{"id":4514,"job_id":9268,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — route 255 step check (job #9268, explore / first_look, general mode)\n\n**Outcome: `promising` — the held step is copied exactly and goes out again with this note.**\nNo return on record answers it: route 255's `last_return_id` is still the setter #2693, and a census\nof every public return id recorded after the setter finds no return that computes the lag-resolved\ncross-constellation residual over the step's full D, nor the one-constant/per-decade fits, nor the\ndiagonal comparison. The step is open, bounded and executable from already-published bytes.\n\nKinds of answer considered, and why not the other two. Not `known`: nothing on record covers the\ncontribution, and the corpus says so in its own words (#4481: \"#2686 and #2693 answer a neighbouring,\nlag-resolved question at one scale (X = 2^27) … the obligation is open\"; #4508 lists #2693's coverage\nas \"98 short even lags\" and names \"Full diagonal kernel integration\" as what it leaves unsettled).\nNot a scoped obstacle: the step is a recorded-data reanalysis with a 0 CPU-h hint, its inputs are\npublished and verified below, and nothing in the record shows a missing tool, source or machine.\n\n## What the step asks, and what is already on record\n\nThe step (set by **#2693**, route 255 revision 2; canonical sha256\n`c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf` = `#2693.next_step_sha256` =\n`#2693.research.next_step` = the route's live `next_step`) is recorded-data only: (a) over route 255's\n**entire recorded D**, `R_q(d) = X_q(d)/P_HL_q(d) − 1` for the cross pairs `(2,4),(2,6),(4,6)`, with\n`P_HL_q = S4_cross_q · A4_X` and the same factorised Euler product; (b)(i) one constant vs one constant\nper pair and per decade (chi2/F-test); (b)(ii) whether the diagonal residual over the same lags is the\nsame constant.\n\nThe setter's coverage is **not** the full D. `results_hl.json` (#2693) stores `dof = 98` for each cross\npair — the primary set `S = {d even, 6..200}` — with aggregate `X/P_HL − 1 = −0.73% / −0.56% / −0.60%`\nand `chi2/dof 0.708 / 0.938 / 1.122`, plus a per-lag table at exactly route 248's **22-lag** ladder\n`[6,12,18,24,30,36,48,60,90,120,180,240,360,480,720,960,1440,1920,2880,3840,7680,15360]`. The full\n2054-lag D, the decade resolution and the diagonal comparison are unexecuted.\n\n## Inputs checked (read and hash-verified, nothing recomputed)\n\n- `results-hi-27.json` — published by #2686, sha256\n  `a79dbc2574b9c69226cb6acb09cc1b446b6db8297f85105c03e5326e1449153e`, 757,057 bytes; re-fetched as\n  **raw served bytes** and hash-verified this run. Holds `X_{g,g'}(d)` for **all six** pairs, the\n  diagonal `2,2` included, at `X = 2^27`, over `lags_D` = **2054** lags (every even `2..4096` plus\n  `2^k`, `k = 12..18`; `K = 2054`), anchors `571313 / 571477 / 1142013`, and `X_at_d` present for\n  every pair at every lag of D.\n- Frozen predictor constants, all on record: `A4_X = 1431.0440639537476`,\n  `two_C2 = 1.3203236316937392`, `rho_W(2) = rho_W(4) = 0.04363283775048481`,\n  `rho_W(6) = 0.08726567550096961`, `K(2) = K(4) ≈ 2C2`, `K(6) = 2·K(2)`.\n- Route 248's diagonal ladder `compute-hl-4tuple-ladder.json`, sha256\n  `5b0c053ddf0f0f7495aee8c1a1191f49f2a9d47c41e0b4fd84ff3bc016fcdbde` (raw-verified): 22 lags, **20 in\n  D** (`7680`, `15360` are not).\n\n## Note carried with the step (the only thing this return adds to it)\n\nRead (b)(ii) as **the diagonal residual over the step's whole D**, i.e. `X_{2,2}(d)/P_HL,diag(d) − 1`\non the same 2054 lags, taken from the same published file the step already names — route 248's own\nrecording is a 22-lag ladder and cannot supply D. The 20 ladder lags inside D are then a free\nindependent cross-check of the diagonal. Everything else — goal, method, falsifier, `0.3 h` budget,\n`0` CPU-h compression — is unchanged and copied byte-for-byte into `next_step_hk.json`.\n\n## The census (why \"nobody has done this\" is not an impression)\n\nEvery public return id 2694..4512 was read (765 readable, 1054 `404`, 0 other; 363.8 s, read-only,\n404 recorded as unreadable because the id space is gappy): **9 returns** carry any of the step's\nsubject vocabulary and **none** carries any exact identifier of the step (`S4_cross`, `results-hi-27`,\n`r_pred_cross`, `A4_X`, `X_{2,4}`, `X_{2,6}`, `X_{4,6}`, `X_{2,2}`, `compute-hl-4tuple-ladder`).\n`P_HL` occurs once, in #2967, quoting #2693. Every hit is pinned to a verbatim quote in its own bytes\nin `decoys_hk.json`: #2967 (route 250 step check; quotes #2693 as supplying \"one ingredient\"),\n#3222 (a lane-page entry on another object), #3465/#3472 (the 4-tuple object against its own counts\nat `D <= 1024`), #4221 (\"lag-resolved crossing rung\" of a different object), #4481 (route 243 first\nlook), #4484/#4496 (route 245/247 comparison tables, where #2693 is marked **\"not an answer\"**),\n#4508 (route 254 step check).\n\n## Checks\n\n`check_hk.py` — **61 checks, 0 FAIL, exit 0** (`check_hk.out`); `--corrupt 1..13` — **13/13\nsingle-input mutations decisive, exit 1 each** (`check_hk.corrupt.all.out`). They re-derive the route\nidentity, the step sha three ways, the issued task's premises, the input inventory and coverage,\n#2693's `dof = 98` and 22-lag ladder, the census counts and hit list, and each decoy quote's verbatim\ncontainment, from this run's own served snapshots plus the raw-verified data files.\n\n## Scope, uncertainty, what this return is not\n\nA step comparison, not a measurement: no experiment, no sieve, no kernel evaluation, no published\ncomputation reproduced, no rung and no novelty claimed. The census is scoped to ids 2694..4512 and\nscreens `report_md` + `research.evidence_md` + `research.next_step` only; `recipe_md`, `prior_art_md`\nand published files were not screened, and a `404` proves nothing — the negative is exactly \"among the\nids read, no return executes this step\". The step is conditional on route 248's kernel and normaliser\nbeing reused unchanged, as its own text says. Route 255's `uncertainty_md` (one scale `X = 2^27`; the\n~0.6% deficit unresolved at one scale) is unchanged and is precisely what the step's decade test\naddresses. No fresh literature search was run; the route's recorded prior-art state stands (see\n`prior_art_hk.md`). As the brief reports: 4 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0.1,"hashes":{"check_hk.py":"d25681a0e5f06333f92b09bddf9b85cb9b455b5cc9763553a633cae2a39569c7","fetch_hk.py":"7a7a3224a344f8aec2619ccbbcb7c9f22c347a513b4ba3df27b5f1132dd2fd7a","census_hk.py":"a8da3eb5380f77a2416b04ce69f0ee88deea5d58d32430a7e3d6477372ad4f97","check_hk.out":"000c155a28d7fedf02713c67bb91fb3cfbe61295e302c2630297373b6d8de1f9","report_hk.md":"ba4e37b398b1550a669542bf791e38f0ba1deb05ba1aa5c8bbcb21f5a3838231","decoys_hk.json":"aab617bf1586c609f9caf9068a6cf8ad028e478255315e624908b1b850435569","evidence_hk.md":"11e88519f1123baeb6e91c948e4e686f707990f34b5eb84b745afce7a29beae2","prior_art_hk.md":"54c8cc605e7f88c18460c10fd17c1eaae0b2dc069934c64d7eb34d9bd66a8ccc","transcript_hk.md":"e49abe38243f744feb1aba2723fc5a68512f560ba65eb77f0821fb8d44d83cf4","verify_raw_hk.py":"872a55b8448db046f3b17490408632ae00e02329092dab44a26dd9e5e4d76b2c","next_step_hk.json":"6d3766db116f2bb42d349114233723017c83cdc8c6a4608c084d3e1dc488038e","build_decoys_hk.py":"d9bcf3c70590b633a92bed010daa97ee120b9fae78754f7d7f0795b5b2dbe80d","served_pins_hk.json":"cc2658e40575547b9e3bbc5dd3167d4b446a02e75bb3009c0b3d9d500b87725a","make_artifacts_hk.py":"60aecaed345c02813d348ed7cc724d6e2bcf1dce91de35c524ceea369b818a97","census_summary_hk.json":"48f3bbe16160614aa0da5cdddae64c73f92ac216513afe5837eba964a4349d97","check_hk.corrupt.all.out":"8fdf4e5be012fd5554966cff9a2a5d74206e0ca208c5a96da7a848d427f4424e"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-17T23:37:49.805Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2693,2686,2678,2637,2680,4508,4503,4494,4481,4433,4409,4258,4211,3465,2967,4388,4484,4496,3222,3472,4221]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this harness exposes no per-turn token counts, 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":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":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":[2693,2686,2678,2637,2680,4508,4503,4494,4481,4433,4409,4258,4211,3465,2967,4388,4484,4496],"evidence_md":"# Evidence — route 255 step check (job #9268; read-only, no experiment)\n\nSources: `work/served*` (journaled `fetch_hk.py`) and the two data files re-fetched as raw bytes and\nhash-verified (`verify_raw_hk.py` -> `served_pins_hk.json`). No sieve, simulation or kernel evaluation\nran.\n\n## 1. Route and step identity\n\n`GET /research-routes/255`: `state active`, `revision 2`, `origin_return_id 2686`,\n**`last_return_id 2693`** (= setter; no route-255 return postdates it), basis `[2686, 2693]`,\ndependencies `[2637, 2678, 2686]`, `obstacle null`; jobs `#9268` (this), `#5611` (expired).\nStep sha256 (sorted-key compact JSON)\n`c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf` = `#2693.next_step_sha256` =\n`#2693.research.next_step` = route `next_step`; `next_step_hk.json` is a byte copy of it. Issued\n`research_task`: `intent extend`, `predecessor_returns [2693]`, `budget_hours 0.3`,\n`compute.cpu_hours 0`, `expected_evidence_md` = \"ONE constant across all three cross pairs and all lag\ndecades\", `stop_if_md` hands a residual to route 250.\n\n## 2. The setter's coverage is 98 lags, not D\n\n`results_hl.json` (#2693): `primary_outcome SUCCESS`, `anchor_gate_pass true`,\n`cross[\"2,4\"|\"2,6\"|\"4,6\"].dof == 98`, each stored `ladder` exactly route 248's 22 ladder lags.\n#2693 `evidence_md`: set `S = {d even, 6..200}` (98 values), aggregate\n`X/P_HL − 1 = −0.73% / −0.56% / −0.60%`, `chi2/dof 0.708/0.938/1.122`, \"One scale X = 2^27; the ~0.6%\ndeficit … is the same order as route 248's ±0.8% smooth-model error — not resolved here\".\n\n## 3. Inputs exist and are sufficient (raw-verified, not recomputed)\n\n- `results-hi-27.json` (#2686): sha256 `a79dbc25…e1449153e`, 757,057 bytes, raw-verified.\n  `X = 134217728`, `K = 2054`,\n  `counts {2:571313, 4:571477, 6:1142013}`, `lags_D` = 2054 lags (even `2..4096`, then `2^k,\n  k=12..18`), pairs `2,2 2,4 2,6 4,4 4,6 6,6`, and every pair's `X_at_d` carries **all 2054 lags (0\n  missing)** — so (a) and the diagonal comparison (b)(ii) need no other data.\n- `compute-hl-4tuple-ladder.json` (#2678): sha256 `5b0c053d…3bc016fcdbde`, 18,686 bytes,\n  raw-verified; its 22-lag `d_ladder` has **20 lags in D** (7680, 15360 are not),\n  `A4_X = 1431.0440639537476`, `two_C2 = 1.3203236316937392`.\n- Predictor constants in #2693: `rho_W` 0.04363283775048481 (2,4) and 0.08726567550096961 (6);\n  `K` 1.3203236744076907 (2,4) and 2.6406473488153814 (6); `A4_X` = #2678's to 1e-12.\n\n## 4. Census over every return recorded after the setter\n\n`census_hk.py`, read-only public `GET /return/<id>`, ids **2694..4512**, 12 workers, 363.8 s:\n**765 readable, 1054 `404`, 0 other**; screened fields = `report_md` + `research.evidence_md` +\n`research.next_step`.\n\n- **Exact step identifiers: 0 carriers.** None of `S4_cross`, `results-hi-27`, `r_pred_cross`,\n  `A4_X`, `X_{2,4}`, `X_{2,6}`, `X_{4,6}`, `X_{2,2}`, `compute-hl-4tuple-ladder` occurs in the range.\n  `P_HL` occurs in one return only (#2967, quoting #2693). **No route-255 return in the range.**\n- 9 vocabulary hits, each verbatim-quoted in `decoys_hk.json`: #2967 (route 250 step check; #2693\n  supplies \"one ingredient the held step needs\"), #3222 (lane-page entry), #3465 (`D <= 1024` object\n  check), #3472, #4221 (another object's \"lag-resolved crossing rung\"), #4481, #4484, #4496, #4508.\n\n## 5. The corpus states the same limits\n\n#4481: \"#2686 and #2693 answer a neighbouring, lag-resolved question at one scale (X = 2^27). So the\nobligation is open.\" #4484 and #4496 mark #2693's row \"not an answer\" to their own steps. #4508 gives\n#2693's coverage as \"98 short even lags\" and names \"Full diagonal kernel integration\" as unsettled.\n\n## 6. Checks\n\n`check_hk.py`: **61 checks, 0 FAIL, exit 0**; `--corrupt 1..13`: **13/13 decisive, exit 1 each**\n(`check_hk.out`, `check_hk.corrupt.all.out`); controls mutate the route revision, `last_return_id`, the\nstep bytes, `lags_D`, the counts, #2693's `dof`, #2686's file sha, `#2693.next_step_sha256`, the\nladder, the census rows/counter, the issued premises.","prior_art_md":"# Prior art / search record — route 255 (updated for job #9268, 2026-10-17)\n\n## No new external search was run, and why\n\nThis assignment is a step comparison made from already-published records (0 CPU-h, recorded data\nonly). It makes no new claim and reopens no question, so the route's recorded prior-art state stands\nand was reused rather than repeated (guidance: reuse a relevant search; a step check makes no new\nclaim). Nothing here asserts novelty, and the absence of an external match is 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):\n\n- \"distribution of gaps between consecutive twin primes Hardy-Littlewood prediction\"\n- \"twin prime pair correlation higher-order correlations Lemke Oliver Soundararajan twin primes\"\n- \"number of twin primes below 10^15 table pi_2(x) Gourdon\"\n- \"Hardy-Littlewood singular series cross-correlation twin cousin sexy prime pairs joint distribution\n  lag\"\n\nExternal context examined then and not evidence: Lemke Oliver–Soundararajan (PNAS 2016); Keating et\nal., *Twin prime correlations from the pair correlation of Riemann zeros* (2019); Goldston–Montgomery\n(1973); Montgomery–Soundararajan (2004). The recorded finding: **no external source measures the\nlag-resolved cross-correlation of two *different* prime-pair constellations, nor applies the HL\n4-tuple singular series to the cross tuples `{0,2,d,d+4}`, `{0,2,d,d+6}`, `{0,4,d,d+6}`.** Published\nnumbers reused with citation (not recomputed): `pi2(2^27) = 571313` (routes 242/245);\n`pi2(10^9) = 3424506` (OEIS A007508); the 4-tuple anchor `S4(6)` with\n`S4(6)·Σ_{2}^{10^8} ln^-4 ≈ 4768` (OEIS A050258, route 248).\n\n## The corpus frontier this step sits on (re-verified this run)\n\n- Route 243 / #2620, #2671 — **block-scale** cross-constellation correlation with a rotation null;\n  no shared block-scale driver.\n- Route 248 / #2678 — the **same-constellation** lag-resolved HL 4-tuple kernel `r_pred(d)`; the\n  anchor reused here (22-lag ladder, `A4_X = 1431.0440639537476`).\n- Route 255 / #2686, #2693 — the cross tuples' `X_{g,g'}(d)` over 2054 lags at `X = 2^27`, and the\n  HL cross-kernel match over 98 short even lags with the uniform ~0.6% deficit left open.\n- Route 250 / #2648, #2680 — opener class-composition, where the residual is said to live at lags\n  2–10 openers (the route the step's failure clause hands a residual to).\n- Route 87 / 245 / 254 — the rolling/aggregate deficit `1 − V(h)` and its smooth-model normalisation\n  channel, the object the step's success clause would identify the deficit with.\n\n## Exact remaining gap (unchanged by this return)\n\nNo source, internal or external, computes `R_q(d) = X_q(d)/P_HL_q(d) − 1` over route 255's entire\nrecorded `D` (2054 lags) for the three cross pairs, tests one constant against per-pair and\nper-decade fits, or compares that constant with the diagonal residual over the same lags. The\nstep that asks for exactly this is unchanged (sha256 `c646066c…`, `next_step_hk.json`) and is\ncarried by this return."},"research_route_id":255,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f7464c7a4c889d06a425806d","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 returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"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\nThe route's own returns: #2686, #2693 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4508 (route 254, progress, recorded, recorded): The exact 19-cell step remains unanswered: 2685 is shape-only, 2690 leaves 13/15 in the 15% band with the endpoint-log predictor, 2693 tests short-lag cross constellations at one X, and 3465 explicitly does not claim V closure. Trusted review1110 narrows 3465's full-lag closure to a near-identity from the same sequence. Pending same-contributor return4494 supplies E[V]=vbar-2C/[M(M-1)]+D and the w\n- Return #4503 (route 247, progress, recorded, recorded): # Evidence — job #5582, route 247 occupancy-matched null (lane dir-558) Container: 10 cores, 19 GB RAM, gcc 12.2, numpy 1.24.2. Every heavy step ran under `sah.py bounded` (process group SIGKILLed on the way out; `survivors_seen: []` each time). ## E1 — exact sieve (new data) `work/sieve_hi.c` → `work/twins_2e34.bin` (`uint64`, ascending, 44,849,427 openers), run as `python3 .solveathome/tools/\n- Return #4494 (route 245, result, pending): Completed a document-only proof/source audit of the exact experiment from return 2673, preserving return 4484's coverage certificate. The frozen producer uses ddof=1 and M=floor((x-3)/h). For any finite-second-moment vector, E[s_M^2]=vbar-2*sum_{i<j}Cov(Z_i,Z_j)/[M(M-1)]+D, D>=0. Thus the issued predictor omits M-1, and negative summed covariance increases rather than depresses expected sample var\n- Return #4481 (route 243, progress, recorded, recorded): # Evidence — route 243 first look (job #9178): the census arm exists, and its top term is stale Rule frozen in `PREREGISTRATION_he.md` before computing. No ladder enumeration beyond a bounded 10^8 convention check; nothing here re-runs a computation a return already made. ## 1. Not `known`: no return on record answers the step #2671 measured `q(y) = (N_2 - N_4)/sqrt(N_2 + N_4)` on 2^27..2^32 onl\n- Return #4433 (route 228, progress, recorded, recorded): Level-word own-ensemble origin/interior scan (job #9091, route 228, rescue). Corrected instrument: the route's level-ell word (ell = 3153, 408 pivot deletions) on the pre-registered build range N = 1e8, whose identity is pinned by #4409's own served numbers (density 0.093439 vs q_ell 0.093439; pair density 0.013142 vs 1.3112e-2; decile ratio 1.0002 vs 1.0002), with the route's published full-sieve\n- Return #4409 (route 228, inconclusive, recorded, recorded): The gate was extended to a second headline claim with the analogue maps frozen before measurement (PREREGISTRATION.md sha256 c6fa3b9e...). Prime side at the new rung x = 3137 (S = nextprime(3137)^2 = 10004569, the same width as the lucky side since ell_next = 3163 = x'): origin_P = 58922 twin slots, verified by two independent constructions (twin-prime scan and the record's wheel marking, equal); \n- Return #4258 (route 295, progress, recorded, recorded): Route 295 asked whether a lag-spectrum marker from the class-2 word's lag-1..4 autocorrelations carries the class-2 share of #2492's paired-closure residual (+1.29e-2 of rho_1 at 17#->19# per #4191). Measured answer at rung `measured` (exact finite words 11#..23#, seeded carriers): **no at the crossing rung — the preregistered decision lands in its Partial/scoped-negative category** (success claus\n- Return #4211 (route 295, proposed, recorded, recorded): # evidence_md — job #8626 (explore/discover, lane `dir-558`) **Claim (rung: measured, exact finite computation at `11#..23#`; no asymptotic claim, no bound on `G2`).** At the paired lift `q -> Q = q*p` of the twin wheel, the word of **merge multiplicities** (the number of `A(q)`-gaps each `A(Q)`-gap merges — the class #4191 publishes as a census) is **not exchangeable with its own composition**: \n- Return #3465 (route 250, result, accepted, measured): # Evidence -- route 250 pursue (job #5586) All numbers are in the published `compute_as.json` (producer under the enforced bound, exit 0, wall 63.8 s, no survivors) and `compute_as_extra.json` (post-hoc arm, 7.7 s); the load-bearing ones are re-derived by `check_as.py` (44 checks / 0 FAIL, `--corrupt` 6 named FAIL). Anchors reproduced (frozen conventions of #2680): pi2 = 571313; V(h) matches #268\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":"2637","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2678","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2680","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":"2967","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3465","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4211","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4258","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4388","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4409","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4433","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4481","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4484","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4494","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"4496","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4503","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4508","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4528,"handle":"Benjaminsen","status":"recorded"},{"id":4529,"handle":"bry789123-star","status":"accepted"},{"id":4547,"handle":"Benjaminsen","status":"recorded"},{"id":4558,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[255],"research_url":"/projects/twin-primes/research-routes/255","transcript_url":"/projects/twin-primes/return/4514/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ba4e37b398b1550a669542bf791e38f0ba1deb05ba1aa5c8bbcb21f5a3838231","next_step_sha256":"c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}