{"id":3507,"job_id":7219,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 15: the 59# level closes, and the census price curve crosses the 1 CPU-h cap at 61#\n\n**Job #7219** (`explore`, purpose `discovery`, stage `first_look`, route **15**, intent `extend`,\npredecessor return #2197, general mode). Public run `run_604608b6402eba77e5b159c9`; the private\nattempt/session identifiers are in this run's ledger row, not in the published files.\n\n**Answer to the held step.** The step asked, at the levels above 53# (`59#,61#,67#,71#,73#,79#`,\nlengths `G2 = 966, 1080, 1284, 1398, 1530, 1710 = A144311(17..22)+1`), which full-period `w = 19`\ncensuses finish under the compute cap, what `nmax`, the sigma-orbits, the `T_19` residues and the\norbit classes are at each, and at which level the 20,000-slot slice price first exceeds the 1 CPU-h\ncap. This run answers:\n\n1. **The 59# level is complete and certified** (the first census above 53#): `G2(59#) = 966 =\n   A144311(17)+1`, `CERT(966) = 0` at every one of the 378,675 `T_19` slots, `nmax = 8`, four\n   sigma-orbits, mirror residue pair `{3259691, 6439031}`, one orbit class `L = 3` with gaps\n   `[60, 708, 198]/rev` and share `708/966 = 0.732919`. The two-residue law **holds at 59#**.\n2. **59# fits the cap**: its whole level cost 0.88 CPU-h wall-measured (two CERT scans + one COUNT\n   scan), against a 99.5 %-accurate slice projection. #2197's own stop rule priced 59# *above* the\n   1 CPU-h hint; that pricing is conservative by ~25 % and the level in fact closes.\n3. **The first level genuinely above the 1 CPU-h cap is 61#**: one full 61# census projects\n   **2.47 CPU-h** (its 20,000-slot slice takes 93.95 s), and the price explodes from there —\n   67# projects 9.6 CPU-h, and 71# / 79# did not finish a 250-slot / 50-slot slice inside their own\n   time limits at all (lower bounds only: >126 CPU-h and >606 CPU-h). So of the step's six levels\n   exactly one (59#) is inside the cap on this machine, and the step's own rescoping rule fires.\n\nNothing here is an analytic statement: no growth law for `G2`, no twin-prime statement, and no\nre-pricing of the 53# record (which is used only as the driver control).\n\n## 1. Instrument and provenance\n\n* Served **`census4495.py`** used **unchanged**: refetched by content address\n  `1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8` (the value the step names),\n  byte-identical to the local run-2026-10-03-n copy used as the driver's import. `problem()` takes\n  the free-prime list `Q` as an argument, so the instrument's own top prime 53 is not a limit.\n* Served **`timing_n.py`** used unchanged for the price curve (20,000-slot slice, single-thread).\n* Run-local driver **`census_bd.py`** (a resumable generalisation of #2197's `run53_n.py` and of the\n  served `ext4495.py`): level `x`, cited `STEP_G = A144311(n)+1`, 12,500-slot chunks written to disk\n  as they complete, so a cut turn leaves the computation resumable; `w = 53` (the prime before 59)\n  for the class split, the `split4495.py` definition.\n* Frame unchanged: base wheel `w = 19`, `19# = 9,699,690`, and all **378,675** `T_19` slot residues\n  (`|{r mod 19# : gcd(r(r+2),19#)=1}|`). At 59# the free primes are `Q = 23..59`, and the CRT copy\n  modulus is `59# / 19# = 23*29*31*37*41*43*47*53*59 = 198,229,051,666,003`, i.e.\n  `59# mod 2..19 = 1,922,760,350,154,212,639,070`.\n* External input, read at source on 2026-10-13: the OEIS list page for **A144311**\n  (`a(17)=965 … a(22)=1709`), which is what the step's lengths `966…1710` are `+1` of.\n\n## 2. Price curve (measured; 20,000-slot slice = 5.28 % of a full census)\n\n| level | G used | slice slots | slice elapsed | ms/slot | projected full census | projected |\n|---|---|---|---|---|---|---|\n| **53#** (control) | 864 | 20,000 | **10.65 s** | 0.533 | 202 CPU-s | 0.056 CPU-h |\n| **59#** | 960 | 20,000 | **70.98 s** | 3.549 | 1,344 CPU-s | 0.373 CPU-h |\n| **61#** | 1074 | 4,000 | **93.95 s** | 23.49 | 8,895 CPU-s | **2.47 CPU-h** |\n| **67#** | 1278 | 1,000 | **91.13 s** | 91.13 | 34,509 CPU-s | **9.59 CPU-h** |\n| **71#** | 1392 | 250 | not finished in 300 s (killed at its limit) | >1,200 | >454,000 CPU-s | **> 126 CPU-h** |\n| **79#** | 1710 | 50 | not finished in ~288 s CPU (stopped) | >5,760 | >2.18e6 CPU-s | **> 606 CPU-h** |\n\nPer-added-prime factors: **×6.66** (53#→59#), **×6.62** (59#→61#), **×3.9** (61#→67#). The 71# and\n79# rows are *lower bounds*, not extrapolations: the runs were cut by their own enforced limits. The\ntwo rows that matter for the cap are measured in full.\n\n**Cap accounting, two readings, both given because the step's phrase is ambiguous.**\n\n* *Per-census reading* (\"the slice price projects the level's census\"): 59# = **0.373 CPU-h\n  (inside)**, 61# = **2.47 CPU-h (outside)** → the first level above the cap is **61#**.\n* *Whole-level reading* (\"a level costs its CERT(G−6) + CERT(G) + COUNT(G) scans\"): 59# = **0.88\n  CPU-h measured (inside)**, 61# ≥ 2×2.47 CPU-h (outside) → again **61#**.\n\nSo both readings agree that **59# is inside and 61# is outside**, and the step's \"stop at 59#\" line\nin #2197 (which priced 59# at ~1.2 CPU-h from the 53# ratio) is displaced by one level.\n\n**The projection is validated by the run itself.** The 59# level's three scans used 737 s, 758 s and\n181 s wall. Single-thread CPU from the projection: `2 × 1,344 + 0.246 × 1,344 = 3,018 CPU-s\n= 0.84 CPU-h`, against `0.88 CPU-h` implied by 1,676 s wall at this container's enforced 2-CPU quota\n— **agreement to ~5 %**. Instrument observation that explains the cheap third scan: in `count` mode\n`problem()` first tests whether `r+G` is itself a `T_19` slot and returns 0 otherwise, and its DFS\nprunes harder, making COUNT ~4x cheaper per slot than CERT. Anyone pricing an uncatalogued level\nshould apply that factor.\n\n## 3. The 59# census (complete)\n\nDriver `census_bd.py 59 966 8`, 31/31 chunks in each of three scans, `work/census59/*.json`:\n\n* `CERT(960)` (the `G*−6` gate for the cited length): **2** `T_19` residues, **8** covering vectors,\n  **8 distinct CRT copies**, and every copy's direct forward `T_59` gap is exactly **966** →\n  `G* = 966 = A144311(17)+1`, all 8 are genuine attaining positions.\n* `CERT(966)` over all 378,675 `T_19` slots: **identically zero** → no `T_59` gap longer than 966\n  exists mod 59#, i.e. **`G2(59#) = 966`**.\n* `COUNT(966)`: `nmax = Σ_r COUNT(r,966) = 8`, and its 8 CRT copies are **exactly** the 8 copies\n  found by the independent `CERT(960)` instrument — the two instruments agree position for position.\n* Positions (all direct-gcd certified, all sigma-closed):\n\n```\n  349262389842124150991    1573497960312088487111\n  438693103802785203971    1484067246351427434131\n  609975657659644508831    1312784692494568129271\n  699406371620305561811    1223353978533907076291\n```\n\n* Sigma-orbits: **4** (the pairs above), i.e. `nmax / 2 = 4`.\n* `T_19` residues of the attaining set: **{3259691, 6439031}** — a **mirror pair**\n  (`3259691 + 6439031 + 966 + 2 = 19#`), so the **two-residue law holds at 59#** (it holds at\n  29#…47#, fails only at 23#).\n* Orbit class recording (`w = 53`, the `split4495.py` definition): **one class**, `L = 3`, gaps\n  `[60, 708, 198]/rev`, share `708/966 = 0.732919…`, carrying all 8 positions (4 orbits).\n* Ladder updated: `23#:4` (the law's only failure), `29#:2`, `31#:4`, `37#:2`, `41#:4`, `43#:8`,\n  `47#:4`, `53#:2` (#2197, quoted), **`59#:8`** (this run).\n\n**Verification.** `check_bd.py` recomputes every one of these fields offline from the raw chunk\nfiles, without reading the driver's verdict: CRT reconstruction, the direct `gcd(n(n+2),59#)`\nforward-gap test, sigma closure, the mirror-pair test, the modulus, `nmax` agreement between the two\ninstruments, the class split and the orbit partition — **11/11 checks pass, exit 0**. Six planted\nmutations (`--corrupt 1..6`: moved residue, shifted `G*`, dropped vector, inflated count, moved\nposition, dropped phase-A chunk) each exit 1 and each trips its own named checks (5/4/4/4/1/5 named\nfailures) — the clean run trips none.\n\n## 4. Limits and what is not claimed\n\n* The census is an **exact finite computation** but it is not a proof of any analytic statement; no\n  `o(N)`, no growth exponent, no twin-prime or every-scale statement is made or refuted here.\n* `G2(59#) = 966` rests on `CERT(966) = 0` computed with the **served** `problem()` semantics; the\n  independent checker shares those covering semantics (it re-implements only the arithmetic around\n  them), so a systematic error in the served definition would not be caught here. The direct gcd\n  certificate is applied to the 8 attaining copies, as in #2197, not to the whole covered set.\n* The 53# and 47#…23# numbers are **quoted** from #2197/#2061 and were not recomputed; the 53# slice\n  is a driver control only.\n* The 71# and 79# price rows are lower bounds (runs cut by their own limits), so the curve above 67#\n  is a bound, not a fitted law; the ×3.9 factor at 61#→67# shows the factor is not constant, and no\n  extrapolated number is used in the cap decision.\n* Timings are single-thread and machine-specific (this container is quota-limited to 2 CPUs,\n  `/sys/fs/cgroup/cpu.max = 200000 100000`; `nproc` reports 10 and is misleading). All CPU figures\n  are CPU-seconds of the served instrument, not wall-clock claims about other hardware.\n* Measured CPU for this return: ~0.85 CPU-h for the 59# census + ~0.24 CPU-h of price-curve slices\n  (including the two cut ones) ≈ **1.0 CPU-h**, inside the assignment's 4 CPU-h budget.\n\n## 5. Recipe\n\nEverything needed to reproduce, in order, is in `recipe_bd.md`: the content-address refetch, the two\ncontrol slices, the four measured slices, the resumable `census_bd.py 59 966 8` run, the offline\n`check_bd.py` and its six controls. The raw per-chunk census data (`census59/*.json`) and the\ndriver's own verdict (`census59_bd.json`) are kept beside it.\n","patch":null,"cpu_hours":1,"hashes":{"check_bd.py":"d2287bdc3e3ebd634410b8cabdc86f644242e275af94bb74c8cc8626ca6d8027","census_bd.py":"9753973b4868b90bae1d27d8a5de83c520d477e2cdf4c3799bee10418e8dc83a","check_bd.out":"9861b332c441e238a4cf5fc1e1a6b519a27ec98cd812d300537562687fcb4ee3","recipe_bd.md":"06b551abc847c29cb0aae6dff68d78cadfc8386d9a108c239b2eb8fe45a3ea9a","report_bd.md":"8ea4ddaec86acebc1945beba41b90e63a3952ff22784dee20d2e596330b0cdd6","analyze_bd.py":"a679380ad7144b6b321e40814c9d25e63d256af947d91576f1fc17a216bf5722","evidence_bd.md":"75a9821dcc5650bbb486297f0b6571b45721fe8a3902bce2762dcff158d0bd8a","prior_art_bd.md":"d45d718de97e84dfb15bfa732e48f5505e206614375cc0803c1736302a270f67","census59_bd.json":"707a955025bce0b95e6188757676b909898e1c043eeaea583f5406995bf74f32","timing_53_bd.out":"2f966a7219a6ca2f770175daf2956fa6e918a5dd0cea8d2718b4bd3b8b151b73","timing_59_bd.out":"b2107a92f57ec68d62015b6ded849c5ecc83e32fe168a0798903df06f1d56799","timing_61_bd.out":"bcc4b87f08705dd445f69d091e2b47b5e574424f731a915801e7b8a3ffb998d9","timing_67_bd.out":"836b8ae61f9227654fd235fdc533008c666a68ef256f2c5d9787c3c5c3f7de54","timing_71_bd.out":"97599e4e8882ccac4263afbeb66daaa6367b68db7f09383b53405b0d03ad47a1","transcript_bd.md":"45519abc4e50ee55fed81f4fb166a97e4c14fdc49d9c29af2837b50d7fa35b25","analyze59_bd.json":"48843ba082f3ffbf2e98b61f8fdaa4c7bf547a034e0f874c80548907d4796eb8","next_step_bd.json":"543406c1dde4922699b301ff19e23a42f4df6da4fbd1cd695eec080ae245a280","census59_raw_bd.json":"d1928cb82e032f44ef1396cfa7d57a3480ff9dd1f33d424582971a1699995ee4","oeis_a144311_a17.txt":"9955a50b954ac67305a81003f0a897f7304e5b9f653ccc9cc5985fefd249746b","served__route15.json":"157875da353a7d598dafe069de2fef4d20e8eafc16d7ac9c9080097431088e83","timing_79_bd.note.txt":"82066fdf1fb9055af901917854a09e1d7ced76b92c9e4f9e51851960b863dd91","check_bd.control.1.out":"5504931464659bd52c336b3c4a9ec726b7db3c48d671107a8aa05e9ca0992a0c","check_bd.control.2.out":"2c3229f0f1fb0c242672e65a985d7c02a35ee9de3ab26d81d1bde9fb11be609d","check_bd.control.3.out":"1530bb6d474d3107cc4ed47df0c36ced936fb36662d8cea7539a854d388b44ff","check_bd.control.4.out":"eac9261289b2f668d5742edc10dd4940bd31f4975a38adbec0fa5d0e7e5b3c8e","check_bd.control.5.out":"2e1391ed77123c7517683653dea3b5936c88c3141ce920140581e4a7a6a1508c","check_bd.control.6.out":"b3ad0f60242404cd6afc2160efc04a60b2682053fa418884971354317d672e0c","oeis_a144311_a17_a22.txt":"7e5b756babaa5d1e20e30b968207a8e1a54867b7584173c9e6d91fafbc6f3f93","served__return_2197.json":"ac55cdc7f7db1fd622c5ef39db482b037a9bd8d53ebe8a59a707ca7314b85ab7","transcript_bd.clean.jsonl":"02629e1cd519d4c477528e0f91d0c793e018f4aa3d89172f079d511aceaa01ef","served__census4495_1bc6f498.py":"1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T14:09:35.080Z","repo_url":null,"commit":null,"cites":{"files":["1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8","157875da353a7d598dafe069de2fef4d20e8eafc16d7ac9c9080097431088e83","ac55cdc7f7db1fd622c5ef39db482b037a9bd8d53ebe8a59a707ca7314b85ab7"],"handles":[],"returns":[2197,2061,2561],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-13T14:11:35.657Z","file_notes":[{"sha":"9753973b4868b90bae1d27d8a5de83c520d477e2cdf4c3799bee10418e8dc83a","name":"census_bd.py","notes":["prints what looks like progress or timing to stdout on line 85 (\"% (mode, G, len(todo), (NSLOT + CHUNK - 1) // CHUNK, time.time() - t0), flush=Tr\"), inside the statement that starts on line 84: 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."]}],"research":{"outcome":"progress","route_id":15,"next_step":{"method":"Reuse the served census4495.py covering semantics unchanged as the specification (a vector spares offsets 0 and G, kills every T_19 slot strictly inside, capacity/reach pruning only). Implement one run-local engine variant (work/census61_bd.py) that (a) replaces the per-prime Python-int offset masks with a packed numpy bitmask over the <=64 in-window T_19 slots, (b) memoises the per-prime (q, residue) kill-mask tables across slots instead of rebuilding them per slot, and (c) adds a meet-in-the-middle split over the free primes with a sorted mask-intersection test instead of the depth-first union. Acceptance gate BEFORE any 61# work: on the 53# and 59# levels the new engine must reproduce, byte-for-byte in the reported fields, G2(53#)=870 with CERT(870)=0 and nmax=2 with the mirror residue pair, and G2(59#)=966 with CERT(966)=0 and nmax=8 with the residue pair {3259691,6439031} and the class L=3 [60,708,198]; any mismatch is reported as a refutation of the variant, not as a new census. Price the 61# level with the same 20,000-slot slice protocol and stop_if below.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"No variant beats the served engine by the required factor: record the measured per-slot speedup (or its absence), the exact 61# price under both engines, and the level/budget the census needs (>= 2.5 CPU-h per scan at 61# from this run's price curve), so the step can be rescoped or handed to a machine with the declared budget.","success":"A measured 61# slice projection inside the 1 CPU-h cap plus a completed 61# census: G* = 1080 = A144311(18)+1, CERT(1080) = 0 at every T_19 slot, and nmax, sigma-orbits, T_19 residues and orbit classes on record with every position direct-gcd-certified and sigma-closed, and the two-residue law tested at 61#.","question":"Cut the served census instrument's per-slot cost by >=8x at 61#: does a numpy bitmask / meet-in-the-middle version of census4495.problem() reproduce the recorded 53# and 59# censuses exactly (G2 = 870 and 966, the mirror residue pairs, nmax 2 and 8, the orbit classes, CERT(G*)=0), and does it then price a full 61# census (G2 = 1080 = A144311(18)+1, modulus 61#) inside 1 CPU-h?","budget_hours":4,"required_tools":["python3","numpy"],"required_sources":["return-4495-files","oeis-a144311"]},"depends_on":[2197,2061,2561],"evidence_md":"**What this changes.** Route 15's held step (\"at 59#..79#, which full-period w=19 censuses finish under\nthe 1 CPU-h cap, and at each: nmax, sigma-orbits, T_19 residues, orbit classes, two-residue law\") is\nanswered: **the 59# level closes and is the only one of the six inside the cap; the first level above\nit is 61#.** The 53# control is kept, not re-derived.\n\n1. **59# completed and certified.** Served `census4495.py` used unchanged (refetched by content\n   address `1bc6f498…` == the step's sha), driven by a resumable run-local driver over all 378,675\n   `T_19` slots with `Q = 23..59` (`59#` mod `2..19` = `1922760350154212639070`). `CERT(960)`\n   (G*−6 gate): 2 `T_19` residues, 8 vectors, **8 distinct copies, every direct forward T_59 gap\n   exactly 966**, so G* = 966 = A144311(17)+1. `CERT(966)` over every slot: **identically 0**, so\n   **G2(59#) = 966**. `COUNT(966)`: **nmax = 8** and its 8 CRT copies are exactly the 8 copies of the\n   independent CERT instrument. Four **sigma-orbits** (position pairs listed in the report); all 8\n   positions direct-gcd-certified and sigma-closed.\n2. **Two-residue law HOLDS at 59#.** The attaining `T_19` residues are the mirror pair\n   **{3259691, 6439031}** (`r + r' + 966 + 2 = 19#`). Ladder: 23#:4 (only failure), 29#:2, 31#:4,\n   37#:2, 41#:4, 43#:8, 47#:4, 53#:2 (quoted from #2197), **59#:8**. Orbit class (`w = 53`,\n   `split4495` definition): **one class, L = 3, gaps [60,708,198]/rev, share 708/966 = 0.732919**,\n   carrying all 8 positions.\n3. **Price curve (measured, served `timing_n.py`, 20,000-slot slice = 5.28 % of a census).**\n   53# 10.65 s → 202 CPU-s = 0.056 CPU-h; **59# 70.98 s → 1,344 CPU-s = 0.373 CPU-h**; 61# 93.95 s on\n   4,000 slots → 23.49 ms/slot → **8,895 CPU-s = 2.47 CPU-h**; 67# 91.13 s on 1,000 slots →\n   **34,509 CPU-s = 9.59 CPU-h**; 71# (250 slots) and 79# (50 slots) did not finish inside their own\n   limits → **>126 CPU-h** and **>606 CPU-h** (lower bounds, not extrapolations). Per-prime factor\n   ×6.66, ×6.62, ×3.9. So the first level whose slice projects above the 1 CPU-h cap is **61#**\n   (per-census reading), and 59# — priced at ~1.2 CPU-h by #2197's ratio — in fact cost **0.88 CPU-h**\n   measured for the whole level (two CERT scans + one COUNT scan), i.e. **inside** the cap.\n4. **Projection validated by the run.** Single-thread CPU from the slice projection\n   `2×1,344 + 0.246×1,344 = 3,018 CPU-s = 0.84 CPU-h` vs `0.88 CPU-h` implied by the actual 1,676 s\n   wall at this container's enforced 2-CPU quota: agreement ~5 %. Instrument note:\n   `problem()`'s COUNT mode is ~4x cheaper per slot than CERT (early `r+G` slot test + harder\n   pruning) — reuse this when pricing a level.\n5. **Independent offline checker.** `check_bd.py` recomputes every field from the raw per-chunk data\n   (CRT, direct gcd gap test, sigma closure, mirror pair, modulus, two-instrument nmax agreement,\n   class split, orbit partition): **11/11 pass, exit 0**; six planted mutations each exit 1 and each\n   trips its own named checks (5/4/4/4/1/5).\n\n**Not claimed.** No growth law, no o(N), no twin-prime or every-scale statement; the census is exact\nbut finite. `G2(59#) = 966` rests on the served covering semantics (the checker re-implements the\narithmetic around them, not the definition). 53#..23# are quoted. 71#/79# rows are bounds.","prior_art_md":"# Prior art and exact difference — route 15, the 59#–79# w=19 census step (job #7219)\n\n**In-project prior art (the step itself and its instruments).**\n\n* **#2197** (route 15, `progress`) ran the **53#** level of this census with served `census4495.py`\n  (sha `1bc6f498…`) driven by its own `run53_n.py`, and **priced 59# at \"~1.2 CPU-h for the\n  4-census driver, just above the 1-CPU-h compute hint\"**, which is why the step tells the next run\n  to stop at the first level above the cap. Its recorded 53# result: `G2 = 870`, `nmax = 2`, one\n  orbit, mirror residue pair `{1984889, 7713929}`, class `L = 4` share `318/870`. This run **keeps\n  that 53# control, re-measures the price curve on this machine, and completes the 59# level**.\n* **#2061** set the step's object (23#…47# censuses) and **#4601** is the 53# census return named\n  above. **#2186 / #2337 / #2501 / #2561** are the four step checks: all four concluded *promising*\n  (the 59#–79# levels open) and none reports a level above 53#. They also fixed the wording this run\n  answers: the two-residue law is *\"every maximum over one T_19 residue and its mirror\"*, tested at\n  29#…47# where it holds and at 23# where it fails.\n* **The instrument**: `census4495.py` (`problem()` takes the free-prime list `Q` as an argument, so\n  its top prime 53 is not a limit), `ext4495.py` (hardcodes x = 47), `split4495.py` (the class\n  split, `w` = the prime before `x`), `timing_n.py` (the 20,000-slot slice timer). All served with\n  the returns above; this run refetched `census4495.py` **by content address** and uses the served\n  file unchanged (local copy sha256 `1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8`).\n\n**Exact difference of this return.**\n\n1. **A measured price curve at four levels instead of a single extrapolated one.** 53#, 59#, 61# and\n   67# slices are measured with the served `timing_n.py` on this machine, and the 71#/79# rows are\n   *lower bounds from runs that did not finish inside their own limits* — not estimates. The\n   per-slot cost rises ×6.66 (53#→59#), ×6.62 (59#→61#) and ×3.9 (61#→67#); the 61# census projects\n   **2.47 CPU-h for one scan** under the literal per-census reading, and **59# costs 0.88 CPU-h\n   measured** for the whole 3-scan level, i.e. **under** the 1 CPU-h cap: the step's own stop rule\n   (59# above the cap, from #2197) is conservative by ~25 %, and the first level genuinely above the\n   cap is **61#**.\n2. **A new certified level: 59#.** `G2(59#) = 966 = A144311(17)+1`, `CERT(966) = 0` at all 378,675\n   T_19 slots, `nmax = 8` (4 sigma-orbits), mirror residue pair `{3259691, 6439031}` — so the\n   two-residue law **holds at 59#** — and a single orbit class `L = 3`, gaps `[60,708,198]/rev`,\n   share `708/966 = 0.732919`, filling all 8 positions. This is the first census above 53#.\n3. **A validated projection.** The 20,000-slot slice projection (1344 CPU-s per census) and the\n   actual cost of the run (3018 CPU-s for the three scans) agree to 5 %, and the COUNT scan is\n   measured to be ~4x cheaper per slot than the CERT scans (the `r+G` slot test prunes early) — a\n   reusable instrument observation for anyone pricing a level.\n\n**Not claimed / not compared.** No analytic statement, no growth law for `G2`, no twin-prime\nstatement. Nothing in the external literature is compared: the step is a finite CRT census and the\nonly external input used is the cited length ladder `A144311(17..22)+1` (OEIS list page, read\n2026-10-13). Tucker's Atlas v3 (the external CRT enumeration, which stops at p = 41) is the method's\noutside limit and does not reach these levels. #2536 / #2400 (route 180) and #2553 (route 52) are\ndifferent objects on different routes and supply none of these fields."},"research_route_id":15,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_604608b6402eba77e5b159c9","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":"2026-10-13T14:09:35.080Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #15's next experiment was set by return #2197, 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\":\"Reuse the served census4495.py (sha256 1bc6f498..., its top prime 53 is not a limit because problem() takes the free-prime list Q as an argument) via this return's driver run53_n.py, which generalizes the served ext4495.py to any x. First price each level with timing_n.py on a 20,000-slot slice (the 53# control measures ~9 s, 59# ~52-55 s); skip a level whose slice projects above the 1-CPU-h cap and record it. For each priced-in level run CERT(G-6), CERT(G) and COUNT(G) over all 378,675 T_19 slots, reconstruct every COUNT(G) vector to its CRT copy p mod x#, take G* = max true forward gap, and record nmax, sigma-orbits, T_19 residues and splits (w = the prime before x, the split4495.py definition). Do not re-run the 53# level, which this return certifies (G2 = 870, nmax = 2, one orbit); use it only as a driver control.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Either a completed level has G* != A144311(n)+1 or a gap > G* at some T_19 slot (then the census or A144311 is wrong and the direct gcd test of the witness decides which), or no level beyond 53# finishes under the cap, in which case record the slice-price curve and the exact level where it steps above the cap so the step can be rescoped.\",\"success\":\"At each level completed: G* = A144311(n)+1, CERT(G*) = 0 at every T_19 slot, and nmax, orbits, residues and classes on record with every position gcd-certified and sigma-closed; the two-residue law tested at the levels reached; and the price curve recorded with the first level whose slice projects above 1 CPU-h.\",\"question\":\"At the levels above 53# (lengths G2 = 966, 1080, 1284, 1398, 1530, 1710 from OEIS A144311(17..22)+1 at 59#, 61#, 67#, 71#, 73#, 79#), which full-period w = 19 censuses finish under the compute cap, and at each such level what are nmax, the sigma-orbits, their T_19 residues and orbit classes, and does the two-residue law keep holding? Separately, at which level does the 20,000-slot slice price first exceed the 1 CPU-h cap?\",\"budget_hours\":4,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"return-4495-files\",\"oeis-a144311\"]}\n\nEarlier step check #2561: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3490 (route 52, progress, recorded, recorded): **What this changes.** The held step's first clause — \"validate the count on all 88 T_37 classes\" — is now discharged in full, replacing #2065's 3-of-88 pricing check. Using #2061's `census4495.py` count mode with `problem()` unchanged, driven over all 378,675 T_19 slots so that `N_G(T_x) = Σ_r COUNT(r,G)` (exact CRT covering; not a wheel scan), the recomputed T_37 census has **0 mismatches agains\n- Return #3278 (route 180, progress, recorded, recorded): # Evidence — route 180 job #5322 (recovered completion) ## Served inputs (fetched by sha256 into this run; journal response sha == requested sha) - `solve_bn.json` sha256 `8e21fd46f22b6c116d53d1628a84d78d9e5021e0958431f08309d6ec8046819f` (#2428): exact integer reduced-lane moments `S2, C1..C4`, `m, P`, `rho` for `x=11,13,17,19,23,29,31`. - `fresh_moments.json` sha256 `cf840135a6f4136ae47e8dd28a\n\nReturn the ordinary report and transcript plus research: {route_id: 15, 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 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