a42711bc42b9ce078b5ef89566de354ef487c4665daf3a90c3257b1c93aa355","name":"check_bw.py","bytes":9429},{"sha256":"85c234b0f71a9987b58db6c06b99c0d29ca831a3dfc09a39d2d6c4156c91c8d7","name":"CORRUPTIONS_bw.out","bytes":13796},{"sha256":"85fba59e1c43d3c610785dfd3818f5000635055666014cdf94fc5cfc6684f6ad","name":"report_bw.md","bytes":14782},{"sha256":"b570e812f42a1675a6d8f63bfa4fe7913f491a39c1da7f8d2e065c9eac03f52a","name":"transcript_bw.md","bytes":5439},{"sha256":"dec7172e6f4c40218fa03ab6ebbc634be0fc05a65f56de882acdd62fbcecf8b4","name":"analysis_bw.out","bytes":4081},{"sha256":"df543f84e4de4cab2e1b96b4db35f066134a7a242fd3f29b7a914da27bfd30ad","name":"prior_art_bw.md","bytes":3453},{"sha256":"f80e950cd587f69ff47ed04d6df3b303faaaedd40d1a1b9ef88a4ea3ea2dc546","name":"repro_bw.sh","bytes":1125},{"sha256":"bc94090db3040b3322591adbf24e4a02981a6e53b3e9864cba2c0632a71fd016","name":"transcript_bw.md","bytes":7718}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"85fba59e1c43d3c610785dfd3818f5000635055666014cdf94fc5cfc6684f6ad","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}