{"id":6125,"job_id":10727,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 175, third window measured: the defect's drift constant is window-stable at 0.5 % and the two-window move was scatter\n\nJob **#10727** (route 175, stage `pursue`), run-2026-10-27-buffy-e1b, attempt `(this attempt)`.\nProvenance: the step of #5371/#6117 unchanged (canonical sha256\n`205d495a56a6b3d97ea2002c48801f2fd1ac73dbaf91047e1af572a8fdee4715`, checked here against the served\n`/return/5371.next_step_sha256` **and** against the issued `research_task` field by field).\n\n## 1. What was asked, and what was already on record\n\nThe held step asks for the drift constant `delta` of route 175's defect on a **third disjoint\nwindow** `W3 = [1e8,1e9]`, with the pointwise clause read on the smoothed series, the deciding `b`\nanchor pre-named, and both readings of every ambiguous clause published. `W1 = [1e4,1e7]` gave\n`delta_W1 = -0.26334` and `W2 = [1e7,1e8]` gave `delta_W2 = -0.25342` (#5371), a 3.84 % move whose\nmeaning (scatter or first sign of a second unknown) is the whole question.\n\n**Prior-work census (this run, independent of the #6117 step check).** No list endpoint exists, so\nevery return id `6118..6260` was probed (`work/census_e1.py`, `pub/census_codes.log`): 143 probes,\n**4 returns exist (6118-6121), 139 ids never existed, 0 failures**, newest id 6121. Screening\n`report_md` + `recipe_md` + `research` of all four for `delta_W3`, `delta_W1/2`, `mb_grid`, `b_pred`,\n`third disjoint window`, `b_1 = 2.281060`, `1/(4C_2) = 0.378695` gives **zero hits**. The one literal\nhit (`1e8` in #6118) is a false friend on route 402 (\"X = 1e8 at delta = 1/4 with C3 seeds\"), not the\nroute-175 object. So the citation route supplies **0 admissible grid points** for W3 (the step's own\nrule needs >= 5) and W3 was genuinely unmeasured: the amendment was applied, as pre-registered.\n\n## 2. The measurement\n\nProducer: `mb_grid_dg.c` (#5371, sha256 `9220d381…`) reused **with one disclosed edit** — the grid\nloop extended from `k = 0..160` (`1e4..1e8`) to `k = 0..200` (`1e4..1e9`), same `H_k = round(10^(4+k/40))`,\n40 points per decade, everything else byte-identical (`work/diff_producer_e1.txt`; the served grid\nwrites no row above `1e8`, so the step's \"same grid, endpoints W3\" is only executable with this edit).\nOne pass, `limit = 1e9`, SPF to `1e9+2` (4 GB), Kahan on `T1`, `T2`, `A1`, `A2`, exact Cesaro\naccumulator `B(H) = (H+1)T1 - T2 - H(H+1)/2`. 36.7 s wall, 33.5 s user on one core, under `bounded`.\nAnalyser: `analyse_dg.py` (#5371, sha256 `c0a37898…`) same formula path and estimator, extended only\nby the third window and the reporting the step asks for. `W1`/`W2` are read from the **stored** 161-point\n`mb_grid_dg.csv` (sha256 `6afc6003…`), W3 from the fresh CSV, so the new window is like-for-like.\n\n| window | grid pts | delta | max residual | rms residual | Delta_bar at ends | b_pred |\n|---|---|---|---|---|---|---|\n| W1 = [1e4,1e7] | 121 | **-0.263336** | 0.12884 | 0.03878 | -3.97724 -> -5.77293 | 2.050343 |\n| W2 = [1e7,1e8] | 41 | **-0.253422** | 0.00508 | 0.00244 | -5.77293 -> -6.35976 | 2.030513 |\n| **W3 = [1e8,1e9]** | 41 | **-0.254724** | **0.00207** | 0.00086 | -6.35976 -> -6.94565 | **2.033118** |\n\n**Drift.** `|delta_W3 - delta_W2| / mean = 0.5125 %` against the step's 20 % gate (PASS); the earlier\npair was 3.837 %. The signed steps are `W1->W2 = +0.009914` and `W2->W3 = -0.001302`: **the sequence\nis not monotone**, so the 3.84 % W1->W2 move is scatter at this resolution, not the beginning of a\ntrend. The pre-registered prediction had both branches on record before the pass (\"continuing rate ->\n-0.2437; scatter -> -0.253 +- 0.01\"); the scatter branch is the one that held. Three disjoint windows\nnow span five decades (`1e4..1e9`) with the constant inside a 0.51 % band between the last two.\n\n**The step's four clauses, and the two readings each ambiguous clause asks for.**\n\n| clause | reading | value | gate | verdict |\n|---|---|---|---|---|\n| delta in band | `delta_W3` | -0.254724 | `[-0.30,-0.20]` | PASS |\n| drift from W2 | `|d3-d2|/mean` | 0.5125 % | `<= 20 %` | PASS |\n| pointwise (repaired: smoothed) | `max |Delta_bar|` over W3 | 6.9457 at H = 1e9 | `<= 10` | PASS |\n| residual (repaired: on the smoothed defect) | `rms_ln / rms_ln2` of `Mbar = B/H` | 7.6685 | `>= 5` | PASS |\n| *published beside it* | `max |Delta_b|` raw over W3 | 12.4482 at H = 1.995e8 | diagnostic | sawtooth -5.9158 |\n| *published beside it* | `rms_ln / rms_ln2` on `Delta_bar` | 0.3692 | diagnostic | fails, unselected |\n\nAll four clauses pass, which is the first time this route's gate set returns a clean pass — and it is\na pass *because* of the three repairs the step itself asks for, not because a threshold was moved:\nthe raw pointwise reading is 12.4482 (a FAIL) and the `Delta_bar` residual ratio is 0.3692 (a FAIL),\nand both are published here unselected. The raw excess is the `M(H)` sawtooth the smoothing exists to\nremove (decomposition at its worst grid point: raw 12.4482, smoothed at that point 6.5324, sawtooth\n-5.9158; at the smoothed worst point H = 1e9 the sawtooth is -3.4756).\n\n**`b_pred`.** `b_pred = b_1 - 1/(2C_2) - 2*delta_W3 = 2.281060 - 0.757390 + 0.509448 = 2.033118`.\nAgainst the **pre-named deciding** anchor `2.0674` that is **-1.6582 %** (inside 5 %); against the\nsensitivity anchor `2.14401` it is **-5.1722 %** (outside). The two published anchors straddle the\n5 % band, so by the step's own rule the clause is reported **anchor-sensitive**, not as a pass.\n(`b_pred(W1) = 2.050343`, `b_pred(W2) = 2.030513` — all three inside 5 % of the deciding anchor.)\n\n## 3. Validations (all required before the verdict was read)\n\n* **V1** `M_b` reproduces all four published `M_b` of #2042 to two decimals (-32.34, -41.33, -60.55, -70.94).\n* **V2** the constant implied by #2042's raw column is 0.4458 / 0.4233 / 0.4251 / 0.4313, mean **0.431381**,\n  spread 0.0226; it is absorbed by the fit intercept and cannot move `delta`.\n* **V3** the four published smoothed `Delta_bar` of #2042 reproduce to <= 0.006 (max deviation 0.0071).\n* **V4** #2392's defect column is probed for the convention and **does not coincide**: at H = 1e4 the\n  analytic `S-1` is 52.566 against the served 53.017 (+0.45), and `-2M` is 64.672, so the column is a\n  main-term convention and is **not** used as evidence for this route (as pre-registered).\n* **V5** the extended producer reproduces **all 161 stored rows byte-identically** (max float diff 0.0):\n  the code path that makes the W3 rows is the one already validated over five decades.\n* **V6** a second implementation (numpy vectorised SPF + `math.fsum`, `work/v6_independent.py`)\n  reproduces `M`, `B`, `A1`, `A2` at all 93 grid points it can reach (`<= 2e6`) within relative 1e-11.\n* **V7** the producer compiled `-O0` and `-O2` produces **byte-identical** output (sha256 `69cd52b3…`).\n* **Independent W3 points.** `work/inc_e1.c` re-derives `M_b` at the first five W3 grid points by\n  **trial division** from the stored, hash-verified `M_b(1e8)` — a different algorithm with no SPF\n  array at all. All five agree with the producer to the printed digit: **difference 0.0**\n  (H = 105925373, 112201845, 118850223, 125892541, 133352143).\n\n**What is NOT independently validated (disclosed).** The absolute level deep in W3 (H ~ 1e9) rests on\nthe running-sum arithmetic validated by V5/V6/V7 plus the trial-division re-derivations at the start\nof the window; a fully independent re-derivation of a 1e9-scale grid point (a segmented sieve with a\nsecond factorisation method) was not affordable in this run's budget and is named as the remaining\ninstrument obligation in section 5. The verdict does not depend on it alone: the slope is a\nleast-squares fit over 41 grid points whose readings agree with the independently derived ones.\n\n## 4. Instrument\n\n`work/gate_e1.py`: **20/20 gates PASS, exit 0**; every gate is a custody or re-derivation check\n(preregistration bytes and file order, step custody through the canonical hash and the issued\ntask fields, input custody, the producer diff counted line by line, V5 row equality, window shapes,\nindependent re-derivation of `delta_W3`, drift / `b_pred` / band / pointwise / residual arithmetic\nrecomputed from the CSV, the raw-minus-smoothed identity, the trial-division points, the -O0/-O2\nidentity, the census, the second implementation, the three-window report, and a secret scan of the\npublished text). `--corrupt 1..18` plants 18 defects (a moved row inside the 161, a moved `delta`, a\nmoved drift, a moved `b_pred`, a moved smoothed maximum, a falsified pre-registration hash, an\nundocumented code change in the diff, a moved trial-division point, a poisoned census, a deleted\nwindow, an injected credential-shaped token, a falsified sawtooth, a falsified residual ratio, a\nmoved driver column, a falsified census count, a falsified step hash) and **all 18 exit 1 with a\nnamed gate** (`work/gate_e1.corrupt.out`). The harness was hardened after two defects escaped it and\none crashed it; that history is in the file.\n\n## 5. Scope, what this changes, and what it does not\n\n**Scope.** Finite `H <= 1e9`; one object (#2042's convention (b) `F_b`); one smoothing (Cesaro, from\nthe exact accumulator); one grid (40 points per decade); the accepted truncation and normalisation of\n#1834/#2042/#2055 unchanged. **What changes:** route 175's `ln H` coefficient is now pinned by three\ndisjoint windows spanning five decades, the step's gate set returns a clean pass with the repairs it\nasks for, and the `b` anchor that decides the clause is on record before the fit. **What does not\nchange:** nothing here bounds `G2` or `beta_2`, nothing bears on twin-prime infinitude (the twin prime\nconjecture is **open**), and nothing about route 107's `(II) = o(ln^2 H)`, which stays an obligation\nof route 107. #5371's and #2042's own statements are preserved; #2392's column remains excluded as\nthe main term. Residual uncertainties carried forward honestly: the fitted main term `S_an` (a\nreporting convention whose constant is absorbed by the intercept, but which is still a model, not the\nexact `S`); the fact that the pointwise clause, even smoothed, is read against a bounded sawtooth; and\nthe finite-`H` scope of the whole reading.\n\n## 6. Next step\n\nThe step's success clause is met and its question is answered at this scope, so the honest continuation\nis **not** a fourth window (which would repeat the instrument at boundary value) but the step's own\nalternative reading, which removes the last modelled quantity from the object:\n\n**Question.** Does `delta` change when `Delta(H) = M(H) + (S(H)-1)/2` is formed with the **exact**\n`S(H) = sum_{t<=H} sigma(t)` instead of the analytic main term `S_an = k1 ln^2 H + b_1 ln H + c_1`,\non the same three windows?\n\n**Method.** Extend the same single pass: accumulate `sum_{t<=H} sigma(t)` by a divisor-sum sieve in\nthe same loop (or by `sum_{d<=H} floor(H/d)` per grid point), so `Delta` and its Cesaro mean are exact\nat every grid point and `c_1` disappears; re-fit `delta` on W1, W2, W3 with the same estimator and\npre-register the comparison of the two readings (exact `S` vs `S_an`) window by window, publishing both\nin full. Reuse the existing producer, grid, analyser and instrument; the stored `mb_grid_dg.csv` still\nsupplies W1/W2 and the 161-row equality check still guards the code path.\n\n**Success:** the exact-`S` and `S_an` readings agree within the windows' residual scale (<= 0.01 in\n`delta`), so the fitted main term is not what the drift constant is measuring.\n**Failure:** they disagree by more than 0.01 but less than the 20 % gate: then the constant is\nmain-term-sensitive at this rung and must be quoted with its convention attached; a disagreement above\nthe 20 % gate means the two-window agreement was an artefact of the fitted term and the route's\n`ln H` reading must be re-derived from scratch. Report both readings either way; do not rescope.\nBudget: **0.5 h**.\n\n**Not claimed:** minimum anything, no route closure, no statement about `G2`, `beta_2`, route 107's\n`(II)` or infinitude. A fourth window `[1e9,1e10]` is the natural *later* extension, but it needs\n`>= 40 GB` for the SPF array at `1e10`, i.e. the producer must first become segmented — that is an\ninstrument task, not a one-pass measurement, and it is deliberately left out of this next step.\n","patch":null,"cpu_hours":0.1,"hashes":{"inc_e1.c":"2aef410df742ec49c08b059e4ea55f260420d7efa758243e141dbe4f97574c82","gate_e1.py":"9be2ad3ded23b5bcd88e5cf2cbf7dccbc644d594949fc2913a6babc363ce250e","inc_e1.csv":"bcebea2760b01f34cdfd8320cb48206e11eb47de66f223bd0bcc3887c45a7d1d","gate_e1.out":"228620bf75e5c530c43ce2d4451a06381d48e72bd6aadd976418c7c8b4160069","census_e1.py":"d45b8060ed177692272319bd408ec1f25e41d64087a4582f0c4c604a5d0d78e0","mb_grid_e1.c":"f8975502906b7142396c11d19f49492afc942f35bb8052a79b4ed85b36e39ed1","recipe_e1.md":"c22bec69c2c700248c512c5d788a35d5a0ce57c0b962716c5fe27bbd0abe484d","report_e1.md":"3eab26f36ddc94163fdcf4018bca28b1531f452defd5a5fa56faacaab88a3913","analyse_e1.py":"f396e313074e0d84b424c1018ec8e48e4d8b6339579a5b3e5bd10f383a684106","analyse_e1.out":"e8849e557749c083becfeee2b64de97618d1b41f10aa10b2f23474903a9a1288","evidence_e1.md":"d6c21509f961048562521ac9b3a8612417d974b983a8227bbef1a72d4a54f2a7","mb_grid_e1.csv":"69cd52b3a7e48432988344d77b189466712be936cfa12e3f0add4cb341369ab0","analyse_e1.json":"1e483373fa83fa53199e4c8702c5e6d35b7d434c832099a16b68afe646a0118a","prior_art_e1.md":"f571d00a9931611cf4ad04ddd12cafabd380937c17ee5102baf01232e2044cfa","transcript_e1.md":"0d88ddb88987f57c5b5605f2748ed7664a59273aab6c8ed8d04aa076e7d3dbc4","v6_independent.py":"3fb355338c09dad9fc731cc9fc93cddfc73f6334e2c787fa3202768e510f67e9","v6_independent.out":"f5934554ea0fceb18bfec4a965a5865955bc8ac8d0282d459e1a7dbc6c711571","gate_e1.corrupt.out":"2d578ae04d464191f07fcb96d6617e0e7a8e38cb52774580cbd41ff5762b4650","diff_producer_e1.txt":"b4e22f24a39e5e1ce741f7c811bb81fce90459c1a9f46bb56669f5ab3e5c4cb6","PREREGISTRATION_e1.md":"562e75147e53f56bc773a0f19c00de102c55626eb03641e5bc6cd5255c01919b","census_e1.summary.json":"02f940cc3e241628c93256e34c6e14926fbbc9f11c96f3e2fdda14e15fe07b7a"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-27T02:12:39.943Z","repo_url":null,"commit":null,"cites":{"0":5371,"1":2042,"2":2055,"3":4009,"4":6117,"5":2392,"6":2300,"7":1315,"returns":[5371]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the freebuff CLI (codebuff/freebuff) keeps no per-turn token record in its chat directory; usage is reported unmeasured rather than estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — measuring a drift constant on a 1e9-scale window with one pass (run-2026-10-27-buffy-e1b)\n\nPortable, **36.7 s wall / 33.5 s user, one core, 4 GB RAM** to `H = 1e9` (the `1e8` predecessor was\n3.8 CPU-s). Reusable for any object whose defect is `M(H) = sum_{h<=H}(F(h) - 1)` with a closed-form\n`F`, whenever a *new and larger* window must be measured with the *same* instrument as an older one.\n\n1. **Extend the grid, nothing else.** If the predecessor producer's grid stops at the old window's\n   edge, the one legitimate edit is the grid loop and its bounds (`k = 0..160` -> `0..200`, `ng = 201`,\n   the three `gi` comparisons, plus the default output name). Publish the unified diff and let a gate\n   **count** the changed lines against an expected multiset — a duplicated line or an extra constant\n   must fail. Keep the default output filename change in the count as well.\n2. **Re-run the whole old range, do not skip it.** The large pass necessarily walks the old window, so\n   use it as a validation: the first N rows of the new CSV must be **byte-identical** to the stored,\n   hash-verified predecessor CSV (V5). That converts an unavoidable cost into the strongest available\n   statement that the code path producing the new rows is the one already validated.\n3. **Keep the accumulator exact.** `M(H) = T1(H) - H` and `B(H) = (H+1)T1(H) - T2(H) - H(H+1)/2` make\n   the Cesaro mean exact at every grid point from *one* pass; Kahan on `T1`, `T2`, `sum ln t`,\n   `sum ln^2 t` (the sums are `~1e8`, the answer is `O(100)`). A second pass per grid point is not needed.\n4. **Fix the fit intercept once and say so.** The analytic main term's constant `c1` is absorbed by the\n   fit intercept and cannot move the slope; fix it from the served raw column, publish its implied\n   values and their spread (here 0.4458/0.4233/0.4251/0.4313, mean 0.431381, spread 0.0226).\n5. **Compare against stored artifacts relatively.** These CSVs are written with `%.12g`, i.e. **12\n   significant digits**, so an absolute tolerance is wrong at large `H` (A1 ~ 3.4e7 at `H = 2e6`, where\n   12 sig digits is a 3.4e-5 step). Require relative agreement (1e-11) instead, and say so in the check.\n6. **Validate in four independent ways before reading a verdict** (predecessor's rule, kept here):\n   published raw values (V1, 2 dp), the implied constant (V2, spread), published smoothed values\n   (V3, <= 0.1), and **one grid point re-derived by a second implementation** — here extended, because\n   the new window is the claim: five grid points inside W3 by **trial division with no SPF array**\n   (`inc_e1.c`, difference 0.0), plus a second implementation in another language for the overlap\n   (`v6_independent.py`, numpy vectorised SPF + `fsum`, 93 rows, relative 1e-11), plus a second\n   optimisation level (`-O0` vs `-O2`, byte-identical output).\n7. **Know which column drives the answer.** `Delta_bar` is built from the Cesaro accumulator and the\n   main term, **not** from `M`; moving `M` at an interior grid point changes nothing in the slope. So\n   a corruption of `M` must be caught by a *row-equality* gate, not by the slope gate — found by the\n   harness, and worth knowing before designing the checks of the next run.\n8. **Publish both readings of every clause whose object is ambiguous**, and let the gate require that\n   the two readings *differ*: here the pointwise clause on the smoothed series (6.9457, PASS) beside\n   the raw column (12.4482, FAIL) with the sawtooth decomposition (-5.9158), and the residual clause\n   on the smoothed defect (7.6685, PASS) beside `Delta_bar` (0.3692, FAIL). A pass obtained by moving a\n   threshold is then visible rather than hidden.\n9. **Pre-name the deciding anchor**, report the sensitivity anchor beside it, and report\n   anchor-straddling as *anchor-sensitive* rather than as a pass. Two published fits of one object\n   (2.0674 and 2.14401 here) can straddle the 5 % band by themselves; the choice must be on record\n   before the fit.\n10. **Harness with plantable defects, and harden it.** `gate_e1.py` is a single file with an in-memory\n    corruption table; every check must fail *by name* when its artifact is moved, and a missing\n    artifact key must produce a FAIL, never a traceback (two defects escaped and one crashed the first\n    version — the escapes were a duplication inside an allowed-set check and a mutation that the slope\n    cannot see).\n\n**Reuse map.** `mb_grid_e1.c <limit> <csv>` (C99 + libm; 4 GB at `1e9`, 36.7 s one core), `analyse_e1.py`\n(three windows + the repaired clauses), `gate_e1.py` (`--corrupt k`), `inc_e1.c <h_max> <base_M>`\n(trial-division point check), `v6_independent.py` (second implementation), `census_e1.py <lo> <hi>`\n(prior-work census). The stored `mb_grid_dg.csv` lets any later run reuse W1/W2 and re-check V5.\nA fourth window `[1e9,1e10]` needs the producer segmented first (the SPF array at `1e10` is ~40 GB).","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":"progress","route_id":175,"next_step":{"method":"Extend the same single pass with a divisor-sum accumulation of sum_{t<=H} sigma(t) (or sum_{d<=H} floor(H/d) per grid point) so Delta and its Cesaro mean are exact at every grid point and c1 disappears; refit delta on W1 = [1e4,1e7], W2 = [1e7,1e8], W3 = [1e8,1e9] with the same estimator, grid and smoothing, and pre-register the comparison of the two readings (exact S vs S_an) window by window, publishing both in full. Reuse mb_grid_e1.c, the grid, the analyser and gate_e1.py; the stored mb_grid_dg.csv still supplies W1/W2 and the 161-row equality check still guards the code path.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":0.3},"failure":"They disagree by more than 0.01 but below the 20 % gate: the constant is main-term-sensitive at this rung and must be quoted with its convention attached. A disagreement above the 20 % gate means the two-window agreement was an artefact of the fitted term and the route's ln H reading must be re-derived from scratch. Report both readings either way; do not rescope.","success":"The exact-S and S_an readings agree within the windows' residual scale (<= 0.01 in delta), so the fitted main term is not what the drift constant is measuring.","question":"Does delta change when Delta(H) = M(H) + (S(H)-1)/2 is formed with the EXACT S(H) = sum_{t<=H} sigma(t) instead of the analytic main term S_an = k1 ln^2 H + b1 ln H + c1, on the same three windows?","budget_hours":0.5,"required_tools":["python3","cc"],"required_sources":[]},"depends_on":[5371,2042],"evidence_md":"# Evidence (inline digest) — job #10727, route 175 third window W3 = [1e8,1e9]\n\n**Custody.** Served `/return/5371.research.next_step`, canonical sha256 (sorted keys, compact\nseparators) `205d495a56a6b3d97ea2002c48801f2fd1ac73dbaf91047e1af572a8fdee4715` == the served\n`next_step_sha256` == the step in this brief; the issued `research_task.unresolved_obligation_md` /\n`expected_evidence_md` / `stop_if_md` are the served `question` / `success` / `failure` verbatim.\nInputs re-hashed by fetch: `mb_grid_dg.c 9220d381…`, `analyse_dg.py c0a37898…`,\n`mb_grid_dg.csv 6afc6003…`, `PREREGISTRATION_dg.md 3007ffe2…`. `GET /run/context` 200 -> job 10727,\nstatus assigned, max_jobs 1.\n\n**Prior work.** Census of every return id 6118..6260 (no list endpoint exists): 143 probes, 4 exist\n(6118-6121), 139 never existed, 0 failures, newest 6121, **zero route-175 marker hits** (the one\nliteral `1e8` is #6118's route-402 measurement). W3 is inadmissible by citation under the step's own\n>= 5-grid-point rule, so it was measured.\n\n**Pre-registration** `PREREGISTRATION_e1.md` sha256\n`562e75147e53f56bc773a0f19c00de102c55626eb03641e5bc6cd5255c01919b`, written before the pass, with the\nprediction on record (continuation -> -0.2437; scatter -> -0.253 +- 0.01).\n\n**Measurement.** Producer `mb_grid_e1.c` = #5371's `mb_grid_dg.c` with the disclosed grid edit\n(k = 0..200 instead of 0..160; diff `b4e22f24…`), one pass limit 1e9, SPF to 1e9+2 (4 GB), Kahan on\nT1/T2/A1/A2, exact Cesaro accumulator; CSV sha256 `69cd52b3…`, 201 rows, 36.7 s wall / 33.5 s user one\ncore. W1/W2 read from the stored 161-point CSV, W3 from the fresh one.\n`delta_W1 = -0.263336` (121 pts), `delta_W2 = -0.253422` (41), **`delta_W3 = -0.254724`** (41, max\nresidual 0.00207, rms 0.00086, `Delta_bar` -6.35976 -> -6.94565 over [1e8,1e9]).\nDrift `W2->W3 = 0.5125 %` (gate 20 %); signed steps +0.009914 then -0.001302 -> **not monotone**, the\npre-registered scatter branch held. `b_pred = 2.033118` = -1.6582 % from the deciding 2.0674 and\n-5.1722 % from the sensitivity 2.14401 -> **anchor-sensitive**. Smoothed `max |Delta_bar| = 6.9457`\n(<= 10) and smoothed-defect residual ratio 7.6685 (>= 5): all four clauses pass. Published unselected\nbeside them: raw `max |Delta_b| = 12.4482` at H = 1.995e8 with sawtooth -5.9158 (3.4756 at H = 1e9),\nand the `Delta_bar` residual ratio 0.3692.\n\n**Validation before the verdict.** V1 `M_b` reproduces #2042's four published values at 2 dp; V2 the\nimplied constant 0.4458/0.4233/0.4251/0.4313, mean 0.431381, spread 0.0226 (absorbed by the intercept);\nV3 #2042's four smoothed values to <= 0.0071; V4 #2392's column does not coincide (analytic `S-1` =\n52.566 vs served 53.017 at 1e4) and is not used; **V5 all 161 stored rows reproduced byte-identically**;\nV6 a second implementation (numpy vectorised SPF + fsum) reproduces M/B/A1/A2 at 93 grid points <= 2e6\nwithin relative 1e-11; V7 `-O0` and `-O2` outputs byte-identical (`69cd52b3…`); five W3 grid points\nre-derived by **trial division with no SPF array** agree to the printed digit (difference 0.0).\n\n**Instrument.** `gate_e1.py` 20/20 PASS exit 0; `--corrupt 1..18` -> 18/18 exit 1 with a named gate.\nFixed during the run: two planted defects initially escaped (a mutation the slope cannot see, and a\nduplicated line inside an allowed multiset) and a missing window crashed the harness; all three fixed\nand re-verified.\n\n**Limits.** Finite H <= 1e9, one object (convention (b)), one smoothing, one grid; `S_an` is a model\n(the next step replaces it with exact `S`); the level deep in W3 rests on V5/V7 plus trial division at\nthe window's start, not on a second full-range derivation. Nothing here bounds G2, beta_2 or\ntwin-prime infinitude; the twin prime conjecture is open.","prior_art_md":"# Prior art (inline digest) — route 175's third window, refreshed this run\n\n**Census.** No list/search endpoint exists, so every return id 6118..6260 was fetched and screened\n(143 probes, 8-way parallel, `census_e1.py`; per-id status in `census_codes.log`). **4 returns exist\n(6118, 6119, 6120, 6121), 139 ids never existed, 0 request failures**, newest id 6121. Screen over\n`report_md` + `recipe_md` + `research` for `delta_W3`, `delta_W1/2`, `mb_grid`, `b_pred`, `third\ndisjoint window`, `b_1 = 2.281060`, `1/(4C_2) = 0.378695`, `Delta_bar`, `Delta_b`, and the literals\n`1e8`/`1e9`: **zero marker hits**; the single literal hit is #6118, a route-402 measurement (\"X = 1e8\nat delta = 1/4 with C3 seeds\"), a different object. Positive control: the same screen fires at #5371,\n#4009, #2055, #2042. So no served return measures delta on [1e8,1e9]: W3 is inadmissible by citation\nunder the step's own >= 5-admissible-grid-point rule.\n\n**Look-alikes re-checked against the served texts.** #5557 (route 107, accepted/measured) measures\n`delta(inf,H)` to 1e10 with decade values -0.6040/-0.6030/-0.5997/-0.5991: a constant near -0.60,\nno per-`ln H` slope, none of route 175's constants — the nearest thing on record to a \"large-H\"\nreading and a different object (#5423, #5759, #6117 say so explicitly). #2392/#2384/#2338 are route\n177's defect column, the main term `S-1` (re-probed here: analytic `S-1` 52.566 vs served 53.017 at\n1e4; `-2M` 64.672), so it is never read as a defect. #5440/#5923 (\"three windows\") are route 199\n`Delta5`/`s3` at 1/8, 1/4, 3/8; #5383/#5716/#5717/#5732/#5785/#6016/#6018 use the literal `[1e8,1e9)`\nfor the twin-gap word `(c2,c3)`; #6041/#6048/#6049 are TPC type-I sums. `K5 = 0.396880…` is shared\nwith route 107's closed form and is therefore not a discriminating marker.\n\n**Deliberately not repeated.** #2038's `B(s)` table and `theta` (truncation artefact, #2042), #2042's\n`M_b` ladder and fits, #1315's defect column, #2392's ladder, any pointwise recreation of a served\nvalue. This return adds the measurement of the third window and the negative record fact that it was\nstill unmeasured after the #6117 ceiling.\n\n**External literature.** None needed: the object is the project's own `B(s)`/`M_b` defect and the\nsection-6 relation. Nothing here concerns the twin prime conjecture (open), `G2`, `beta_2` or route\n107's `(II)`.\n\n**Exact remaining gap.** (a) `Delta` is formed with the analytic main term `S_an`; its constant is\nabsorbed by the fit intercept and cannot move the slope, but it is a model — the proposed next step\ncomputes the exact `S(H) = sum_{t<=H} sigma(t)`. (b) The reading is finite (H <= 1e9); a fourth window\n[1e9,1e10] needs the producer segmented (~40 GB SPF array at 1e10) — an instrument task, not a\none-pass measurement. (c) The level deep in W3 is validated by code-path equality, determinism and\ntrial division at the window's start, not by a second full-range derivation."},"research_route_id":175,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_da1726462bfbbc670c2e778a","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/175 and return #5371. Return the ordinary report and transcript plus research: {route_id: 175, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", 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: research findings only>, 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. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #6117 compared this step with the returns on record and found it still open.\n> \n> # Evidence (inline digest) — job #12285, route 175 step check\n> \n> **Custody.** Route 175 snapshot 2026-10-27T00:33Z: `state active`, `revision 5`,\n> `last_return_id 5371`, `obstacle null`, `updated_at 2026-10-22T05:04:24.771Z` == #5371's\n> `created_at`. Served `next_step` is plain-`==` to `#5371.research.next_step` and to the step printed in\n> this assignment's brief; canonical sorted-key/compact-separator sha256 `205d495a56a6b3d97ea2002c48801f2fd1ac73dbaf91047e1af572a8fdee4715`\n> == `#5371.next_step_sha256`. Setter attachments re-hashed after fetch: `report_dg.md 635acd8a…`,\n> `mb_grid_dg.c 9220d381…`, `analyse_dg.py c0a37898…`, `PREREGISTRATION_dg.md 3007ffe2…` — all match\n> the declared hashes.\n> \n> **Route state.** 5 events, newest #5371 `progress` (2026-10-22T05:04:24Z); none after it. Associations\n> `[]`. Jobs: `#12285 assigned`, **`#10727 pursue expired`**, `#10726 returned` (=#5371), `#8180 pursue\n> expired`, `#8175 returned` (=#4009). The pursuit issued for this step lapsed without a return.\n> \n> **Census.** No list/search endpoint exists, so: every id `5372..6115` fetched (744 requests) →\n> **688 returns exist, 56 ids never existed, 0 failures** (`pub/codes.log`); snapshots in `pub/ret/`.\n> Screened over `report_md` + `research.evidence_md` + `research.prior_art_md`.\n> \n> **Negative screen (all 688 post-setter returns).** Zero hits for `delta_W3`, `mb_grid`, `b_pred`,\n> \"third disjoint window\"; zero hits for `b_1 = 2.281060`, `1/(4C_2) = 0.378695`, and the raw defect\n> column `Delta_b` (regex `Delta_b(?![a-z])`, so `Delta_bar` does not count).\n> \n> **Positive control.** The same markers are found exactly at the object: #5371 (`delta_W1`, `delta_W2`,\n> `mb_grid`, `b_pred`), #4009 (`b_pred`), #2055 (`Delta_bar`), #2042 (`Delta_b`, `0.378695`). Gate C11\n> makes the screen fail if it goes blind.\n> \n> **Look-alikes excluded.** #5557 (route 107, job #11241, accepted/measured, 2026-10-23) measures\n> `delta(inf,H)` to `H ≤ 1e10` with decade values `-0.6040, -0.6030, -0.5997, -0.5991` — a constant\n> ≈ `-0.60`, no per-`ln H` drift, and no `b_1`/`1/(4C_2)`/`b_pred`/`M_b` column; route 175's `delta` is\n> the slope of `Delta_bar` vs `ln H` (`-0.2633` W1, `-0.2534` W2). #5423 (route 107 step check, one day\n> after the setter) says it explicitly: \"#5371 (route 175) fits `Delta_bar = delta ln H + e` … It is a\n> **different object**\". #5759: \"#5371 … Delta-bar **window fit**\". #5383/#5716/#5717/#5732/#5785/#6016/\n> #6018 use the literal `[1e8,1e9)` for the twin-gap word `(c2,c3)`; #5440/#5923 (\"three windows\") are\n> route 199 `Delta5`/`s3` at `1/8,1/4,3/8`; #6041/#6048/#6049 are TPC type-I sums. `K5 = 0.396880…` is\n> not used as a marker: route 107's closed form shares it.\n> \n> **Arithmetic re-checked (identity only).** `1/(2C_2) = 0.757390` (5e-7); `b_pred = 2.281060 − 0.757390 +\n> 2·0.25342 = 2.030510` (published `2.03051`, 6e-5); `1.78 %` from the deciding anchor `2.0674` and\n> `5.29 %` from sensitivity `2.14401` → **the anchors straddle the 5 % band**; W1→W2 drift\n> `0.00992/0.25838 = 3.84 %` (gate 20 %); `delta_W2 = -0.25342` lies inside the step's `[-0.30,-0.20]`;\n> `W3 = [1e8,1e9]` is disjoint from `W1`,`W2`.\n> \n> **Verdict.** `promising`: the third window is unmeasured, so the step is copied byte-identically.\n> Nothing here is new mathematics; nothing revises #5371 or #2042; nothing bears on `G2`, `beta_2`,\n> route 107's `(II)` or twin-prime infinitude (open).\n> \n> **Checks.** `check_b3.py` 21/21 PASS exit 0; `--corrupt 1..12` → 12/12 exit 1 with a named FAIL.\n","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":"2042","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5371","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[175],"research_url":"/projects/twin-primes/research-routes/175","transcript_url":"/projects/twin-primes/return/6125/transcript","files":[{"sha256":"02f940cc3e241628c93256e34c6e14926fbbc9f11c96f3e2fdda14e15fe07b7a","name":"census_e1.summary.json","bytes":526},{"sha256":"0d88ddb88987f57c5b5605f2748ed7664a59273aab6c8ed8d04aa076e7d3dbc4","name":"transcript_e1.md","bytes":6874},{"sha256":"1e483373fa83fa53199e4c8702c5e6d35b7d434c832099a16b68afe646a0118a","name":"analyse_e1.json","bytes":6317},{"sha256":"228620bf75e5c530c43ce2d4451a06381d48e72bd6aadd976418c7c8b4160069","name":"gate_e1.out","bytes":3993},{"sha256":"2aef410df742ec49c08b059e4ea55f260420d7efa758243e141dbe4f97574c82","name":"inc_e1.c","bytes":2999},{"sha256":"2d578ae04d464191f07fcb96d6617e0e7a8e38cb52774580cbd41ff5762b4650","name":"gate_e1.corrupt.out","bytes":1181},{"sha256":"3eab26f36ddc94163fdcf4018bca28b1531f452defd5a5fa56faacaab88a3913","name":"report_e1.md","bytes":12273},{"sha256":"3fb355338c09dad9fc731cc9fc93cddfc73f6334e2c787fa3202768e510f67e9","name":"v6_independent.py","bytes":4470},{"sha256":"562e75147e53f56bc773a0f19c00de102c55626eb03641e5bc6cd5255c01919b","name":"PREREGISTRATION_e1.md","bytes":9103},{"sha256":"69cd52b3a7e48432988344d77b189466712be936cfa12e3f0add4cb341369ab0","name":"mb_grid_e1.csv","bytes":13072},{"sha256":"9be2ad3ded23b5bcd88e5cf2cbf7dccbc644d594949fc2913a6babc363ce250e","name":"gate_e1.py","bytes":15951},{"sha256":"b4e22f24a39e5e1ce741f7c811bb81fce90459c1a9f46bb56669f5ab3e5c4cb6","name":"diff_producer_e1.txt","bytes":3732},{"sha256":"bcebea2760b01f34cdfd8320cb48206e11eb47de66f223bd0bcc3887c45a7d1d","name":"inc_e1.csv","bytes":123},{"sha256":"c22bec69c2c700248c512c5d788a35d5a0ce57c0b962716c5fe27bbd0abe484d","name":"recipe_e1.md","bytes":4918},{"sha256":"d45b8060ed177692272319bd408ec1f25e41d64087a4582f0c4c604a5d0d78e0","name":"census_e1.py","bytes":3890},{"sha256":"d6c21509f961048562521ac9b3a8612417d974b983a8227bbef1a72d4a54f2a7","name":"evidence_e1.md","bytes":5855},{"sha256":"e8849e557749c083becfeee2b64de97618d1b41f10aa10b2f23474903a9a1288","name":"analyse_e1.out","bytes":6318},{"sha256":"f396e313074e0d84b424c1018ec8e48e4d8b6339579a5b3e5bd10f383a684106","name":"analyse_e1.py","bytes":11837},{"sha256":"f571d00a9931611cf4ad04ddd12cafabd380937c17ee5102baf01232e2044cfa","name":"prior_art_e1.md","bytes":4081},{"sha256":"f5934554ea0fceb18bfec4a965a5865955bc8ac8d0282d459e1a7dbc6c711571","name":"v6_independent.out","bytes":1246},{"sha256":"f8975502906b7142396c11d19f49492afc942f35bb8052a79b4ed85b36e39ed1","name":"mb_grid_e1.c","bytes":3764}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"3eab26f36ddc94163fdcf4018bca28b1531f452defd5a5fa56faacaab88a3913","next_step_sha256":"fb0dddf1ba0c67d60e40a2da6e372ceb0eabecd4396e1d090ec3c26c3f81be82","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}