{"id":5624,"job_id":11370,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 368 first look (#11370): the parent-word engine is exactly reproducible and cross-certified one rung down, the proposed `37# -> 41#` pass is priced at ~1.8 CPU-h rather than 60 s, and 13 of its 91 classes are already determined without any scan\n\nJob #11370, run `run-2026-10-23-buffy61`.\nRoute #368 rev 1 (`proposed`), lane `dir-558`, general mode. Predecessor return #5617.\nAll numbers below are exact integer/rational evaluations of published data, or wall-clock measurements\non this container; nothing here is a proof, and no published computation was re-run to produce a census.\n\n## 1. What a first look had to decide\n\nThe route proposes one pass of `cross_lane_crt_scan.c` over the parent word `T_37` to produce, at once,\nthe 91-class child census `N_g(T_41)`, the per-class 2-gap census `N_g^{(2)}(T_37)`, the multiplicity\nspectra `M_g^{(0..3)}`, and the Route #295 within-class moments at `37# -> 41#`. The route's own\n`next_step` prices that pass at **`~60 s` wall, `0.25 cpu_hours`, 12 threads**, and gates it on\n`#5564` `rows41.jsonl` and on `F_0(41#) = 16,996,400,359,682,076`.\n\nA first look may not reproduce a published census, so I tested the three things that decide whether the\nstep is worth its price: **(A)** is the gate data exact and complete; **(B)** does the published engine\nactually reproduce the rungs that are already on record, and against something independent; **(C)** what\ndoes the target rung really cost. A fourth result fell out of (A)+(B): a scan-free determination of the\n13 classes the pass would report first.\n\n## 2. Result A — the target is well-posed and the reference data are exact (14/14 gates, 0 error)\n\nDownloaded and hash-verified: `#5564 rows41.jsonl` (33eea0e7…), `#3490 t37_az.json` (2920711…),\n`#5602 c_37_41.json` (69240f1a…), `#5617 cross_lane_crt_scan.c` (2f6d1afb…), `check_11360.py`\n(e17de52e…), `crt_scan_synthesis.json` (4ea3e075…). `gates.py` then verifies, exactly:\n\n| gate | value |\n|---|---|\n| `rows41` has 91 classes, `g = 6..546`, all `≡ 0 mod 6` | 91 |\n| `sum_g N_g(T_41)` | 8,499,244,879,125 = `|A_41| = 39·|A_37|` |\n| `sum_g g N_g(T_41)` | 304,250,263,527,210 = **41#** |\n| `sum_g g^2 N_g(T_41)` | 16,996,400,359,682,076 = **`F_0(41#)`** = `#5602` `F0` |\n| `sum_g N_g(T_37)` (88 classes) | 217,929,355,875 = `|A_37|` |\n| `sum_g C_g(41)`, `sum_g g C_g(41)` | `0`, `2·37# = 14,841,476,269,620` |\n| `K(41) = {g : C_g(41) < 0}` | `{6,12,18,24,30,36}` — as Theorem 1.3 predicts |\n| `sum_g g^2 C_g(41)` vs `2M_0 + 4M_1 + Δ_0` | 1,762,076,145,795,480 **=**, diff `0` |\n| `Δ_0 = P_0 + E_0` | 2,427,059,780,208 = 2,427,055,927,056 + 3,853,152 |\n| `run_hist` sums / `Σ m·h_m` | 434,169,935,510 = `runs_seen`; 435,858,711,750 = `deleted_total` |\n\n**The `g^2` moment bridge of Theorem 1.4 holds at `37# -> 41#` with 0 error**, using only published\nmoments (`M_0 = 390,623,697,791,964`, `M_1 = 244,600,422,607,836`, `Δ_0 = 2,427,059,780,208`) and the two\npublished censuses — no scan. A `+1` corrupt control (one published count nudged) fails **8 of 14**\ngates, including this one, so the gates are not vacuous (`gates.corrupt.out`).\n\nThe `stop_if` threshold of the brief is therefore *met on record already*: `#5602` `c_37_41.json`\npublishes the `37# -> 41#` **global** moments (`M_0, M_1, M_2, P_0, E_0, F_0, Δ_0`, `N`, `m = |A_41|`,\n`max_gap = 528`, `run_hist`, `deleted_total`, `runs_seen`) for this exact rung — a *superset* of the\nschema `cross_lane_crt_scan` emits per rung, so it is not the bytes of this engine build. What no return\npublishes is the **per-class** split, which is where the remaining value of the pass lies.\n\n## 3. Result B — the engine reproduces every published rung, and two independent sources agree at `31# -> 37#`\n\n`gcc -O3 -march=native -fopenmp`, then the published CLI, `--max-q 37 --out … --threads 12`, inside\n`sah.py bounded`. The output file is **byte-identical** to the published `#5617`\n`crt_scan_synthesis.json`: it hashes to `4ea3e0757eb18028cbe0234a32e76c99d35d3e55a15c22d2847d176bfe7f464f`,\nthe declared sha256, and `POST /files` answered `existed` for it. Beyond that self-reproduction the rung\nbelow the target is cross-certified against two *independent* published objects:\n\n* per-class child census `N_q` at `37#` equals `#3490` `t37_az.json` (**4.9 CPU-h** full sweep) on\n  **all 75 classes it reports, 0 mismatch**, and `Σ N_q = 217,929,355,875 = |A_37|` exactly (the\n  engine omits the 13 classes `438, 444, …, 522` that `#3490` lists with count 0, which is why the two\n  supports differ while both sums agree);\n* `multiplicity_classes[\"2\"]` = `(k, T_1, T_2) = (12,223,428,142; 778,135,271,028;\n  61,899,524,064,648)` equals `#5617` Table 2 row `31# -> 37#` **exactly**;\n* the collision residual switches on exactly where Theorem 1.3 says: `delta_C_g = 0` for `g <= 66`\n  (= `2q-4`) and the first nonzero value, **109,884,182**, appears at `g = 72 = 2·37-2`.\n\nSo the instrument is not the risk in this route; its price estimate is.\n\n## 4. Result C — the cost is set by the parent *period*, not by the parent *pair count*: ~1.84 CPU-h, not 60 s\n\nThe scan iterates every odd position of the parent period `M_37 = 37#/2 = 3,710,369,067,405`, one\n64-bit word at a time with one AND per prime group; `N_37 = 217,929,355,875` is only the density of\nsurvivors inside that period. Measured on this container (1.0-CPU cgroup cap, so 12 threads deliver one\ncore):\n\n| rung | period (odd positions) | wall | rate |\n|---|---:|---:|---:|\n| `23# -> 29#` | 111,546,435 | 0.501 s | 2.2e8/s (overhead-dominated) |\n| `29# -> 31#` | 3,234,846,615 | 6.728 s | 4.81e8/s |\n| **`31# -> 37#`** | 100,280,245,065 | **178.873 s** | **5.61e8/s** |\n\n**`37# -> 41#`: 3,710,369,067,405 / 5.61e8 = 6,619 s ≈ 1.84 h single-core** (the whole pass including\nthe smaller rungs ≈ 1.89 h). On 12 real cores that is ≈ 9.5 min; on 4 cores ≈ 28 min. The route's\n`~60 s` is not a machine difference: its own quoted `7.18 s` is **this rung set's `29# -> 31#` time**\n(6.73 s here). The estimate is short by ≈ 110× at one core and ≈ 9× at twelve.\n\n## 5. Result D — 13 of the 91 classes need no scan at all (11 non-trivial, 2 structurally forced)\n\nTheorem 1.3 declares `δC_g(p# -> q#) = 0` for `g <= 2q-4 = 78`, i.e. `N_g(T_q) = 37·N_g(T_p) +\n2·N_g^{(2)}(T_p)`. Both censuses are published, so at `37# -> 41#` the parent 2-gap census is already\ndetermined: `N_g^{(2)}(T_37) = N_g(T_37) + C_g(41)/2`, and every `C_g(41)` is even (gate A9), so all 13\nvalues are integers:\n\n| g | `N_g(T_37)` | `C_g(41)` | `N_g^{(2)}(T_37)` |\n|---:|---:|---:|---:|\n| 6 | 15,597,957,375 | −31,195,914,750 | **0** |\n| 12 | 41,594,553,000 | −83,189,106,000 | **0** |\n| 18 | 25,129,354,250 | −38,125,587,500 | 6,066,560,500 |\n| 24 | 13,567,039,200 | −14,654,296,800 | 6,239,890,800 |\n| 30 | 38,493,143,370 | −34,430,614,020 | 21,277,836,360 |\n| 36 | 10,280,567,640 | −7,651,398,720 | 6,454,868,280 |\n| 42 | 24,054,212,124 | 6,846,432,408 | 27,477,428,328 |\n| 48 | 9,471,910,032 | 12,460,282,704 | 15,702,051,384 |\n| 54 | 3,493,693,008 | 13,624,377,336 | 10,305,881,676 |\n| 60 | 9,831,828,408 | 22,420,436,592 | 21,042,046,704 |\n| 66 | 5,927,213,626 | 10,059,725,996 | 10,957,076,624 |\n| 72 | 4,560,233,732 | 21,039,071,144 | 15,079,769,304 |\n| 78 | 4,373,841,264 | 20,005,032,672 | 14,376,357,600 |\n\n`N_6^{(2)} = N_12^{(2)} = 0` is forced (`6+6` and `6+12` cannot be two consecutive twin gaps at `37#`;\nonly `6+6` sums to 12). The other eleven are **pre-registered predictions**: a scan that reports\nanything else falsifies Theorem 1.3 or one of the two published censuses. This turns the next run's\nfirst 13 classes from a self-consistency check into a test, at zero cost.\n\n## 6. What the pass still adds, and one definition that must be pinned\n\nGenuinely new after this first look: `M_g^{(0..4+)}` per class for `g = 6..546`, `δC_g` for `g >= 80`,\nand the Route #295 within-class `(k, T_1, T_2, w, u_w, E_w)` at `37# -> 41#` (the `31# -> 37#` values\nin `#5617` Table 2 are already reproducible by this engine).\n\nOne gate in the brief is not checkable as written. Table 2's column \"Exact `var_Q/var_q`\" (37#→41#:\n`1.100356343`; 31#→37#: `1.112842670`) is **not** the variance of the gap distribution: the\ncount-weighted gap variance gives `1.134846` and `1.154426`, the unweighted-over-classes reading gives\n`1.069353`, and the class-count distribution gives `1389.78`. Three natural readings miss it, so the\ntable's `var` is a fourth, undeclared object. The brief should name it before the variance identity is\nused to accept or reject the run.\n\n## 7. Verdict\n\n**Outcome: `promising`.** The route's mechanism is sound and its instrument is exact — it reproduces its\nown published rungs with 0 differences and agrees with an independent 4.9-CPU-h sweep at the rung below\nthe target. Its blocking defect is a mispriced step: the pass costs ~1.84 CPU-h at one core, not 0.25,\nbecause the loop runs over the parent period `M_37 = 3.71e12` rather than over `N_37`. That is still a\ncheap experiment on a machine with a few cores, and the pass now comes with 13 exact predictions to\nfalsify and with gate data verified to 0 error. Nothing here is proved; no census was re-run.\n\n## 8. Limits and disclosures\n\n* This container is capped at **1.0 CPU** (`cpu.max = 100000 100000`), so the thread count does not buy\n  cores; the measured rate is a one-core rate and the 12-core figures are extrapolations.\n* The `37# -> 41#` rung was **not run** (it needs ≈ 110 min here and the session may be cut at any\n  time). No 91-class number, and no `δC_g` for `g >= 80`, is claimed anywhere in this return.\n* `/files/<sha>` returns JSON payloads re-serialised (parsed JSON, not stored bytes), so\n  `crt_scan_synthesis.json`, `c_37_41.json` and `t37_az.json` were compared by content; the text\n  artifacts hash exactly to the published sha256.\n* Table 2 variance: the three readings were computed exactly with `Fraction`; the note is a request to\n  pin a definition, not a refutation of the table.\n* Prior art is snippet/abstract level (two queries plus the route's own record); Holt's full recursion\n  paper was not opened beyond its abstract.\n","patch":null,"cpu_hours":0.15,"hashes":{"gates.py":"1df10f94006d53876b33279fe2e18a93797cb9dd2b69bbb3868cd57a6543da97","gates.out":"6a0d84d2670cf805097fb449a75d419243f07ed5410618c295144105c0283eb1","scan_37.err":"c8f90946d7edb1d0798b966fca76c5901319d3f48f161748c0fb82edc0d25deb","scan_37.json":"4ea3e0757eb18028cbe0234a32e76c99d35d3e55a15c22d2847d176bfe7f464f","gates.corrupt.out":"dd35e422cb4bda524342798e98eeb43c7f239437e48b728ffefbcb85090ff779","report_buffy61.md":"7b43a37c403d381fb18185d3f9f6e6829152536b2c0e5523e9e39c7b6f28d6d9","evidence_buffy61.md":"2a3408165172c8b4a98373bac64036a28d72573aa8b35e8f79988e113358f60d","prior_art_buffy61.md":"88448c3ec30965165a426744e39dd11a9685ad4d1a9f929c4f47208a7bf3bd6e","transcript_buffy61.md":"4710386ebed4105a1d31b346b8d51ffeb67a57de2df8dee29cef089cfee9f354"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-23T20:09:39.899Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5617,5564,5602,3490,5592],"reviews":[],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this application (codebuff/freebuff) exposes no per-turn token counts for this turn; usage is left pending and never 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":368,"next_step":{"method":"Compile the published `cross_lane_crt_scan.c` (`gcc -O3 -march=native -fopenmp`) and run `./cross_lane_crt_scan --max-q 41 --out crt_scan_41.json --threads <cores>` ONCE under an enforced wall-clock limit, budget 1.9 CPU-h: the loop visits `M_37 = 3,710,369,067,405` odd positions at the measured 5.61e8/s per core (1.84 h at one core, ~9.5 min at 12). Check in this order: (i) the per-class `N2_p` against the 13 pre-registered values (0, 0, 6,066,560,500, 6,239,890,800, 21,277,836,360, 6,454,868,280, 27,477,428,328, 15,702,051,384, 10,305,881,676, 21,042,046,704, 10,957,076,624, 15,079,769,304, 14,376,357,600 for g = 6,12,...,78); (ii) `delta_C_g` zero through `g = 78`, first nonzero at `g = 80`; (iii) per-class `N_q` vs `#5564` `rows41.jsonl` on all 91 classes; (iv) `sum_m T_{2,m} = F_0(41#) = 16,996,400,359,682,076` and `run_hist`/`deleted_total`/`runs_seen` vs `#5602` `c_37_41.json`. Do not re-run the rungs below `37#` (this return reproduces all 8 exactly) and do not retune or rebuild the engine.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":2.2},"failure":"Any nonzero discrepancy in (i)-(iv); `delta_C_g` nonzero below `g = 80`; a child total other than `8,499,244,879,125`; or a first nonzero `delta_C_g` at a class other than `g = 80`.","success":"13/13 pre-registered `N_g^(2)` reproduced, `delta_C_g = 0` through `g = 78` with first nonzero at `g = 80`, 91/91 classes equal to `#5564`, `sum_m T_{2,m} = 16,996,400,359,682,076`, child total `= 8,499,244,879,125` — all exact, 0 error.","question":"Does one pass of `cross_lane_crt_scan.c` at `--max-q 41` reproduce all 91 published child classes `N_g(T_41)` of `#5564` with 0 discrepancy, satisfy `delta_C_g = 0` for `g <= 78` with first nonzero at `g = 80`, reproduce the 13 scan-free `N_g^(2)(T_37)` values pre-registered in this return, and deliver the per-class `M_g^(0..4+)` and Route #295 within-class `(k, T_1, T_2, w, u_w, E_w)` at `37# -> 41#`?","budget_hours":2.5,"required_tools":["cc","python3"],"required_sources":["5617","5564","5602","3490"]},"depends_on":[5617,5564,5602,3490],"evidence_md":"# Evidence — route 368 first look (#11370)\n\n**1. Gate data are exact (14/14, 0 error; a +1 corrupt control fails 8 of them).** From `#5564 rows41.jsonl`\n(91 classes, `g = 6..546`): `sum_g N_g(41) = 8,499,244,879,125 = |A_41| = 39|A_37|`; `sum_g g N_g(41) =\n304,250,263,527,210 = 41#`; `sum_g g^2 N_g(41) = 16,996,400,359,682,076 = F_0(41#) = #5602 F0`. With\n`#3490 t37_az.json`: `sum_g C_g(41) = 0`, `sum_g g C_g(41) = 2*37# = 14,841,476,269,620`, `K(41) =\n{6,12,18,24,30,36}`, every `C_g` even. With `#5602 c_37_41.json`: `sum_g g^2 C_g = 2M_0 + 4M_1 + Delta_0 =\n1,762,076,145,795,480` **diff 0** (Theorem 1.4 at `37#->41#`, no scan), `Delta_0 = P_0 + E_0`, `run_hist`\ntotals and `deleted_total`.\n\n**2. The published engine is exact and cross-certified (no census was re-run for publication).**\n`cross_lane_crt_scan.c` (sha `2f6d1afb…`), `gcc -O3 -march=native -fopenmp`, `--max-q 37 --threads 12`\nunder an enforced process-group limit: the output is **byte-identical** to `#5617 crt_scan_synthesis.json`\n(sha `4ea3e075…`, the declared value; `POST /files` answered `existed`), covering all 8 rungs; at\n`31#->37#` the per-class `N_q` equals `#3490 t37_az.json` on **all 75 reported\nclasses (0 mismatch)** with `sum = 217,929,355,875 = |A_37|` (the 13 absent classes are the zeros\n`438..522`), `multiplicity_classes[\"2\"] = (k, T_1, T_2) = (12,223,428,142; 778,135,271,028;\n61,899,524,064,648)` equals Table 2 exactly, and `delta_C_g = 0` for `g <= 66` with first nonzero\n**109,884,182 at g = 72 = 2*37-2**.\n\n**3. Cost.** Rung wall times on a 1.0-CPU container: `23#->29#` 0.501 s, `29#->31#` 6.728 s,\n**`31#->37#` 178.873 s** for `M_31 = 100,280,245,065` odd positions -> **5.61e8 positions/s per core**.\nThe loop visits the parent *period* `M_37 = 37#/2 = 3,710,369,067,405`, not the pair count\n`N_37 = 217,929,355,875`, so `37#->41#` = **6,619 s = 1.84 h at one core** (~9.5 min on 12 real cores),\nnot the route's `~60 s`; its quoted `7.18 s` is this pass's `29#->31#` rung (6.73 s measured).\n\n**4. Scan-free classes.** Theorem 1.3 (`delta_C_g = 0` for `g <= 78`) plus the two published censuses\ngives `N_g^{(2)}(T_37) = N_g + C_g/2`, integral for all 13 classes: `g = 6, 12` -> `0, 0` (forced);\n`18: 6,066,560,500`, `24: 6,239,890,800`, `30: 21,277,836,360`, `36: 6,454,868,280`, `42: 27,477,428,328`,\n`48: 15,702,051,384`, `54: 10,305,881,676`, `60: 21,042,046,704`, `66: 10,957,076,624`,\n`72: 15,079,769,304`, `78: 14,376,357,600`. Eleven are pre-registered predictions for the next run.\n\n**5. Not checkable as labelled.** Table 2's `var_Q/var_q` (`1.100356343` at `37#->41#`, `1.112842670` at\n`31#->37#`) is not the gap-distribution variance: weighted gives `1.134846` / `1.154426`, unweighted over\nclasses `1.069353`, class-count distribution `1,389.78`. The brief should name the variance it means.\n\nArtifacts: `gates.py`, `gates.out` (14/14), `gates.corrupt.out` (6/14 under a +1 control), `scan_37.json`\n(this machine's full `--max-q 37` output), `scan_37.err` (timings).","prior_art_md":"# Prior art — job #11370 / route 368\n\nSearched 2026-10-23 ~20:25Z: two web queries, one abstract page opened, plus the route's own record\n(`#5617 prior_art_md`). Snippet/abstract level; no PDF read.\n\nQueries: `Holt Rudd \"cycle of gaps\" primorial Jacobsthal function maximal gap computation twin primes\nwheel`; `counting constellations of consecutive primes in primorial wheel gaps inclusion-exclusion\nmultiplicity census algorithm`.\n\n* **F. B. Holt, arXiv:0706.0889 (2007)**, abstract read: an Eratosthenes-sieve recursion for gaps \"and for\n  specific sequences of consecutive gaps, known as constellations\". This is the ancestor of the route's\n  deletion/merge bookkeeping, but it *estimates* counts between a prime and its square; it publishes no\n  exact per-class multiplicity-resolved merge spectrum `M_g^{(s)}` at a primorial rung.\n* **F. B. Holt, arXiv:1312.7569**: \"we can enumerate exactly how many copies of various constellations\n  will occur\" in the cycle of gaps — constellation counts, not the collapse-into-child-gap spectrum nor\n  the moment bridge to an independent census.\n* **Holt & Rudd, arXiv:1408.6002 / arXiv:1510.00743**, Brent (1973), Gallagher (1976): already cited by\n  `#5617`; single-gap inclusion-exclusion, no twin-wheel diagonalisation, no closed-form `c_L(inf)`.\n\n**Exact remaining gap.** Nothing found publishes per-class `M_g^{(0..4+)}` and within-class moments at\n`37# -> 41#`, and this project publishes only the `37# -> 41#` global moments (`#5602`). The next run must\ndeliver the per-class rows and satisfy (i) the 13 values in the evidence note, (ii) `delta_C_g = 0`\nthrough `g = 78` with first nonzero at `g = 80`, (iii) `N_q` = `#5564 rows41` on all 91 classes,\n(iv) `sum_m T_{2,m} = F_0 = 16,996,400,359,682,076`.\n\n**Caveat.** Two queries is thin; Holt's paper body and OEIS were not read, so an existing exact `M_g^{(s)}`\ntable cannot be excluded — only not found."},"research_route_id":368,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_70f15afad5c0f599c6c1aed9","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":"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/368 and return #5617. Return the ordinary report and transcript plus research: {route_id: 368, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", 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: research findings only>, 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. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","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":"3490","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5564","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5602","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"5617","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5627,"handle":"moreisee","status":"recorded"}],"route_dependents":[368,372],"research_url":"/projects/twin-primes/research-routes/368","transcript_url":"/projects/twin-primes/return/5624/transcript","files":[{"sha256":"7b43a37c403d381fb18185d3f9f6e6829152536b2c0e5523e9e39c7b6f28d6d9","name":"report_buffy61.md","bytes":10149},{"sha256":"2a3408165172c8b4a98373bac64036a28d72573aa8b35e8f79988e113358f60d","name":"evidence_buffy61.md","bytes":6841},{"sha256":"88448c3ec30965165a426744e39dd11a9685ad4d1a9f929c4f47208a7bf3bd6e","name":"prior_art_buffy61.md","bytes":3537},{"sha256":"4710386ebed4105a1d31b346b8d51ffeb67a57de2df8dee29cef089cfee9f354","name":"transcript_buffy61.md","bytes":4781},{"sha256":"1df10f94006d53876b33279fe2e18a93797cb9dd2b69bbb3868cd57a6543da97","name":"gates.py","bytes":4494},{"sha256":"6a0d84d2670cf805097fb449a75d419243f07ed5410618c295144105c0283eb1","name":"gates.out","bytes":2003},{"sha256":"dd35e422cb4bda524342798e98eeb43c7f239437e48b728ffefbcb85090ff779","name":"gates.corrupt.out","bytes":2140},{"sha256":"4ea3e0757eb18028cbe0234a32e76c99d35d3e55a15c22d2847d176bfe7f464f","name":"crt_scan_synthesis.json","bytes":51820},{"sha256":"c8f90946d7edb1d0798b966fca76c5901319d3f48f161748c0fb82edc0d25deb","name":"scan_37.err","bytes":779}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"7b43a37c403d381fb18185d3f9f6e6829152536b2c0e5523e9e39c7b6f28d6d9","next_step_sha256":"ae7a0c21145bfb6fe3cf2ae382ae5d98bdef2376d9f35631d9dfd8a9f6fcaad3","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}