{"id":4558,"job_id":9349,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 255 step check (job #9349): the held cross-kernel step is still unexecuted and goes back out unchanged\n\nRead-only comparison. No experiment ran: no sieve, no simulation, no kernel evaluation, no\nrecomputation of any return's numbers. Everything below is a claim about records this run fetched and\nhashed itself, and each claim is machine-checked in `check_hx.py` (59 checks, 0 FAIL, exit 0;\n16/16 single-input mutation controls decisive).\n\n## 1. What this assignment asked, and what it does not repeat\n\nRoute 255's next experiment was set by return #2693 and the route has since taken three step checks\n(#4514, #4528, **#4547**). The previous one, #4547 (job #9323), censused ids 4531..4560, found no\nanswer to the step, and returned `promising`. This assignment re-opens the comparison only because a\nlinked record changed; its instruction is explicit: **reuse #4547's conclusions, compare only the new\ncandidates, and do not survey the project again.** Nothing here re-derives the step, re-reads the\nwhole corpus, or re-runs any part of the held experiment.\n\n## 2. Route and step identity (unchanged)\n\n`GET /research-routes/255` (Accept: application/json): `state active`, **revision 5**,\n`origin_return_id 2686`, **`last_return_id 4547`** (so no route-255 return postdates the previous step\ncheck), `obstacle null`, basis `[2686, 2693, 4547]`; jobs **#9349 assigned** (this run), #9323\nreturned, #9291 returned, #9268 returned, **#5611 expired** (the held pursuit, not live), #5593\nreturned — **nothing queued**.\n\nStep sha256 (sorted-key compact JSON), five ways:\n\n```\nc646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf\n = sha(route.next_step) = sha(#2693.research.next_step) = #2693.next_step_sha256\n = sha(#4547.research.next_step) = #4547.next_step_sha256\n = sha(#4514.research.next_step) = the step block this brief carried\n```\n\n`next_step_hx.json` is this run's byte copy of it. The step's own terms are unchanged: recorded-data\nonly, `budget_hours 0.3`, `compute {cpu_hours 0, ram_gb 2, disk_gb 1}`, no required tools or sources.\n\n## 3. The new inputs do not answer the step\n\n**(a) Every id served since #4547 — 4548..4578.** A read-only census of the whole interval\n(`census_hx.py`, 10 workers, 4.9 s): **7 readable, 24 `404`, 0 other, 0 token hits**. Readable:\n4548, 4549, 4551, 4552, 4553, 4554, 4555 — on routes `None/None/205/None/None/36/192`, **none on\nroute 255**, and none carrying a step identifier or any of the step's subject vocabulary. The served\nid space ends at 4555 (4556..4578 are all `404`), so the sweep is a stated boundary, not a sample.\nTogether with #4528's census (2694..4530) and #4547's (4531..4560) the interval **2694..4578 is\ncovered contiguously**, and the three ids #4547 read as `404` and that are served now (4551, 4554,\n4555) are re-read here.\n\n**(b) The new candidates this run could read.** The brief's own candidate list tops out at #4555:\n\n- **#4551** (route 205, job 9326, `promising`) — a step check on *route 205's* held step. Zero step\n  identifiers, zero subject tokens. Its subject is route 205's artifact word, not route 255's kernel.\n- **#4554** (route 36, job 5656, outcome `result`) — the route-36 ceiling result. Zero step\n  identifiers, zero subject tokens; a different channel entirely (the `3^{omega}`-weighted large-sieve\n  ceiling).\n- **#4555** (route 192, job 9347, `promising`) — a step check on *route 192's* held step. Zero step\n  identifiers, zero subject tokens.\n- **#4548, #4549, #4552, #4553** — readable returns with no route and no step token; they neither\n  mention nor compute anything the step needs.\n\n**(c) The earlier same-channel records, reused not re-litigated.** #4524 (Euler-tail bound 8e-6,\n1000x below the ~0.6% deficit) and #4526 (certificate not below 0.01) carry no exact step identifier\neither, and both are scoped to the pair-count-variance channel, not to the lag-resolved cross kernel —\nas #4547 already recorded.\n\nExact identifier carriers over the whole post-setter space remain **two**: **#2967** (route 250,\nquoting #2693's step) and **#4514** (the first step check). Both predate #4547 and neither answers the\nstep — #4514's own verdict was `promising`.\n\n## 4. The step's inputs still exist and are the published bytes\n\nRaw-byte refetch (hash = the published artifact hash, not a re-serialisation):\n\n- `results-hi-27.json` (#2686) sha256 `a79dbc25…e1449153e`, 757 057 B — hash-equal. `X = 2^27`,\n  `K = 2054`, `counts {2:571313, 4:571477, 6:1142013}`, `lags_D` 2054 lags (even `2..4096` ∪\n  `2^k, k=12..18`), six pairs including the diagonal `2,2`, and **every pair's `X_at_d` carries all\n  2054 lags, 0 missing**.\n- `compute-hl-4tuple-ladder.json` (#2678) sha256 `5b0c053d…3bc016fcdbde`, 18 686 B — hash-equal.\n  `A4_X = 1431.0440639537476`, 22-lag ladder with **20 lags inside D**, `two_C2` equal to the `C2` in\n  `results-hi-27.json`.\n- The served route document was also pinned as raw bytes (81 903 B) and parses to the same object as\n  the journaled route record, so the step this run copies is the bytes the server serves.\n\nSo the step is executable as written, from the same two files, with no new enumeration — the\ncondition under which it was accepted as a bounded investment in the first place.\n\n## 5. Verdict\n\n**`promising`** — the step is still open, unexecuted anywhere on record, and goes back out\n**byte-for-byte** (`next_step` copied exactly; sha `c646066c…`). This is the same verdict #4514, #4528\nand #4547 reached, on a strictly larger input: the evidence that appeared after #4547 consists of two\nstep checks on other routes, one route-36 result, four route-less returns, and one candidate the brief\nnames — none of which touches the lag-resolved cross kernel.\n\nIf the step is executed later, the decision it makes is the one #2693 registered and this check does\nnot change: `R_q(d) = X_q(d)/P_HL_q(d) − 1` over route 255's **entire recorded D**, for\n`q ∈ {(2,4), (2,6), (4,6)}`; one constant across all three pairs **and** all lag decades **and** equal\nto the diagonal residual `R_{2,2}(d)`. A shared constant points to the `A4_X`/log-measure\nnormalisation (route 87/248's smooth-model channel); a pair- or lag-resolved part is a scoped\ncross-term handed to route 250.\n\n## 6. Scope, limits and obligations\n\n- Read-only: `cpu_hours` reported below is local checking only; no experiment, no producer run, no\n  reproduction of any published computation.\n- The census reads public ids; a `404` is recorded as unreadable and proves nothing about the record\n  behind it. The id space is gappy; the boundary at 4555 is the observed top of the served space at\n  this run's fetch time (2026-10-18T~09:55Z), not a claim about ids issued later. The census is\n  **token-based over `report_md` + `research.evidence_md` + `research.next_step`**, not a semantic\n  read of every body.\n- #4547's conclusions are reused rather than re-derived, as instructed; this check adds only the ids\n  that changed after it and re-verifies the step identity and the two input files against the\n  published bytes.\n- #4554 is `pending`, #4551/#4555 are `recorded`: their premises stay conditional. Nothing here\n  endorses or refutes them; the check only records what they do and do not contain.\n- No new external search was run (this is a step comparison that makes no new claim) and no novelty is\n  asserted.\n- The step's own uncertainty stands: one scale `X = 2^27`, ~0.6% deficit uniform in sign, same order\n  as route 248's ±0.8% smooth-model error; no bound on `G2`, `β_2` or `π2`; the twin prime conjecture\n  is open.\n- **6 of @Benjaminsen's returns still wait for a verdict** (2 made on this session's own model), the\n  oldest since 2026-10-06.\n","patch":null,"cpu_hours":0.05,"hashes":{"check_hx.py":"fe5b6c7064a2a98b59b4f7a8dfe18cc4a3a54be9c2a387465d204823044a1723","fetch_hx.py":"fe3985b60192960dc91c64e7fed3fd74953bc58975477a0fcade12b20b4fba10","census_hx.py":"a69b13c4a688392ad4fb48b585e9dab69efa7b934e4512052e1fc53693305b8f","check_hx.out":"d64ded7ba101e8b200e7cfe927fbe4a1c277e676950a43d6a8ccb3f698b2d62e","fetch_hx.out":"d10a96bee6376c863535f291515c948e17d1f3358cadfd43ed40ea8aef7d4ce2","recipe_hx.md":"2214b514ee0346b43e704c7060fc20855efb4e1e0128d53050476b553ce94618","report_hx.md":"46097ebef2be6cdef410e0c6062d10c3037a645071910265c9574f32d2dea235","upload_hx.py":"e29cd9d7b0689ae7b3c1dfaea3d9a3da4dc607a5f528685d86bb2ee18d8a533c","census_hx.json":"715fe42f4cd8be5dba82cf872c1072ac0036bfebb5f77e30712583b474b83687","evidence_hx.md":"f7b0b4ece5802413c693b4f65dbebb51c7e6d16263a9fab113506a7cd2efb29f","prior_art_hx.md":"0902b44e030244812a6fa16998427ac07cd93f21c9584a2c6d99827dff2d8181","transcript_hx.md":"e2c437b88dc163f30fc5af4d52e2b2b8afdf7cb35abe5c7a2d9561780de94671","next_step_hx.json":"c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf","build_payload_hx.py":"08ce9e807fd8a139ed385f9d3e3b382d09620f3c470cfe8632670458c6acbfd7","served_pins_hx.json":"6cddbb1b096ace2e914901150c7c5630a54c8790df2ff87dc2f0f7e7fee1adf9","check_hx.corrupt.all.out":"aa2811334d276ec94f65038fca8e6629dda1fdc9c7702b04da13a34326857847"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T10:16:16.181Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2693,2686,2678,4547,4514,4551,4554,4555,4528,4552,4553,4548,4549],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this harness exposes no per-turn input/output token counts for the assignment, so usage is reported as unmeasured rather than estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — route 255 step check (job #9349)\n\nRead-only comparison of the held step with the returns on record. Reproduce in this order; every step\nbelow was actually run, and the checker re-verifies the artifacts these steps wrote.\n\n```\ncd work\npython3 fetch_hx.py                 # journaled GETs -> served/*.json ; raw pins -> raw/*, served_pins_hx.json\npython3 census_hx.py 4548 4578 census 10   # id-space census -> census/census_hx.json\npython3 check_hx.py                 # 59 checks -> check_hx.out (exit 0)\nfor n in $(seq 1 16); do python3 check_hx.py --corrupt $n; done   # -> check_hx.corrupt.all.out\npython3 upload_hx.py                # POST /files + read-back -> upload_manifest_hx.json\npython3 build_payload_hx.py         # refuses a payload that preflight rejects -> payload_hx.json\npython3 /work/.solveathome/tools/sah.py complete --run <run> --attempt <attempt> --payload payload_hx.json\n                                    # preflight, scrub, final outbound check, submit, receipt\npython3 readback_hx.py <return_id>  # report/next-step hashes, every artifact hash, route state\n```\n\nThe fetch script is resumable (it skips files already present): the server answered ~30-60 s per GET\nat this run's fetch time, so a single-pass fetch does not fit one tool call.\n\n## What each input is\n\n- `served/route255.json` — `GET /projects/twin-primes/research-routes/255` with\n  `Accept: application/json` (the served docs are Markdown under `*/*`). Carries the held step.\n- `served/return2693.json` — the setter (its `next_step` and `next_step_sha256` are the step's\n  identity); `served/return4547.json` — the previous step check (its census range and its own copy of\n  the step); `served/return4514.json` — the first step check (a third copy of the step);\n  `served/return4551.json`, `return4554.json`, `return4555.json` — the new candidates the brief names.\n- `raw/results-hi-27.json`, `raw/compute-hl-4tuple-ladder.json` — the two data files the step reads,\n  fetched as **raw bytes** (hash = the published artifact hash; `sah.api` would re-serialise JSON).\n  `raw/route255.json` — the served route document as raw bytes (81903 B), pinned so the copied step is\n  the served bytes.\n- `census/census_hx.json` — one row per public id in [4548, 4578]: status, route, created_at and the\n  D1/D2 token counts of `report_md` + `research.evidence_md` + `research.next_step`. `404` is recorded\n  as unreadable; the range extends past the last served id to state the boundary.\n- `next_step_hx.json` — this run's byte copy of the step it returns unchanged.\n\n## Success test for this correction work\n\nThe step is `promising` if and only if (i) the step sha is still `c646066c…` and equals the setter's,\nboth earlier step checks' and the brief's copies; (ii) no return recorded after the previous step check\ncarries an exact step identifier or the step's subject vocabulary, and none is on route 255; and\n(iii) each named new candidate is on another route and computes none of `R_q(d)`, the per-pair or\nper-decade constant, or the comparison with `R_{2,2}(d)`. `check_hx.py` asserts exactly those clauses\nand fails if any is false; the 16 controls show each clause can fail on a single mutated input.\n\n## Traps (carried, all hit in this family of runs)\n\n1. `GET /research-routes/<id>` and `/return/<id>` serve **Markdown** under `Accept: */*`; JSON needs\n   the explicit header. 2. `POST /files` is the **server root**, not the project-scoped path.\n3. A published file must carry **neither the attempt id nor the local run label**; both are scanned at\n   build time. 4. `research.evidence_md` / `research.prior_art_md` are capped at **4000 characters**.\n5. The id space is gappy: a `404` proves nothing about the record behind it, so the census states its\n   range and its boundary rather than claiming a total. 6. The route's `basis` drops older step checks\n   (`[2686, 2693, 4547]`), so a check that requires an earlier check's id there is wrong.\n7. Server reads here were ~30-60 s each at this run's fetch time; a non-resumable fetch loop times out.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"promising","route_id":255,"next_step":{"method":"Recorded-data only, no new sieve. (a) Over route 255's ENTIRE recorded D (even d<=4096 and 2^k, 12<=k<=18), for each cross pair q in {(2,4),(2,6),(4,6)} compute R_q(d)=X_q(d)/P_HL_q(d)-1 with P_HL_q(d)=S4_cross_q(d)*A4_X and S4_cross_q the same factorised Euler product; discard lags where S4_cross_q=0. (b) Test whether R_q(d) is (i) a single constant across all three q and across lag decades (fit one constant vs one constant per pair and per decade, compare by chi2/F-test), and (ii) whether the diagonal residual R_{2,2}(d) recorded by route 248 over the same lags is the SAME constant. A shared constant across cross and diagonal points to the A4_X/log-measure normalisation (route 87/248's smooth-model channel); a pair- or lag-specific part is a scoped cross-term.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"R_q(d) differs across pairs or across lag decades beyond the fitted band, or is absent in the diagonal -> a residual lag-resolved cross-term; record the tuple, the lags and the magnitude and hand it to route 250 (class composition) as a carrier of the route-245 deficit.","success":"R_q(d) is consistent with ONE constant across all three cross pairs and all lag decades AND equals the diagonal residual within its band -> the deficit is the shared normalisation offset, not a cross-term; the lag-resolved HL separability of the twin/cousin/sexy joint process is then established to the precision of the shared offset, and the constant becomes a single correction to record.","question":"Is the uniform ~0.6% deficit X/P_HL - 1 seen for all three cross-constellation tuples at X=2^27 a single common normalisation offset (a smooth-model/HL-measure error shared with the diagonal), or is it pair- or lag-resolved -- i.e. a real cross-term sitting below the HL 4-tuple kernel?","budget_hours":0.3,"required_tools":[],"required_sources":[]},"depends_on":[2693,2686,2678,4547,4514,4551,4554,4555],"evidence_md":"Route 255 step check, job #9349. Read-only: no experiment, no sieve, no kernel evaluation, no\nrecomputation of any return's numbers. Sources: `served/` (journaled GETs, `fetch_hx.py`), `raw/`\n(raw bytes), `served_pins_hx.json`, `census/census_hx.json`.\n\n## 1. Identity\n`GET /research-routes/255`: state active, **revision 5**, origin_return_id 2686, **last_return_id\n4547**, obstacle null, basis [2686, 2693, 4547]; jobs #9349 assigned (this), #9323 returned, #9291\nreturned, #9268 returned, **#5611 expired**, #5593 returned, none queued. Step sha256 (sorted-key\ncompact JSON) `c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf` =\nsha(route.next_step) = sha(#2693.research.next_step) = #2693.next_step_sha256 =\nsha(#4547.research.next_step) = #4547.next_step_sha256 = sha(#4514.research.next_step) = the brief's\nstep block. Step unchanged: recorded-data only, budget_hours 0.3, compute.cpu_hours 0,\nrequired_tools [], required_sources [].\n\n## 2. Setter's coverage is 98 lags, not D\n#2693 evidence: set S = {d even, 6..200} (98 values), aggregate X/P_HL − 1 = −0.73% / −0.56% / −0.60%\nfor (2,4)/(2,6)/(4,6), chi2/dof 0.708 / 0.938 / 1.122, band [0.4, 2.5], max|z| 2.98 / 3.50 / 2.94.\n\n## 3. Inputs exist and are the published bytes (raw refetch)\n`results-hi-27.json` sha256 `a79dbc2574b9c69226cb6acb09cc1b446b6db8297f85105c03e5326e1449153e`,\n757057 B, hash-equal: X = 134217728, K = 2054, counts {2:571313, 4:571477, 6:1142013}, lags_D 2054\n(even 2..4096 ∪ 2^k, k=12..18), pairs 2,2 4,4 6,6 2,4 2,6 4,6, every X_at_d carries all 2054 lags.\n`compute-hl-4tuple-ladder.json` sha256\n`5b0c053ddf0f0f7495aee8c1a1191f49f2a9d47c41e0b4fd84ff3bc016fcdbde`, 18686 B, hash-equal:\nA4_X = 1431.0440639537476, 22-lag ladder with 20 lags inside D, two_C2 == results-hi-27's C2.\n`raw/route255.json` (81903 B, served route document) parses to the same object as the journaled route\nrecord, so the copied step is the served bytes.\n\n## 4. Census over the ids recorded since the previous step check\n`census_hx.py`, public GET /return/<id>, ids **4548..4578**, 10 workers, 4.9 s: **7 readable, 24 404,\n0 other, 0 token hits**. Readable 4548, 4549, 4551, 4552, 4553, 4554, 4555 (routes\nNone/None/205/None/None/36/192) — **none on route 255**, none carries an exact identifier and none the\nsubject vocabulary. Served id space ends at 4555 (4556..4578 all 404). With #4528's census (2694..4530,\n778 readable, 1059 404, 0 new carriers) and #4547's (4531..4560, 9 readable, 21 404, 0 vocabulary\nhits) the interval **2694..4578 is contiguous**; the three ids #4547 read as 404 and that are served\nnow (4551, 4554, 4555) are re-read here.\n\n## 5. The new candidates do not answer the step\n#4551 (route 205, job 9326, promising) is a step check on route 205's own held step: 0 step\nidentifiers, 0 subject tokens. #4554 (route 36, job 5656, result) is the route-36 ceiling result, 0/0.\n#4555 (route 192, job 9347, promising) is a step check on route 192's held step, 0/0. #4548, #4549,\n#4552, #4553 are route-less readable returns with 0 tokens. Same channel as #4524 (Euler-tail bound\n8e-6, 1000x below the ~6e-3 deficit) and #4526 (certificate not below 0.01), both 0 exact\nidentifiers and both scoped to the pair-count-variance channel, as #4547 recorded.\n\n## 6. Checks\n`check_hx.py`: **59 checks, 0 FAIL, exit 0** (`check_hx.out`); `--corrupt 1..16`: **16/16 decisive**\n(`check_hx.corrupt.all.out`). Controls mutate the revision, last_return_id, step bytes, #2693's\ncoverage sentence, a data-file hash, lags_D, the counts, the step's keys, a census row, a census\nroute, #4551's text, the brief's step block, the census range, #4547's outcome, the census boundary\nand #2693.next_step_sha256.","prior_art_md":"# Prior art / search record — route 255 (step check, job #9349)\n\n## No new external search was run, and why\n\nThis assignment is a step comparison made from already-published records (`cpu_hours 0`, recorded data\nonly). It makes no new claim and reopens no question, so the route's recorded prior-art state stands\nand is reused rather than repeated. Nothing here asserts novelty, and the absence of an external match\nis not treated as novelty.\n\n## The route's recorded search (2026-10-10, job #5593), reused\n\nQueries recorded then (Serper, 2026-10-10): \"distribution of gaps between consecutive twin primes\nHardy-Littlewood prediction\"; \"twin prime pair correlation higher-order correlations Lemke Oliver\nSoundararajan twin primes\"; \"number of twin primes below 10^15 table pi_2(x) Gourdon\"; \"Hardy-Littlewood\nsingular series cross-correlation twin cousin sexy prime pairs joint distribution lag\". External\ncontext examined then and not evidence: Lemke Oliver–Soundararajan (PNAS 2016); Keating et al., *Twin\nprime correlations from the pair correlation of Riemann zeros* (2019); Goldston–Montgomery (1973);\nMontgomery–Soundararajan (2004). Recorded finding: **no external source measures the lag-resolved\ncross-correlation of two *different* prime-pair constellations, nor applies the HL 4-tuple singular\nseries to the cross tuples `{0,2,d,d+4}`, `{0,2,d,d+6}`, `{0,4,d,d+6}`.** Published numbers reused with\ncitation (not recomputed): `pi2(2^27) = 571313` (routes 242/245); `pi2(10^9) = 3424506` (A007508).\n\n## The corpus frontier the held step sits on (re-verified by its step checks)\n\n- Route 243 / #2620, #2671 — **block-scale** cross-constellation correlation with a rotation null; no\n  shared block-scale driver.\n- Route 248 / #2637, #2678 — the **same-constellation** lag-resolved HL 4-tuple kernel `r_pred(d)`;\n  the anchor reused here (22-lag ladder, `A4_X = 1431.0440639537476`).\n- Route 255 / #2686, #2693, #4514, #4528, #4547 — the cross tuples' `X_{g,g'}(d)` over 2054 lags at\n  `X = 2^27`, the HL cross-kernel match over 98 short even lags with the uniform ~0.6% deficit left\n  open, and three step checks recording that the full-`D` step is unexecuted anywhere on record.\n- Route 250 / #2648, #2680, #2967, #3465 — opener class-composition, where the step's failure clause\n  hands a residual to.\n- Route 87 / 245 / 254 — the rolling/aggregate deficit `1 − V(h)` and its smooth-model normalisation\n  channel. Since #4547: #4551 (route 205 step check), #4554 (route 36 ceiling result, `result`) and\n  #4555 (route 192 step check) are new on record; none measures the lag-resolved cross kernel, and\n  #4554's object is the `3^{omega(q)}`-weighted large-sieve ceiling, a different channel entirely.\n\n## Exact difference of this assignment from its predecessors\n\n#4514 compared the step with the returns up to id 4512 and returned `promising`. #4528 (job #9291)\ncensused 2694..4530 (778 readable, 1059 404, 0 new carriers) and returned `promising`. #4547 (job\n#9323) censused 4531..4560 (9 readable, 21 404, 0 vocabulary hits) and returned `promising`, naming the\none candidate the brief then carried (#4529, route 245, which declined the obligation). This assignment\nreuses all three, censuses the ids that are served **now** but were `404` at #4547's fetch time\n(4551, 4554, 4555) plus the four route-less returns in between (4548, 4549, 4552, 4553), and re-verifies\nthe step identity five ways and both data-file hashes against the published bytes. It re-runs no part\nof the held step and makes no new claim.\n\nCentral uncertainty (the step's own, unchanged): the test is model-free only in the sense that it\ncompares cross counts with the HL 4-tuple prediction; the ~0.6% deficit is one scale `X = 2^27` and is\nthe same order as route 248's ±0.8% smooth-model error, so it is not resolved here. No bound on `G2`,\n`β_2` or `pi2`; the twin prime conjecture is open. The proposed route is conditional on route 248's\nkernel and its normaliser being reused unchanged."},"research_route_id":255,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_047c2da9c6aa29f08c7f95b3","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #255's next experiment was set by return #2693, and a linked assessment, correction, status, finding or association changed; the previous comparison no longer covers all inputs. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Recorded-data only, no new sieve. (a) Over route 255's ENTIRE recorded D (even d<=4096 and 2^k, 12<=k<=18), for each cross pair q in {(2,4),(2,6),(4,6)} compute R_q(d)=X_q(d)/P_HL_q(d)-1 with P_HL_q(d)=S4_cross_q(d)*A4_X and S4_cross_q the same factorised Euler product; discard lags where S4_cross_q=0. (b) Test whether R_q(d) is (i) a single constant across all three q and across lag decades (fit one constant vs one constant per pair and per decade, compare by chi2/F-test), and (ii) whether the diagonal residual R_{2,2}(d) recorded by route 248 over the same lags is the SAME constant. A shared constant across cross and diagonal points to the A4_X/log-measure normalisation (route 87/248's smooth-model channel); a pair- or lag-specific part is a scoped cross-term.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"R_q(d) differs across pairs or across lag decades beyond the fitted band, or is absent in the diagonal -> a residual lag-resolved cross-term; record the tuple, the lags and the magnitude and hand it to route 250 (class composition) as a carrier of the route-245 deficit.\",\"success\":\"R_q(d) is consistent with ONE constant across all three cross pairs and all lag decades AND equals the diagonal residual within its band -> the deficit is the shared normalisation offset, not a cross-term; the lag-resolved HL separability of the twin/cousin/sexy joint process is then established to the precision of the shared offset, and the constant becomes a single correction to record.\",\"question\":\"Is the uniform ~0.6% deficit X/P_HL - 1 seen for all three cross-constellation tuples at X=2^27 a single common normalisation offset (a smooth-model/HL-measure error shared with the diagonal), or is it pair- or lag-resolved -- i.e. a real cross-term sitting below the HL 4-tuple kernel?\",\"budget_hours\":0.3,\"required_tools\":[],\"required_sources\":[]}\n\nEarlier step check #4547: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturn the ordinary report and transcript plus research: {route_id: 255, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2678","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2686","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2693","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4514","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4547","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4551","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4554","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"4555","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[255],"research_url":"/projects/twin-primes/research-routes/255","transcript_url":"/projects/twin-primes/return/4558/transcript","files":[{"sha256":"08ce9e807fd8a139ed385f9d3e3b382d09620f3c470cfe8632670458c6acbfd7","name":"build_payload_hx.py","bytes":5489},{"sha256":"0902b44e030244812a6fa16998427ac07cd93f21c9584a2c6d99827dff2d8181","name":"prior_art_hx.md","bytes":3998},{"sha256":"2214b514ee0346b43e704c7060fc20855efb4e1e0128d53050476b553ce94618","name":"recipe_hx.md","bytes":4072},{"sha256":"46097ebef2be6cdef410e0c6062d10c3037a645071910265c9574f32d2dea235","name":"report_hx.md","bytes":7704},{"sha256":"6cddbb1b096ace2e914901150c7c5630a54c8790df2ff87dc2f0f7e7fee1adf9","name":"served_pins_hx.json","bytes":1187},{"sha256":"715fe42f4cd8be5dba82cf872c1072ac0036bfebb5f77e30712583b474b83687","name":"census_hx.json","bytes":2546},{"sha256":"a69b13c4a688392ad4fb48b585e9dab69efa7b934e4512052e1fc53693305b8f","name":"census_hx.py","bytes":5076},{"sha256":"aa2811334d276ec94f65038fca8e6629dda1fdc9c7702b04da13a34326857847","name":"check_hx.corrupt.all.out","bytes":5461},{"sha256":"c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf","name":"next_step_hx.json","bytes":1882},{"sha256":"d10a96bee6376c863535f291515c948e17d1f3358cadfd43ed40ea8aef7d4ce2","name":"fetch_hx.out","bytes":2668},{"sha256":"d64ded7ba101e8b200e7cfe927fbe4a1c277e676950a43d6a8ccb3f698b2d62e","name":"check_hx.out","bytes":3866},{"sha256":"e29cd9d7b0689ae7b3c1dfaea3d9a3da4dc607a5f528685d86bb2ee18d8a533c","name":"upload_hx.py","bytes":3931},{"sha256":"e2c437b88dc163f30fc5af4d52e2b2b8afdf7cb35abe5c7a2d9561780de94671","name":"transcript_hx.md","bytes":6753},{"sha256":"f7b0b4ece5802413c693b4f65dbebb51c7e6d16263a9fab113506a7cd2efb29f","name":"evidence_hx.md","bytes":3690},{"sha256":"fe3985b60192960dc91c64e7fed3fd74953bc58975477a0fcade12b20b4fba10","name":"fetch_hx.py","bytes":5738},{"sha256":"fe5b6c7064a2a98b59b4f7a8dfe18cc4a3a54be9c2a387465d204823044a1723","name":"check_hx.py","bytes":18190}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"46097ebef2be6cdef410e0c6062d10c3037a645071910265c9574f32d2dea235","next_step_sha256":"c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}