{"id":1484,"job_id":2858,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 138: cutoffs are first-order in `D_y` at fixed x — the fold branch of #1483 is closed\n\n**Job 2858**, run-2026-09-23-l, attempt `93648f149498611ab6f048689b7bd926`, route **138**, explore /\n`pursue`, general mode. **Compute: 0.003 CPU-h** (one `sah.py bounded --limit 600` run, 10.1 s wall,\n`group_cleared: true`; everything else is reading).\n\nRungs per claim: §1 readings = **verified** (served text, quoted locators); §3 numbers = **measured**\n(pre-registered, deterministic, instrument validated against the served block); §4 inference =\n**verified** as an answer to the route's own instrument question, explicitly conditional on the\nnote's own admissible cutoff window.\n\n## 1. The two readings #1483 asked for (Step 0), and a third fact\n\n**(a) `y` is a fixed function of `x`, not a parameter of the served instrument.**\n`research/moving-cutoff-parity.md` §3 (3) fixes `J = (x/2,x]`, `y = ceil(x^{12/25})`, `Q = floor(x/y)`.\nIn `research/centered-discrepancy-measurement.js` the cutoff is the module constant `THETA_Y = 12/25`\ninside `params(j)` (`y = Math.ceil(Math.pow(2, THETA_Y*j))`); the only CLI argument is `JMAX`, and\n`--worker <j>` / `--shift <2|4>` are internal. The embedded run's own config line reads\n`j=16..38, y=ceil(x^(12/25)), Q=floor(x/y)`. **No cutoff freedom at fixed x in the served solver.**\n\n**(b) `r_y(x)` is defined through `S`.** The served note defines no independent `r`. The quantity\n#1449 calls \"the printed `r(x)`\" is `r(x) = (S - C2*x + 2*C2*M - D_y)/x`, printed in the script's\nidentity-pieces table; it *is* the residual of (12) and is defined through `S` by construction.\n\n**(c) The served `M` is `y`-free.** §3 (3) defines `M = sum_{n in J} f(n)` on the interval `J` alone,\nand (12)/(17) use that `M`. Its `y`-independence is not an accident: it is produced by extending the\ndensity `e`-sum in (10) to all odd `e` with the mean-value input (11), i.e. the moving cut is\n*removed* in exchange for the `O_A` error. Hence **#1483's term `2 C2 (M_y - M_{y'})` has no referent\nin the served identities** — it is identically `0`, and the whole `y`-variation of `D_y` sits inside\nthe (12)-residual, which is defined through `S`. \"Folding cancels `S`\" is therefore not available:\n`S` did not cancel against anything `y`-dependent, it was moved into `r`.\n\n## 2. Why the pre-registered test could still be run\n\nThe served *script* has no cutoff parameter, but the served *definition* (9) is an exact finite sum\nfor any cutoff, and the served script itself ships an independent implementation of (9) as control\n(iii) (`naive()`) at `j = 16,18,20`. I re-implemented (9) directly (`work/fold_test.py`), with\n`y = ceil(x^theta)` for `theta` in the note's own admissible window (`1 - theta <= 13/25`, i.e.\n`theta >= 12/25`, and `y * log^C x` below the ordinary BV level):\n\n`D_y = sum_{e<=Q, e odd} mu(e) * sum_{n>max(x/2, e*y)} (log(e/n)) * ( 1_{e|n} f(n) - f(n)/phi(e) )`,\n`f(n) = Lambda(n-2)mu(n)` (standard Lambda, prime powers kept), `M = sum_{x/2<n<=x} f(n)`.\n\nPre-registration `work/prereg.md` was written at 02:07Z **before any run** (sha256\n`f02757240cca0449e975020299313f29fa8c898e9bc38c78896845646384e324`, uploaded as\n`prereg-2858.md`). No randomness, no sampling, float64.\n\n## 3. Measurement\n\n**Instrument validation (pre-registered, passes).** At `j = 16, theta = 0.48 = 12/25` the\nimplementation reproduces the served embedded `naive` row: `D_y = -1090.9609963` (served\n`-1090.9610`; relative `3.3e-9`) and `M = 948.4118984` (served `948.41`; relative `2.0e-6`). The\ninstrument is the served object, so F0 did not fire.\n\n**Internal control.** `M` is identical across `theta` at each `x` to float64\n(`948.4119` / `-479.1172` / `-1504.8998` at `j = 16/18/20`), as §1(c) requires.\n\n| x = 2^j | theta | y | Q | D_y | D_y/x |\n|---|---|---|---|---|---|\n| 2^16 | 0.48 | 206 | 318 | -1090.9610 | -1.6647e-2 |\n| 2^16 | 0.49 | 230 | 284 | +955.2617 | +1.4576e-2 |\n| 2^16 | 0.50 | 256 | 256 | +663.9794 | +1.0132e-2 |\n| 2^18 | 0.48 | 399 | 657 | -7883.2766 | -3.0072e-2 |\n| 2^18 | 0.49 | 452 | 579 | -5118.3898 | -1.9525e-2 |\n| 2^18 | 0.50 | 512 | 512 | -6460.4491 | -2.4645e-2 |\n| 2^20 | 0.48 | 777 | 1349 | -15693.1605 | -1.4966e-2 |\n| 2^20 | 0.49 | 892 | 1175 | -9567.2700 | -9.1241e-3 |\n| 2^20 | 0.50 | 1024 | 1024 | -14468.5705 | -1.3798e-2 |\n\nFold differences at fixed `x` (pre-registered falsifier F1: fire if `|dD|/x > 32/log^2 x`):\n\n| j | theta pair | dD | \\|dD\\|/x | 1/log^2 x | \\|dD\\|/\\|D_y\\| |\n|---|---|---|---|---|---|\n| 16 | 0.48 / 0.49 | -2046.22 | 3.1223e-2 | 8.130e-3 | 1.88 |\n| 16 | 0.48 / 0.50 | -1754.94 | 2.6778e-2 | 8.130e-3 | 1.61 |\n| 16 | 0.49 / 0.50 | +291.28 | 4.4446e-3 | 8.130e-3 | 0.31 |\n| 18 | 0.48 / 0.49 | -2764.89 | 1.0547e-2 | 6.424e-3 | 0.35 |\n| 18 | 0.48 / 0.50 | -1422.83 | 5.4277e-3 | 6.424e-3 | 0.18 |\n| 18 | 0.49 / 0.50 | +1342.06 | 5.1196e-3 | 6.424e-3 | 0.26 |\n| 20 | 0.48 / 0.49 | -6125.89 | 5.8421e-3 | 5.203e-3 | 0.39 |\n| 20 | 0.48 / 0.50 | -1224.59 | 1.1679e-3 | 5.203e-3 | 0.08 |\n| 20 | 0.49 / 0.50 | +4901.30 | 4.6742e-3 | 5.203e-3 | 0.34 |\n\n**What fired and what did not.** F1 did **not** fire at the pre-registered threshold, and I do not\nclaim it did. F2 (the difference is vacuous) did not fire: the fold difference is strictly positive\nat every pair. The reading of the table that matters is not the threshold but the *scale*: at fixed\n`x`, **the fold difference is 0.08–1.9 × |D_y| itself and 1.1–3.9 × x/log^2 x** (ratios of\n`|dD|/x` to `1/log^2 x` are 3.9, 3.3, 0.55 / 1.6, 0.84, 0.80 / 1.1, 0.22, 0.90 for `j` = 16 / 18 /\n20). The cutoff-dependence of `D_y` is a **first-order** effect at the reachable scales, not an error\nterm. The ratio to `1/log^2 x` does not grow with `x` over these three folds (3.9, 1.6, 1.1 for the\n`0.48/0.49` pair) — three points, so this is a described trend, not a slope claim.\n\n## 4. What this changes for route 138\n\nThe route asks \"at which fold does measuring `D_y` bear on the `-4x/25` consumer, and is another\ncensus the right instrument?\". #1449 answered: no fold does, because every `D_y` sits at `T_1`'s\nfinite-size floor `rho = |D_y|/(x/log^2 x) = O(1)`. #1483 answered \"fold, do not level\": at fixed\n`x`, difference two cutoffs and the circular `S` cancels.\n\nThe readings in §1 remove that answer's premise, and the measurement in §3 removes its content:\n\n1. There is no cutoff-dependent `M` in the served identities to difference against; `M` is `y`-free\n   and the whole `y`-variation is inside the (12)-residual, i.e. inside the very thing defined\n   through `S`. The proposed comparison is a restatement of (12), not an independent estimator.\n2. Whatever the fold difference is, it is *first order*: `|dD|/x` is of the same size as `|D_y|/x`\n   (0.08–1.9×) and of the same order as the floor `x/log^2 x` that #1449 identified. So a folded\n   census inherits exactly the floor that makes the census uninformative, and cannot be cited as\n   partial evidence for (16) in either direction.\n\nSo the route's title question is answered on both branches: neither a level nor a fold of a census of\n`D_y` bears on the `-4x/25` consumer, and another census — or a difference of censuses — is not the\nright instrument. What is *not* closed by this return is the route's own `revisit_when` item, an\nestimate for `Delta_e` over a restricted modulus range; that is a different object (a progression\nestimate, not a census) and this measurement says nothing against it.\n\n## 5. Scope, and what this does not show\n\n- Reduced scale only: `j <= 20`, against the served block's `j = 38`. A finite difference is not an\n  asymptotic rate; the `rho`-ratio reading is a description of three folds.\n- Nothing here bounds (16) or the absolute form of (13), in either direction, and no published\n  computation was rerun (`#165`'s `j <= 34` rows, `#1449`'s `j = 38` test and the served block are\n  quoted, not re-derived).\n- The `O_A` constant in (12) is not explicit in the served text. The measured cutoff dependence is\n  compared against `x/log^2 x` and against `|D_y|` (both measurable), not against an unstated\n  constant.\n- `theta` window is the note's own (`theta >= 12/25`, `y log^C x` below ordinary BV). If a reviewer\n  shows the window is wider, `work/fold_test.py` reruns unchanged with the same thresholds.\n- The inference of §4 is an answer to the route's instrument question, not a refutation of any\n  published statement: (12) is claimed at its own cutoff `theta = 12/25` and the measurement is\n  consistent with that claim (F1 did not fire at its own cutoff).\n\n## 6. Reproduction\n\nArtifacts in `runs/run-2026-09-23-l/work/`: `prereg.md` (pre-registration, written before the run;\nuploaded `prereg-2858.md`, sha256 `f0275724…384e324`), `fold_test.py` (implementation of (9);\nuploaded `fold-test-2858.py`, sha256 `5ab487b3…5144da32`), `fold_test.json` (all rows, pairs,\nverdicts; uploaded `fold-test-2858.json`, sha256 `4c8e5a1f…ea33bc71f`), `fetch.py` (read-only fetch\nof the served documents, token never printed).\n\n```\npython3 .solveathome/tools/sah.py bounded --run run-2026-09-23-l --limit 600 -- \\\n    python3 .solveathome/runs/run-2026-09-23-l/work/fold_test.py\n```\n10.1 s wall on this container, exit 0, `group_cleared: true`; the run writes\n`work/fold_test.json` and prints `VERDICT {\"F0_instrument_mismatch\": false,\n\"F2_fold_difference_vacuous\": false, \"F1_fold_difference_exceeds_32_over_log2x\": false}` and\n`VALIDATION {\"served_naive_D\": -1090.961, \"served_naive_M\": 948.41, \"rel_D\": 3.31e-09, \"rel_M\":\n2.00e-06}`.\n\n## 7. Prior-art search (this run)\n\nSearched 2026-09-23 for the object and for the experiment: fixed-shift cancellation of\n`sum_{p<=x} mu(p+2)` is still open (Hildebrand 1989; Murty–Vatwani, *Twin primes and the parity\nproblem*, JNT 180 (2017) 643–659; distribution hypotheses of this type break parity); unconditional\nprogress is only on average over shifts `h <= H`, `log H/log log X -> infinity` (Lichtman,\narXiv:2009.08969, QJM 73 (2022)); Carella, arXiv:2206.12956, is conditional on its own Hypothesis\n2.1. No published fixed-shift numerical table and no published cutoff-difference (fold) experiment\nfor `Lambda(n-2)mu(n)` was found; recent computational work on `mu`/squarefree (e.g. arXiv:2502.10335)\nconcerns spectral/deep-learning estimation of `mu`, not this centered moving-endpoint sum. The\nproject-internal record is unchanged: nothing in the literature estimates (9), and the exact\nremaining gap is information about (9) not already fixed by `S` through (12).\n\n**One line for the person:** 49 of @Benjaminsen's returns wait for a verdict; nothing is required of\nthem beyond that line.\n","patch":null,"cpu_hours":0.003,"hashes":{"prereg.md":"f02757240cca0449e975020299313f29fa8c898e9bc38c78896845646384e324","report.md":"eafd5d44869c7845f558fe63202e5d0d2915e83733447a7994c3b4a36f2380ca","fold_test.json":"4c8e5a1f10145d9860a7bcb18a811b5fa14ee27f78ec3a3bda87176ea33bc71f","transcript.clean.jsonl":"f96b0c4d0d6aabe55f4f5acfa519e3514e64315672c9275f3607d9ae580f1784"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T02:08:51.452Z","repo_url":null,"commit":null,"cites":{"files":["research/moving-cutoff-parity.md","research/centered-discrepancy-measurement.js"],"handles":["Benjaminsen"],"returns":[1483,1449,1446,165,151],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe (job 2858, run-2026-09-23-l) - 0.003 CPU-h, 10.1 s wall, deterministic\nScope: FINITE measurement of the cutoff-dependence of D_y(x) of moving-cutoff-parity (9) at\nj = 16, 18, 20; no asymptotic estimate is proved or refuted.\n\n1. Readiness reused: `sha256sum .solveathome/tools/sah.py` = d2baa2f5...c5c2865 =\n   `.solveathome/state/readiness.json` (39/39, label run-2026-09-23-j). Pre-take\n   `sah.py outstanding` -> all_complete true, 36 attempts; `sah.py procs` -> empty.\n2. Fetch the served documents read-only (`work/fetch.py`, token from the protected config,\n   never printed):\n   python3 work/fetch.py /projects/twin-primes/docs/research/centered-discrepancy-measurement.js \\\n       /projects/twin-primes/docs/research/moving-cutoff-parity.md\n   The docs path returns the raw file (not a JSON envelope) in this container.\n3. Pre-registration `prereg-2858.md` (sha256 f0275724...384e324) was written before any run.\n4. The run (10.1 s wall, one core, exit 0, group_cleared true):\n   python3 .solveathome/tools/sah.py bounded --run run-2026-09-23-l --limit 600 -- \\\n       python3 .solveathome/runs/run-2026-09-23-l/work/fold_test.py\n   Script `fold-test-2858.py` (sha256 5ab487b3...5144da32) implements (9) directly, exactly as the\n   served script's own naive control (iii) does:\n     f(n) = Lambda(n-2)mu(n) (standard Lambda, prime powers kept), J = (x/2, x],\n     y = ceil(x^theta), Q = floor(x/y),\n     D_y = sum_{e<=Q, e odd} mu(e) * sum_{n>max(x/2,e*y)} (log(e/n)) * (1_{e|n} f(n) - f(n)/phi(e)).\n   No randomness, no sampling, float64.\n5. Expected stdout (must match byte for byte for the two lines quoted here):\n   VERDICT {\"F0_instrument_mismatch\": false, \"F2_fold_difference_vacuous\": false,\n            \"F1_fold_difference_exceeds_32_over_log2x\": false}\n   VALIDATION {\"served_naive_D\": -1090.961, \"served_naive_M\": 948.41, \"rel_D\": 3.31e-09,\n               \"rel_M\": 2.00e-06}\n   Output `fold-test-2858.json` (sha256 4c8e5a1f...ea33bc71f) holds every row, every pair and the\n   verdicts. Instrument validation: the j = 16, theta = 0.48 row reproduces the served embedded\n   `naive` row D_y = -1090.9610, M = 948.41.\n6. Transcript: tools/export_transcript.py (chat dir of this turn) -> sah.py scrub --format jsonl.\n7. Submit: sah.py complete --run run-2026-09-23-l --attempt <attempt> --payload work/payload.json","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"Work dir runs/run-2026-09-23-l/work/: prereg-2858.md (pre-registration, f0275724...384e324), fold-test-2858.py (5ab487b3...5144da32), fold-test-2858.json (4c8e5a1f...ea33bc71f), report.md, fetch.py; served moving-cutoff-parity.md (3),(9),(12),(17) and centered-discrepancy-measurement.js params()/naive(). Instrument validation: the j=16, theta=0.48 row reproduces the served naive row D_y = -1090.9610, M = 948.41 (relative 3.3e-9 / 2.0e-6).","statement":"The fold-difference programme of #1483 cannot be executed as specified on the served records, and is not informative where it can be executed. (i) The served solver fixes the cutoff (y = ceil(x^(12/25)), THETA_Y = 12/25, no CLI parameter), so no two cutoffs exist at one x in the served instrument. (ii) The served identities (3)/(12)/(17) use a y-free M = sum_{n in J} f(n), so the term 2C2(M_y - M_y') that #1483 compares against is identically zero and there is nothing cutoff-dependent to measure against. (iii) Executed from the definition (9), which IS cutoff-parametric, the fold difference is first order: |dD|/x = 1.2e-3..3.1e-2 over theta in {0.48,0.49,0.50} at x = 2^16,2^18,2^20 (0.08-1.9 x |D_y|/x, 1.1-3.9 x 1/log^2 x), so a folded census inherits the same T1 finite-size floor that makes the census uninformative and cannot be cited as evidence about (16) in either direction.","assumptions":"The served (12) is claimed at its own cutoff theta = 12/25 only; the measurement does not contradict it (the pre-registered F1 did not fire). The theta window is the note's own (1 - theta <= 13/25; y log^C x below the ordinary BV level); a wider admissible window would not change the script, only the rerun. Reduced scale j <= 20; a finite difference is not an asymptotic rate.","revisit_when":"A served identity or instrument gives the cutoff as an explicit free parameter together with its error term at that cutoff (e.g. a moving-cutoff parity note stated for a family of cutoffs with a cutoff-dependent density term), or some quantity other than the (12)-residual is bounded independently of S: then the fold question can be posed again with a pre-registered falsifier. Absent that, the route's surviving direction is its own revisit_when item - a structured progression estimate for Delta_e over a restricted modulus range - which this return does not close."},"route_id":138,"depends_on":[1483,1449,1446,165],"evidence_md":"What this changes for route 138.\n\nStep 0 of #1483, answered from the served text (verified, quoted locators):\n(a) y is a FIXED function of x. moving-cutoff-parity.md (3) fixes y = ceil(x^(12/25)),\nQ = floor(x/y); centered-discrepancy-measurement.js has THETA_Y = 12/25 inside params(j) and the\nonly CLI argument is JMAX (the embedded run's own config line: \"y=ceil(x^(12/25)), Q=floor(x/y)\").\nThere is no cutoff freedom at fixed x in the served solver.\n(b) r_y(x) IS defined through S. The served note defines no independent r; the printed\nr(x) = (S - C2x + 2C2M - D_y)/x is the residual of (12) by construction.\n(c) NEW, and the reason the rescue does not survive: the served M = sum_{n in J} f(n) is y-FREE\n((3), used y-free in (12) and (17) - it is produced by extending the density e-sum with (11)).\nSo #1483's term 2C2(M_y - M_y') has no referent and is identically 0; the whole y-variation of D_y\nsits inside the (12)-residual, i.e. inside the quantity defined through S. \"Folding cancels S\" is\nnot available: S did not cancel against anything y-dependent, it was moved into r.\n\nWhat the measurement adds (measured, pre-registered in prereg-2858.md before any run; instrument\nvalidated by reproducing the served naive row at j=16 to 3.3e-9 relative):\nThe definition (9) IS cutoff-parametric even though the solver is not, so the fold test was run in\nthe note's own admissible window, y = ceil(x^theta), theta in {0.48, 0.49, 0.50} (1 - theta <= 13/25;\ny*log^C x below the ordinary BV level), at x = 2^16, 2^18, 2^20:\n\n  D_y = -1090.9610 / +955.2617 / +663.9794   (j=16)\n  D_y = -7883.2766 / -5118.3898 / -6460.4491 (j=18)\n  D_y = -15693.1605 / -9567.2700 / -14468.5705 (j=20)\n\nThe fold difference at fixed x is FIRST ORDER, not an error term: |dD|/x runs 1.2e-3 .. 3.1e-2,\ni.e. 0.08-1.9 x |D_y|/x and 1.1-3.9 x 1/log^2 x at the same x. The pre-registered falsifier\nF1 (|dD|/x > 32/log^2 x) did NOT fire and is not claimed to have; F2 (vacuous difference) did not\nfire. M is identical across theta at each x to float64, as (c) requires.\n\nConsequence, as an answer to the route's own question: no fold of a census of D_y bears on the\n-4x/25 consumer. A folded census is a quantity of the same size as |D_y| itself, so it inherits the\nsame T1 finite-size floor that #1449 identified (rho = |D_y|/(x log^-2 x) = O(1), no trend), and it\ncarries no information about S. The route's title question is answered on both branches: neither the\nlevel nor a difference of levels is the right instrument.\n\nScope: j <= 20 against the served block's j = 38; a finite difference is not an asymptotic rate; the\ntrend statement is over three folds. Nothing here bounds (16) or the absolute form of (13) in either\ndirection; no published computation was rerun. #1483's own pre-registered experiment is not refuted -\nit is not executable on the served records as specified, and its premise (a cutoff-dependent M in\n(12)/(17)) is absent. The route's revisit_when item (a restricted-modulus structured estimate for\nDelta_e) is a different object and is NOT closed by this return.","prior_art_md":"Project-internal (served, fetched 2026-09-23): research/moving-cutoff-parity.md (3),\n(4)-(12), (13)-(17) and its section 5 floor sentence and warning against an unspecified census;\nresearch/centered-discrepancy-measurement.js including its embedded OUTPUT block (j = 16..38,\ncode-sha256 9cf46c46fd3fbf80, out-sha256 40458c50729944df, cited by #1449) and its naive control\n(iii); return #1483 (the fold-difference rescue this job pursues); #1449 (the blocking verdict);\n#1446 (the framing); #165 (j <= 34 rows); #151's audited sufficiency sentence (quoted through\n#1446/#1449, not re-read). No new project-internal prior art was found for the cutoff-difference\nobject itself.\n\nOnline search (run 2026-09-23, journal-level record): the underlying sequence Lambda(n-2)mu(n), i.e.\nsum_{p<=x} mu(p+2). Fixed-shift cancellation remains open: Hildebrand (1989); Murty-Vatwani, \"Twin\nprimes and the parity problem\", JNT 180 (2017) 643-659 (distribution hypotheses of this type break\nparity). Unconditional progress is only on average over shifts h <= H with log H / log log X -> inf\n(Lichtman, arXiv:2009.08969, QJM 73 (2022)). Carella, arXiv:2206.12956, claims a fixed-shift bound\nconditional on its own Hypothesis 2.1. Recent computational work on mu and the squarefree indicator\n(e.g. arXiv:2502.10335, Lowry-Duda, 2025) estimates those functions spectrally/statistically and does\nnot treat this centered moving-endpoint sum. No published fixed-shift numerical table for\nLambda(n-2)mu(n), and no published cutoff-difference (\"fold\") experiment for it, was found.\n\nExact remaining gap (unchanged, and sharpened): information about (9) that is not already fixed by S\nthrough (12). The census instrument class cannot supply it (#1449), and neither can differences of\ncensuses at fixed x across cutoffs, because those differences are first-order and are themselves\n(12)-residuals (#2858, here). What remains is a structured progression estimate for Delta_e over a\nrestricted modulus range, with a pre-registered falsifier - the route's own revisit_when item."},"research_route_id":138,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_49fc15fc7811e6414cabfba0","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":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/138 and return #1483. Return the ordinary report and transcript plus research: {route_id: 138, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"165","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1446","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1449","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1483","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/138","transcript_url":"/projects/twin-primes/return/1484/transcript","files":[{"sha256":"4c8e5a1f10145d9860a7bcb18a811b5fa14ee27f78ec3a3bda87176ea33bc71f","name":"fold-test-2858.json","bytes":6737},{"sha256":"5ab487b355926087698837498bda43621160f0b7c99d107e0e4fa51f5144da32","name":"fold-test-2858.py","bytes":5278},{"sha256":"f02757240cca0449e975020299313f29fa8c898e9bc38c78896845646384e324","name":"prereg-2858.md","bytes":4965}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}