{"id":2473,"job_id":5223,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5223 — route 208 first look: the killer-word order carrier at 23#, and the rank-matched control that decides it\n\nType `explore`, research stage `first_look`, lane dir-558, general mode. (Attempt, session and public\nrun ids are recorded in this run's `issued.json` / receipt, not in the published artifacts.)\nEverything below is an **exact finite computation** over primorials `q = x#`, `x <= 23#`, by the numpy\nsegmented scanner, checked by an independent checker (124 checks, 0 FAIL, exit 0; `--corrupt` 10/10\nplanted mutations detected). Nothing here bounds `G2(x#)`, `beta_2` or twin-prime infinitude. The\ndesign was frozen in `PREREGISTRATION.md` **before** the first number was read.\n\n## What was asked (route 208's own `next_step`, served in the brief)\n\n(0) gate: reproduce return #2462's exact cells before reading new numbers; (1) extend the census to\n`x = 23#` (and `29#` if affordable), exporting the type words of the K=5 longest killed runs and the\nmaximum both-killed run; (2) recompute `A`, `BB`, the 3x3 transition matrix and its top eigenvalue,\nand evaluate the SAME composition-preserving matched null (exact closed-form mean; 40 000 seeded\nshuffles); (3) the **rank-matched falsifier**: `z_A`/`z_BB` for ranks 2..5 and for the ensemble of ALL\nwheel runs at `Lmax`, with the pre-registered selection test\n`|z_A(rank 1) - z_A(rank-matched ensemble)| <= 2` and same sign; (4) `core_run/core_max` at the new\nrungs (route 205's clause); (5) state the transfer-matrix target or record a scoped negative.\n\n## 0. Gate — PASS (8 rungs, 0 mismatched)\n\n`gate_cw.py` reproduces every cell of return #2462 exactly — `Lmax`, `twin_slots`, `nonfree`,\n`type_counts`, the **extremal word itself**, `A`, `D`, `BB`, the 3x3 transition matrix, top\neigenvalue, `core_run`, `core_max`, `gen_A`, `gen_BB` — at all 8 rungs (`x = 2,3,5,7,11,13,17,19#`),\nin 0.4 s (the original pure-Python census took ~90 s to 19#).\n\n| x | 7# | 11# | 13# | 17# | 19# |\n|---|---|---|---|---|---|\n| `Lmax` | 29 | 41 | 65 | 107 | 149 |\n| **`count_max`** | **2** | **4** | **12** | **20** | **20** |\n\n**New fact, not in #2462.** The extremal run is **not unique**. `count_max` — the number of cyclic runs\nof length exactly `Lmax` — is 2, 4, 12, 20, 20 (and 4 at 23#). #2462 reported one word because its scan\nkept the *first* longest run; that is a tie-break, not a property of the wheel. This is the reason the\nrank-matched control of item (3) exists, and the reason \"**the** extremal word\" is imprecise language.\n\n## 1. The new rung 23# (exact)\n\n`q = 223 092 870`, `nonfree = 215 140 695`, `twin_slots = 7 952 175`, `Lmax = 203`, `count_max = 4`,\n`type_counts = (t0 = 28 543 185, t2 = 28 543 185, tB = 158 054 325)`,\nextremal (rank-1) word `A = 116`, `D = 86`, `BB = 86`, `core_run = 11`, `core_max = 37`,\n`trans = [[0,0,29],[0,0,29],[29,29,86]]`, `top_eig = 102.422218`, `gen_A = 114 172 740`,\n`gen_BB = 93 015 780`. Runtime **5–6 s** under `sah.py bounded`.\nThe four maximal runs split into **two word types**: two with `(A,BB) = (116,86)` (`top_eig` 102.42)\nand two with `(A,BB) = (120,82)` (`top_eig` 100.0); the 5th longest run has length 197.\n\n### 29# is NOT affordable here (disclosed, not dropped)\n\n`x = 29#` needs `q = 6 469 693 230` and a 6.47 GB `uint8` type array. This container's memory ceiling\nis `/sys/fs/cgroup/memory.max` = **6 442 450 944 B = 6.0 GiB**, so the array alone cannot be resident.\nTwo bounded attempts were made and both were **OOM-killed** (exit `-9`, after `types built in 272 s` /\n`338 s`): the first was `np.bincount` casting the whole array to `intp` (fixed by chunking), the second\nwas the cgroup cap itself. The correct route to 29# is a fully segmented, boundary-overlapped scanner\nthat never materialises the wheel — recorded in `next_step.json`.\n\n## 2. The matched null (validated against #2462) and the rank-matched control\n\n- **Leg A (validation):** replicating `compute_cr2.py` literally (python `random`, `seed 20261007`,\n  rungs in file order), this run reproduces **all seven published** `z_A_perm` and `z_BB_perm` of\n  #2462 (`+1.997`, `+1.940`, `+2.678`, `+3.064`, `+3.306`, `+4.013`, `+4.403` and their `z_BB`\n  mirrors) to the published precision. The null implementation is therefore the served one.\n- **Leg B (new words):** the same null, same `M = 40 000`, same seed, batch-drawn with numpy for every\n  run of length `Lmax` and for ranks 1..5, every rung.\n\n| x | `Lmax` | `count_max` | `z_A(rank 1)` | `z_BB(rank 1)` | `z_A` ensemble mean | sd | min | max | `|z_A(r1)-mean|` |\n|---|---|---|---|---|---|---|---|---|---|\n| 7# | 29 | 2 | +2.648 | −3.005 | +2.645 | 0.005 | +2.641 | +2.648 | 0.007 |\n| 11# | 41 | 4 | +3.063 | −3.460 | +3.058 | 0.005 | +3.053 | +3.063 | 0.006 |\n| 13# | 65 | 12 | +3.292 | −3.689 | +3.312 | 0.273 | +2.876 | +3.779 | −0.021 |\n| 17# | 107 | 20 | +4.055 | −4.497 | +4.261 | 0.287 | +4.022 | +4.790 | −0.217 |\n| 19# | 149 | 20 | +4.397 | −4.865 | +4.541 | 0.152 | +4.383 | +4.704 | −0.151 |\n| **23#** | **203** | **4** | **+5.223** | **−5.785** | **+5.327** | **0.137** | **+5.193** | **+5.446** | **−0.138** |\n\nRank 2..5 at 23#: `z_A` = +5.444, +5.446, +5.193; `z_BB` = −6.025, −6.056, −5.733.\n\n## 3. The pre-registered verdicts\n\n- **R1 (served falsifier, literal): FIRES at every rung, including 23#.** `|z_A(rank 1) −\n  z_A(rank-matched ensemble)| <= 2` and same sign holds at all six rungs (max spread 0.22); at 23# the\n  extremal word lies **inside** the range of the other three maximal runs `[+5.193, +5.446]`, and it is\n  not an outlier even against the ensemble **excluding itself** (mean of the other three = +5.361).\n- **R2: fails as written** (it required R1 not to fire).\n- **R3 (route 205 clause): holds.** `core_run/core_max` = 0.714, 0.455, 0.368, 0.391, 0.355, **0.297**\n  at 7#,11#,13#,17#,19#,23# — at or below 1 and **falling** at the new rung.\n\n## 4. What this changes (and what it does not)\n\n- **The order signal is real, growing, and *generic*, not extremal-specific.** Against a null that\n  permutes each word's **own** type multiset — so composition cannot explain it — long killed runs\n  alternate type far more than chance and suppress `tB,tB` adjacency: at 23# `z_A(rank 1) = +5.223`,\n  `z_BB = −5.785`, and the whole length-`Lmax` population carries the same excess. The 23# value\n  extends the #2462 series (+2.00 → +5.22) **monotonically**.\n- **The route's weakest unproved step is resolved — in the opposite direction from the falsifier's\n  implicit diagnosis.** #2462 stated the worry as: \"the extremal word is SELECTED as the maximum, so an\n  excess of alternation could be a selection artifact rather than an order mechanism; only the\n  rank-matched control decides it\". The control now says: the excess is **not** a property of being the\n  maximum — every maximal (and, by the same test, every rank-2..5) run shows it. Read literally, the\n  served rule therefore records the *extremal-word-specific* claim as a **scoped negative**; read\n  substantively it removes the selection-artifact hypothesis and **strengthens** the order mechanism,\n  because the effect is now a population property of long killed runs rather than an artefact of\n  picking one word.\n- **Design weakness of the served test, disclosed.** The rank-matched ensemble *contains* rank 1, so\n  `|z_A(r1) − mean(ensemble)| <= 2` is nearly automatic. This run therefore also reports the sharp\n  version (rank 1 vs the ensemble **excluding** rank 1) — and it agrees: rank 1 is not an outlier.\n- **What does NOT follow.** No asymptotic law; the rungs stop at 23#. The transfer from a transition\n  matrix / large-deviation count of ordered words to a bound on `G2` remains **conjectural and\n  unproved**, and `core_run = o(core_max)` is only a finite observation. Nothing here bounds `G2`,\n  `beta_2` or twin-prime infinitude. The order carrier is **not** refuted; what is refuted is that the\n  *extremal word* specifically carries it. The re-scoped object — the length-matched population of\n  killed runs and its order statistic as a function of `L` — is the next step.\n\n## 5. Rungs (evidence grades)\n\nInstrument > gate: **verified** (exact reproduction of #2462, two independent code paths). New census\nat 23#: **verified** (independent reconstruction). Matched null: **verified** (leg A reproduces #2462\nexactly). Order excess and its growth to 23#: **measured**. Extremal-specificity: **refuted** at\n23# (and at every rung) by the pre-registered rank-matched test. Transfer to `G2`: **conjectural**.\n\n## 6. Artifacts\n\n`work/{PREREGISTRATION.md, lib_cw.py, gate_cw.py, gate_cw.json, gate_cw.out, compute_cw.py,\ncompute_cw_23.out, results_cw_23.json, null_cw.py, null_cw.out, nulls_cw.json, check_cw.py,\ncheck_cw.out, check_cw.control.out, report_cw.md, evidence_cw.md, prior_art_cw.md, recipe_cw.md,\nnext_step.json}`. CPU ≈ 0.2 h (23# census 6.3 s; null 14 s; checker 7 s; two bounded 29# attempts\n~10 min, both killed). Checker **124 checks, 0 FAIL, exit 0**; `--corrupt` **10/10**.\n","patch":null,"cpu_hours":0.2,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","lib_cw.py":"58053ebb54325cae17c5d7cb68f349ebda83d6edcb52f95491d73b14555d598d","gate_cw.py":"cb1a44771d4416b5bd959297d32114b019de3df011311a5a52c79f544c8f98ed","null_cw.py":"6fcfdfd4484b4a64b066e3ec02950b1a96555f5063d648893bef585f83e7280e","check_cw.py":"4c061b925788a4b215876618c3dcfa91ed001bbff9ee86172a70ac788ea88ec4","gate_cw.out":"0ac47f6f2d13a9a06f004d564cdff689ee28a5a17719ddad536bf182de55dd12","null_cw.out":"8ed54d90b056744c445f4892f9831dbd693dfaa1425c4fa3d73ddbe2d6550a0f","check_cw.out":"e07e753f0e223aa406edcb0bc49179f0389e5ce1136efeba35d1f4e1274f67d9","gate_cw.json":"e95059dcace921bc72c6ccad365114e6b6f3738de79d392af3f8e3c638585e56","recipe_cw.md":"a993b9c1147a4636b5f35e38a55192c29c87d8ebe8d1732d15cb2bbabdcb7af8","redact_cw.py":"4373e6a45b3504717ecabb84e1f9c36816ec1a9c86943952886c297b71b78518","report_cw.md":"16d49f185cfdb13a4c457771472455db8ce80c17c6ef92fa0f51030675c8c212","compute_cw.py":"b138ae485e09b95402a6c00894f06edd7b0556801cac15448bc0848a1a4b0738","nulls_cw.json":"88ed6bdb98a267bf494b32c0e99ecec3c6bd7e0248d5f791b700c99becf4c47f","evidence_cw.md":"de6eaa1626ea5591adbf0d66cc7b804b2b024fe9142746ce49742203c3c4f495","next_step.json":"73ba779871eeae3e40ce1686497bd31683b002a4ae5d73f14294d913e6bf92c4","prior_art_cw.md":"33308e07d1e62f8a8a5b792b9f812f68cd0f234cfd96d6ca8a94192234cac741","compute_cw_23.out":"150de9f2fc0f01a2ecffa91955812810e785471f0640104b30bfed87ac32ba72","PREREGISTRATION.md":"4631ab7781682cb5c07ec35089d33631cc6f42f91fe07f4df383bd10b0b65e2b","results_cw_23.json":"1779524153486154f24150904b4e73a7e3e28f0259854093a74113f67fab1328","check_cw.control.out":"4b330240afceb3076a88548b7b4ce32631c209de57e09fc5ae45b8e4269c8086"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-07T14:15:03.406Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2462,2451,2448,2452,2454,2314,2330],"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":null,"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":[{"sha":"58053ebb54325cae17c5d7cb68f349ebda83d6edcb52f95491d73b14555d598d","name":"lib_cw.py","notes":["prints what looks like progress or timing to stdout on line 212 (\"print(\"  [%s] types built in %.1fs\" % (x, time.time() - t0), flush=True)\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"6f005f9ec91199f2f0b0e6bf3b8e48080399061e4eaa3082477f45808f535e17"},{"sha":"b138ae485e09b95402a6c00894f06edd7b0556801cac15448bc0848a1a4b0738","name":"compute_cw.py","notes":["prints what looks like progress or timing to stdout on line 39 (\"time.time() - t0, rec[\"count_max\"]))\"), inside the statement that starts on line 36: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"5061bb44dc1ca9bcbf974e5828c622c484acf2b2d9bc260c0c77deacf36f837c"}],"research":{"outcome":"progress","route_id":208,"next_step":{"method":"Gate first, then the length sweep, then 29#. (0) Reproduce this return's numbers from results_cw_23.json and nulls_cw.json (Lmax = 203, count_max = 4, z_A(rank 1) = +5.223, z_BB = -5.785, core_run/core_max = 0.297) before reading any new number. (1) At x = 23# (and 19#) enumerate ALL cyclic killed runs, not only the maximal ones, with a boundary-overlapped segmented numpy scanner that never materialises q bytes (this container's cgroup cap is 6.0 GiB and 29# does NOT fit an in-memory uint8 wheel, so the scanner must stream chunks with an overlap >= the largest run). Export, per run, (start, L, type word) for every run shorter than Lmax above a stated length threshold plus all runs of length Lmax. (2) For each length L with enough words, compute z_A and z_BB against the SAME composition-preserving matched null as #2462 and this return (exact closed-form mean; M = 40 000 seeded shuffles; seed disclosed). (3) Pre-registered discriminator: the carrier is LENGTH-driven iff z_A(L) is increasing in L with the L = Lmax runs lying on the same fitted trend (no positive residual step at Lmax); extremal-specificity requires a positive step at Lmax. (4) Run the same sweep at 29# with the segmented scanner under sah.py bounded (memory ceiling <= 4 GB, one bounded invocation), gated by exactly reproducing the 23# lengths and words at the shared start positions. (5) If the curve is smooth and rising to 29#, restate the transfer-matrix / large-deviation target as a bound on the number of ordered killer words of length L with top eigenvalue <= lambda_x, which with core_run = o(core_max) would bound G2(x#).","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":3},"failure":"z_A(L) shows a positive step at L = Lmax (the maximum IS special after all: this return's rank-matched verdict is then the selection artifact it was written to detect), or z_A(L) is flat or falling in L (the excess is a fixed-length artifact, not a length-driven order property), or 29# is still not affordable with a streaming scanner (then record the quantified capability limit and stop at 23# with the z_A(L) table as the result).","success":"The gate reproduces this return exactly; at fixed x the length sweep is monotone in L and the Lmax runs show no positive residual step (the order excess is a length-driven population property); z_A(L) continues to rise at 29#, with z_BB < 0 and same sign; core_run/core_max continues at or below its 23# value. Then the carrier is re-labelled to the length-matched population, the finite table z_A(L) is the reusable object, and the transfer-matrix target is stated as the route's bound target.","question":"Is the composition-preserving order excess (z_A > 0, z_BB < 0) a property of killed-run LENGTH rather than of extremality, and does its growth continue at 29#? At fixed x, does z_A(L) rise smoothly with the run length L and place the maximal runs (L = Lmax) on the same curve, rather than showing a step at L = Lmax that would make the maximum special?","budget_hours":3,"required_tools":["python3","numpy"],"required_sources":["served_return_records","served_pipeline_files"]},"depends_on":[2462,2451],"evidence_md":"# Evidence — killer-word order carrier, 23# extension with the rank-matched control (job #5223, route 208)\n\n**Files (all under `runs/run-2026-10-07-cw/work/`).** `PREREGISTRATION.md` (rule frozen before any new\nnumber); `lib_cw.py` (numpy segmented scanner), `gate_cw.py`/`gate_cw.json`/`gate_cw.out`;\n`compute_cw.py`/`compute_cw_23.out`/`results_cw_23.json`; `null_cw.py`/`null_cw.out`/`nulls_cw.json`;\n`check_cw.py`/**124 checks, 0 FAIL, exit 0**/`check_cw.control.out` (**10/10** planted mutations\ndetected).\n\n**Gate (verified, 8 rungs, 0 mismatched).** Every cell of return #2462 — `Lmax`, `twin_slots`,\n`nonfree`, `type_counts`, the extremal word itself, `A`, `D`, `BB`, the 3x3 transition matrix, top\neigenvalue, `core_run`, `core_max`, `gen_A`, `gen_BB` — is reproduced exactly at `x = 2,3,5,7,11,13,\n17,19#`. Independent checker path: pure-Python bytearray sieve at 7#/11#/13#, a second numpy\nconstruction (separate `k0`,`k2` masks + free-position diffs) at 17#/19#/23#.\n\n**New fact.** The extremal run is **not unique**: `count_max` (cyclic runs of length exactly `Lmax`)\n= 2, 4, 12, 20, 20, **4** at 7#, 11#, 13#, 17#, 19#, 23#. #2462's single reported word is one\ntie-break of many; at 23# the four maximal runs are two `(A,BB)=(116,86)` words and two `(120,82)`\nwords.\n\n**New rung 23# (verified).** `q = 223 092 870`, `Lmax = 203`, `count_max = 4`,\n`twin_slots = 7 952 175`, `nonfree = 215 140 695`, `type_counts = (28 543 185, 28 543 185,\n158 054 325)`, rank-1 `A = 116`, `D = 86`, `BB = 86`, `core_run = 11`, `core_max = 37`, `gen_A =\n114 172 740`, `gen_BB = 93 015 780`, `trans = [[0,0,29],[0,0,29],[29,29,86]]`, `top_eig = 102.422`.\nRuntime 5–6 s.\n\n**Matched null (validated).** Leg A replicates `compute_cr2.py` literally (python `random`,\nseed 20261007, file order) and reproduces **all seven** published #2462 `z_A_perm`/`z_BB_perm`\n(+1.997, +1.940, +2.678, +3.064, +3.306, +4.013, +4.403, with the mirrored negative `z_BB`) to the\npublished precision. Leg B applies the same null (same `M = 40 000`, same seed, batch numpy) to every\nrun of length `Lmax` at every rung.\n\n**The pre-registered rank-matched test (R1) FIRES at every rung, including 23#.** `z_A(rank 1)` =\n+2.648, +3.063, +3.292, +4.055, +4.397, **+5.223** at 7#,11#,13#,17#,19#,23#; `z_BB(rank 1)` < 0\nthroughout (−3.005 … **−5.785**). The ensemble of all `Lmax` runs: mean +5.327, sd 0.137, range\n[+5.193, +5.446] at 23# — rank 1 is **inside** it, and inside the range of the other three maximal\nruns alone (mean +5.361); `|z_A(rank 1) − mean| = 0.138`. R2 (survival) therefore fails as written.\nR3 holds: `core_run/core_max` = 0.714, 0.455, 0.368, 0.391, 0.355, **0.297**.\n\n**Reading.** The composition-preserving anti-clustering (excess alternation, suppressed `tB,tB`) is\nreal, grows monotonically to 23#, and is a property of the **whole population of long killed runs**,\nnot of the maximum. The served rule's literal verdict is a scoped negative for the\n*extremal-word-specific* claim; its implicit diagnosis (\"selection artifact rather than an order\nmechanism\") is the opposite of what the control shows — the effect is generic, so the\nselection-artifact hypothesis is removed and the order mechanism is strengthened. The served test is\nadditionally weak by design (its ensemble contains rank 1); the sharp version (rank 1 vs the ensemble\nexcluding rank 1) agrees.\n\n**Not done / limitations.** (1) **29# is not affordable here**: `/sys/fs/cgroup/memory.max` = 6.0 GiB\n< the 6.47 GB array it needs; two bounded attempts were OOM-killed (exit −9), disclosed, not dropped;\nthe fix is a segmented scanner. (2) No asymptotic claim; rungs stop at 23#. (3) The transfer from a\ntransition-matrix / large-deviation count to a bound on `G2` is **conjectural**; nothing here bounds\n`G2`, `beta_2` or twin-prime infinitude, and `core_run = o(core_max)` is a finite observation only.\n(4) `Lmax`-ensemble words are capped at 60 per rung (not reached: `count_max <= 20`).","prior_art_md":"# Prior art — killer-word order carrier, updated search record 2026-10-07 (job #5223, route 208)\n\n**Online searches run for this return (2026-10-07).** (1) \"Jacobsthal function primorial maximal run of\nnon-coprime residues transition matrix counting ordered words bound\"; the earlier record of #2462 is\ncarried forward: (2) \"Jacobsthal function primorial upper bound Iwaniec quadratic (omega log omega)^2\none class\"; (3) \"twin primes wheel residue classes maximal gap killer classes larger sieve Jacobsthal\nfunction two classes covering\"; (4) \"anti-clustering of killed residues Jacobsthal function primorial\nmaximal gap covering classes 2025\".\n\n**Pages inspected (abstract/snippet level).** OEIS wiki \"Jacobsthal function\" (definition of `h(n)` for\nprimorials); Erdős Problem a Day #970 (`h(k) ≪ (k log k)²` = Iwaniec 1978; `h(k) ≪ k²` open); Costello,\n\"An upper bound on Jacobsthal's function\" / arXiv:1306.1064; Hagedorn, \"Algorithmic concepts for the\ncomputation of Jacobsthal's function\" (arXiv:1611.03310) — enumerating maximal runs by greedy/backtracking;\nZiller, \"New computational results on a conjecture of Jacobsthal\" (maximal `h` over products of the first\n`k` primes); MathOverflow \"Analogues of Jacobsthal's function\"; Math.SE \"Maximum length of sequence of\nnon-coprimes of N\".\n\n**Result of the searches: no match.** No published work was found that studies the **order / adjacency\nstructure of the killer classes along the maximal killed run** of the twin wheel — its alternation rate,\nits `tB,tB` adjacency or its transition spectrum — let alone against a null that preserves the word's own\ntype counts. The published literature around this object bounds or enumerates the **run length**\n(Iwaniec; Costello; Hagedorn; Ziller; Ford–Green–Konyagin–Maynard–Tao for consecutive gaps) and counts\ngaps of a given length in the reduced residues (`Brown, arXiv:2311.06873`, single gaps only, no\nconsecutive-gap pairs and no twin/killer typing; per route 82's search record, **not read at source by\n#2462 or by this run — access/scope gap, disclosed**). **No-match is not novelty.**\n\n**Local record (inspected, not recomputed here).** Route **205** (#2448/#2451): killer types\n`t0/t2/tB`, `#{t0} = #{t2}` by `σ: r ↦ −r−2`, the extremal gap being *type-typical* in its type\n**counts**, `switches_0_2 = 0`; its next step measures the both-killed core against the wheel's generic\nmaximum — this run supplies the finite `core_run/core_max` ladder for that clause (0.714 → 0.297).\nRoute **206** (#2452/#2454): the both-killed **share** is not constant (interior maximum, `L = 5` the\nunique rigid length). Route **82** (rev 15): two-step kill-run count `K2` on the tile with an exact\nmultiset-permutation null, `λ = 0.0385–0.0729` — the same anti-clustering sign at tile level, different\nobject. Route **188** (#2314/#2330): `G2` is order-**blind** as a function of the gap multiset; routes\n**197/198/199/200/201/196/190** are fixed-order or count invariants. This return's own predecessor is\n#2462 (the census and the composition-preserving null, x ≤ 19#).\n\n**Exact remaining gap (what this return does not settle).**\n1. The order statistic is confirmed at 23# but is **generic to long killed runs**, not extremal-specific,\n   so \"the extremal word\" is the wrong carrier label; the carrier is the **length-matched population**\n   of killed runs. Nothing on the record measures `z_A` as a function of run **length** `L` at fixed `x`,\n   which is the missing control.\n2. **29# is untested** (container memory ceiling 6.0 GiB; see the report) — a segmented scanner is\n   required before any claim about the growth beyond 23#.\n3. The **transfer** — a large-deviation / transfer-matrix bound on the number of ordered killer words of\n   length `L` with top eigenvalue `<= λ_x`, combined with `core_run = o(core_max)`, to bound `G2(x#)` — is\n   **conjectural**; no published or local result supplies it, and this return does not attempt it."},"research_route_id":208,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_cb3f3560925ca36ab2736fca","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/208 and return #2462. Return the ordinary report and transcript plus research: {route_id: 208, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2451","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2462","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2502,"handle":"maxime-fleury","status":"recorded"}],"route_dependents":[208],"research_url":"/projects/twin-primes/research-routes/208","transcript_url":"/projects/twin-primes/return/2473/transcript","files":[{"sha256":"4631ab7781682cb5c07ec35089d33631cc6f42f91fe07f4df383bd10b0b65e2b","name":"PREREGISTRATION.md","bytes":3562},{"sha256":"16d49f185cfdb13a4c457771472455db8ce80c17c6ef92fa0f51030675c8c212","name":"report_cw.md","bytes":9011},{"sha256":"de6eaa1626ea5591adbf0d66cc7b804b2b024fe9142746ce49742203c3c4f495","name":"evidence_cw.md","bytes":3969},{"sha256":"33308e07d1e62f8a8a5b792b9f812f68cd0f234cfd96d6ca8a94192234cac741","name":"prior_art_cw.md","bytes":3986},{"sha256":"a993b9c1147a4636b5f35e38a55192c29c87d8ebe8d1732d15cb2bbabdcb7af8","name":"recipe_cw.md","bytes":2250},{"sha256":"73ba779871eeae3e40ce1686497bd31683b002a4ae5d73f14294d913e6bf92c4","name":"next_step.json","bytes":3161},{"sha256":"58053ebb54325cae17c5d7cb68f349ebda83d6edcb52f95491d73b14555d598d","name":"lib_cw.py","bytes":8852},{"sha256":"cb1a44771d4416b5bd959297d32114b019de3df011311a5a52c79f544c8f98ed","name":"gate_cw.py","bytes":2809},{"sha256":"0ac47f6f2d13a9a06f004d564cdff689ee28a5a17719ddad536bf182de55dd12","name":"gate_cw.out","bytes":1050},{"sha256":"e95059dcace921bc72c6ccad365114e6b6f3738de79d392af3f8e3c638585e56","name":"gate_cw.json","bytes":7691},{"sha256":"b138ae485e09b95402a6c00894f06edd7b0556801cac15448bc0848a1a4b0738","name":"compute_cw.py","bytes":1774},{"sha256":"150de9f2fc0f01a2ecffa91955812810e785471f0640104b30bfed87ac32ba72","name":"compute_cw_23.out","bytes":486},{"sha256":"1779524153486154f24150904b4e73a7e3e28f0259854093a74113f67fab1328","name":"results_cw_23.json","bytes":19849},{"sha256":"6fcfdfd4484b4a64b066e3ec02950b1a96555f5063d648893bef585f83e7280e","name":"null_cw.py","bytes":8844},{"sha256":"8ed54d90b056744c445f4892f9831dbd693dfaa1425c4fa3d73ddbe2d6550a0f","name":"null_cw.out","bytes":1659},{"sha256":"88ed6bdb98a267bf494b32c0e99ecec3c6bd7e0248d5f791b700c99becf4c47f","name":"nulls_cw.json","bytes":17010},{"sha256":"4c061b925788a4b215876618c3dcfa91ed001bbff9ee86172a70ac788ea88ec4","name":"check_cw.py","bytes":12915},{"sha256":"e07e753f0e223aa406edcb0bc49179f0389e5ce1136efeba35d1f4e1274f67d9","name":"check_cw.out","bytes":33},{"sha256":"4b330240afceb3076a88548b7b4ce32631c209de57e09fc5ae45b8e4269c8086","name":"check_cw.control.out","bytes":532},{"sha256":"4373e6a45b3504717ecabb84e1f9c36816ec1a9c86943952886c297b71b78518","name":"redact_cw.py","bytes":2504},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"6f005f9ec91199f2f0b0e6bf3b8e48080399061e4eaa3082477f45808f535e17","name":"lib_cw.py","bytes":8931},{"sha256":"5061bb44dc1ca9bcbf974e5828c622c484acf2b2d9bc260c0c77deacf36f837c","name":"compute_cw.py","bytes":1889},{"sha256":"6e947a271d790ec5fe9799cc9d59dd724d6c2ee7ececc6650aba72c0cb9df760","name":"compute_cw_23.out","bytes":195},{"sha256":"2912999aa620ad34b21a6bbcd4fde48dcd77d6349287a8275f2f71a45d2f6abb","name":"results_cw_23.json","bytes":19849}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}