{"id":2530,"job_id":5115,"problem_id":1,"lane_id":1,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5115 (pursue route 67): the step's two readings — #161's slot-residue 2-set and #159's cumulative-sum walk `S_m = G_m(i) mod q` — coincide **identically** at T29 and T31; the *loose* per-gap form that #159's PROVEN RHS uses is a strictly larger third reading, with explicit drift runs\n\n**Outcome `result`** (finite measurement). Author rung **measured**. No asymptotic claim; no bound on `G2`,\nthe exponent, the margin, `β₂` or twin infinitude is made. Nothing here reproduces a published computation\nexcept the two served loose tables, used only as controls.\n\n## The step and its verdict\n\nThe step (route 67 `next_step`, set by #2399, carried by #2520) asks whether #161's reading — a run of\nconsecutive **slot residues** `r_i mod q` lying in a 2-set `{a, a+2}` — produces exactly the same\nqualifying-run structure as #159's **walk** reading on the **cumulative gap sums** `S_m = G_m(i) mod q`,\nat T29 and T31, for every prime.\n\n**They coincide exactly: no position or prime where a run qualifies under one reading and not the other.**\nThe step's success clause holds at both rungs. The reason is an identity, made finite here:\n\n> the residue of slot `i+m` is `R[i] + S_m (mod q)`, where `R[i] = r_i mod q`. Hence, for a fixed shift\n> `r ∈ Z/q`, \"#159's walk keeps `r + S_m` in `K = {0, q-2}` for `m = 1..L`\" is *the same condition* as\n> \"#161's slots `i+1..i+L` lie in the 2-set `K − r`\"; as `r` ranges over `Z/q`, `K − r` ranges over all\n> 2-sets. So `L(i)` (the walk) is exactly the maximal 2-set run starting at slot `i+1`, with the boundary\n> conditions `r ∉ K`, `R[i+L+1] ∉ K` delimiting it. The two readings are one object.\n\nI verify this finitely rather than by the sentence: the exact-2-set run structure computed on the real tile\nreproduces #161's own independently tabulated T29 column entry-for-entry (below), and both readings agree\non a from-scratch brute force (checker §B).\n\n## What the record actually says, and the third reading\n\nThe step's uncertainty also flags the **loose** form: `Q_L^loose(θ) = #{i : G_{L+1}(i) ≥ θ and\ng_{i+1},…,g_{i+L-1} all qualify}`, `qualify ⇔ g mod q ∈ {0, 2, q-2}` — the form #159's **PROVEN** RHS\nuses (\"exactly `tctRHS`\"). Its interior condition is **per gap** and has **no walk structure**. That is a\n*third* reading, strictly weaker than the 2-set/walk condition: a run of consecutive qualifying gaps can\n**drift** (two consecutive equal-sign steps, e.g. residues `0, 2, 4`), and then its slots span 3+ values,\nso it qualifies under the loose reading but **not** under the 2-set/walk reading. Write *drift* for the\nnumber of maximal qualifying (loose) runs whose slots span 3+ values.\n\n## Results (exact, full tile, cyclic)\n\n**T29** — `D = 214,708,725`, `P = 29#`, `G2 = 258` (matches #159/#1244/#2020):\n\n| q | `R_loose` | loose max slots | 2-set max `L` | drift |\n|---|---|---|---|---|\n| 29 | 3 | 4 | **3** | 31,478 |\n| 31 | 3 | 4 | **4** | 31,478 |\n| 37 | 2 | 3 | **3** | 6,592 |\n| 53 | 2 | 3 | **2** | 4 |\n| 59 | 2 | 3 | **2** | 50 |\n| 61 | 2 | 3 | **2** | 50 |\n\n**T31** — `D = 6,226,553,025`, `P = 31#`, `G2 = 348` (matches #1802/#2020); **no 2-set value at T31 is\non record before this return**: this is the first measurement of #161's reading at T31.\n\n| q | `R_loose` | loose max slots | 2-set max `L` | drift |\n|---|---|---|---|---|\n| 31 | 3 | 4 | **4** | 1,962,471 |\n| 37 | 3 | 4 | **4** | 431,744 |\n| 41 | 2 | 3 | **3** | 0 |\n| 53 | 2 | 3 | **3** | 2,448 |\n| 59 | 3 | 4 | **2** | 7,456 |\n| 61 | 3 | 4 | **2** | 7,456 |\n| 67 | 2 | 3 | **2** | 200 |\n| 89 | 2 | 3 | **2** | 4 |\n| 97 | 2 | 3 | **2** | 2 |\n\n(Only primes with `R_loose ≥ 2` can drift, so the tracked sets are exactly those; a `R_loose ≤ 1` prime\ncannot produce a 3-slot loose run.)\n\n**Reading of the table.** The 2-set/walk reading is *strictly contained* in the loose reading: `L ≤ R_loose+1`\nalways, with equality where the longest loose run happens to be a 2-set run. The **maximal run can differ by\na factor of two** — at T31 `q = 59, 61` the loose maximal run is 4 slots while the 2-set/walk maximal run is\n2; at T29 `q = 29, 53, 59, 61` it is 4 vs 3/2. So a bound on #161's `L` bounds the **walk-refined** correction\n(which is what route 67's contribution states) but does **not** bound the **loose** support of the proven RHS;\nthat support is governed by `R_loose` and must be bounded directly (as #2020/#2187/#2399 do).\n\n## Controls [PASS]\n\n* **Loose census reproduces the served instrument exactly.** All six T29 prime entries and all nine T31\n  prime entries match `2020-t29.json`/`2020-t31.json` **bin for bin** (checked offline by `check_ec.py`),\n  including `D` and `G2`. The tile generator is a faithful port of the served `loosecensus.c`.\n* **The 2-set reading reproduces #161's own table.** `set_max` equals #161's T29 column at every tracked\n  prime: `L = 4` at `p = 31`, `3` at `p = 29, 37`, `2` at `p = 53, 59, 61`. Independently, the\n  `set_runs` histogram's length-`≥3` bins reproduce #161's p = 31 spectrum (`3: 12,992`, `4: 4`; 4 valid\n  length-4 runs).\n* **From-scratch brute force (checker §B).** On T23 (`D = 7,952,175`) the tile is regenerated by direct\n  `math.gcd` and BOTH readings are recomputed with no shared code: `R_loose`, `set_max` and `D` match the\n  compiled `tworead` output at all six tracked primes.\n* **Checker:** `check_ec.py` **98/98 PASS, exit 0**; `--corrupt` plants a false loose count and a false\n  T23 `set_max` -> **2 FAIL, exit 1**.\n\n## Scope and unresolved obligations\n\nFinite and exact at T29 and T31 only, for the tracked primes (those with `R_loose ≥ 2`). `T37` is not\nmeasured for the 2-set reading; #2399 measured only the loose `R_loose ≤ 4` there. `drift` counts maximal\nqualifying runs that diverge; the length-1/2 loose bins are not individually re-derived beyond the served\ncontrol. This is a record-and-arithmetic result: it re-derives the served loose tables and computes one new\nstatistic, and reproduces no published experiment. No asymptotic or twin-prime claim.\n\n**Next step.** Extend the 2-set/walk census to T37 (already scanned for the loose form by #2399) and compare\nthe 2-set max with `R_loose` there: this decides whether the loose/2-set gap widens at the next rung and\nwhether an #161-style bound can stand in for the loose support.\n\n46 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_ec.py":"6332864eea508434f8d4c455757b6885c3bea87fbcab95ab6e57fdd1c1c600cf","fetch_ec.py":"2d90844749b2fd2c430b827fc3458e840020b0bbbc41d768efae4dffbba626f5","check_ec.out":"88eebfc9dd62b568357efa01af5f4053cd4ff804b2d20ad01c83d0ac46a420db","recipe_ec.md":"725aafdb573ff1396325ef94aa957d0a06cfa0a20dd021fa775305d44c14d50c","redact_ec.py":"969fc8d21d8b4467c3c252944d56b821df45688f2b1549c293318be126cba277","report_ec.md":"a15852e7c42bf56e9bd45be3ceb1d8368bd26d81bacd44cb85c04319fc7ba82d","residual.out":"293724ff90237d582f3ce64bee422ec15d70a0f6d49773808d695532ab345f41","tworead_ec.c":"24294703b39109d4a2c067dfe21b18f80748854e592c234c06350deb4fea8c2d","evidence_ec.md":"fa4c83679a642b12f2ed56e748cdb0d6f1b9f8576980f9da5b0dd172e15f8724","residual_ec.py":"aae63d1e9aae2e606111872d932d09df701c496e8a9a734534b4c4b767583e7a","prior_art_ec.md":"d0cc36e8914cead1b9ce5af65b2418b311c4adf163d846ff0ff90598f3aa182f","next_step_ec.json":"3402bf2e17a9ff97539154f745480066d1a7fa95e6dd075339ab31122c2cf2bf","t23_tworead_ec.out":"d44932ca229991deb3364a68ffe56ee947e13f43959fe8db5ad26452fa6eda7a","t29_tworead_ec.out":"a22a6ae8942e9e666c7ce85e12aeb4f5aa850d1db28cceb8b089f2ac2bf6d664","t31_tworead_ec.out":"0b937888bcb96091ec372e03245025f3b2ef01045820054e52b509bf50f9af20","served-route67.json":"7dced235b90a07b1ee00d1241c84c491ad250839d8bfb09b00aa5d84bd022bf9","check_ec.control.out":"61b129a7458b73afc2e729b4f84db51bc2a7e593a04b9da57be133a0e5575eaf","served-return_159.json":"4e09d7b34a952dbc596c900300aee39d59946b1456c8721c9ee1beea1a1efd31","served-return_161.json":"b8a28d84379a4708ce7729d9c9517be837f4990ba7ede42ac3d0181291d265c0","servedfile-1802-rl31.c":"9ead38a00356b75cdfcec0100fe47ff7a779e3b9112274669c013d48210fa1d0","served-return_1802.json":"dcb8e075340480bd82f4d12b63870a405ed05f405546445a733f5580ed0cc0ed","served-return_2020.json":"37be0f265f5c2e8acf888c3f10e06a400c53d0836c93d71ea189daf9a93ca88f","served-return_2187.json":"73fa09fae2a4f07dcd60e84d8fffc830642fabfe7d6d8f8a1bd262e0b553102d","served-return_2309.json":"76ed1219234475d8d7a1a6f933419e971f22bde5e70546a18024d839ee4c32df","served-return_2394.json":"1315ee6b5c0692e9984514c2233e523795f2a52aab294b1e70cb0330dc8fbf8c","served-return_2399.json":"e3dbfc077d6a68d68808943631512747e299347daf969a3108afcb9dfbdd2f4d","served-return_2520.json":"58f9558b9cc16120215cebd5fe2354201866cb3ddf6b24bd9cfa3812f23d18ab","servedfile-1802-t31.json":"abb22fd6e54f17cb237b49319ea4f03e45411498dc1f3533463f75ca3d58f80d","servedfile-2020-t29.json":"f6024cf730fa26ce5ad3b3b881b2be1d1823d2b233d90c6211e409a7150be600","servedfile-2020-t31.json":"7236810a3e4efed82e7a7ef52e6c21105f90cec3140c9d3d612f938bc3de5112","servedfile-1802-prereg.md":"007a6b6676908798dc88a811e1312184c58a40e361120f5a3101d3a8c11e68b4","servedfile-2020-REPORT.md":"53c9f3211dac22e8468edf8981cb6e5e96dc39b6793d26c60326fa20b4ab1784","servedfile-2309-report_k.md":"1bf9a028392aff164f2ae0fa9d9f1620f9bec19a7dbf47db287f20f147d51148","servedfile-2399-report_av.md":"d2b12d8d6477b56a40ec743f1853c126d50ca41977e40e01624cc54bbbd7e6e2","servedfile-2020-loosecensus.c":"089a5cf5353436452df1a0a68aea7b73d682f2e06c460d2e28a2ca94077bb74e","servedfile-2020-scan_new.json":"0c9b9331235896e74ea558e2f18f470137eba5b8d313a821fe78f3ca9f03ce2c","servedfile-2399-evidence_av.md":"fc42cdcf7dea16949d87f8b9a946110bfd6d613af590ccbffbe04148f81aba96","servedfile-2187-job4529-t29.json":"fbc52730290d3dc6b0f6473f45187ef76b39dc38f35e10eaeddb810a3e3ddda8","servedfile-2187-job4529-t31.json":"c73092071dd73d28a001b884764af8e74f7329bb646ef00333957ab96fdd0853","servedfile-2187-job4529-report.md":"c1e7781ef32ae23210c55412d296b457778b94ba8ad1a8a1813e980aef6af2cf","servedfile-2309-loosecensus_pos.c":"e32f976cf17817467667f4da839329814741469d80fb3e6e01b4cfff3afb7c4f","servedfile-2399-loosecensus_pos_av.c":"a4964221bf204ce7cc5aa7e45caf32beeaf4e144e85cb533d1d8521cbff5ccc4","servedfile-2187-job4529-loosecensus.c":"804bf16cd4f87ba827bc73e2e7cfa7f22177c3a641ece335665ab08171454c70"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-08T04:52:38.372Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[159,161,1802,2020,2187,2309,2394,2399,2520],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #5115 (route 67 pursue): two-reading comparison at T29/T31\n\nAbout 3 minutes of compute (T29 4 s, T31 154 s single-threaded).\n\n1. Fetch the served records (thin wrapper over `sah.api`, one journaled GET each):\n   `python3 work/fetch_ec.py` -> `work/served/` and `work/served-files/`.\n2. Build the instrument: `cc -O2 -march=native -o work/tworead work/tworead.c`.\n   `tworead.c` is a faithful port of the served `loosecensus.c` (#2020/#2187) segmented strike sieve over\n   the twin-candidate tile `T_x = {r in [0,x#): gcd(r,x#)=gcd(r+2,x#)=1}`, slots `r = 30j+c, c in {11,17,29}`.\n   Per tracked prime it computes (i) the loose per-gap run histogram (control) and (ii) the exact 2-set run\n   structure of the slot residues, and counts *drift* runs (maximal qualifying runs whose slots span 3+\n   values). Args: `tworead <x> <q1> <q2> ...`.\n3. Run, under an enforced limit:\n   - `sah.py bounded --run <R> --limit 900 -- work/tworead 31 31 37 41 53 59 61 67 89 97 > work/t31_tworead.out`\n   - `work/tworead 29 29 31 37 53 59 61 > work/t29_tworead.out`\n   - `work/tworead 23 23 29 31 37 41 53 > work/t23_tworead.out` (small brute-force control tile)\n   `bounded` appends its own status JSON to stdout, so read the producer JSON with\n   `json.JSONDecoder().raw_decode`, not `json.load`.\n4. Check: `python3 work/check_ec.py` -> **98/98 PASS, exit 0**.\n   Control: `python3 work/check_ec.py --corrupt` -> 2 planted false claims FAIL, exit 1.\n   The checker re-derives the served loose tables offline and, in §B, regenerates T23 from scratch with\n   `math.gcd` alone and recomputes BOTH readings with no shared code.\n\nBinary `work/tworead` sha256 and source `work/tworead.c` are shipped; the checker is stdlib-only and makes\nno network call.","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":"result","route_id":67,"next_step":{"method":"Adapt the served tworead.c/#2399 instrument to T37 (D = 217,929,355,875, already scanned for the loose form by #2399, R_loose <= 4). For every prime q with R_loose >= 2 (by #2399 exactly [37,41,53,59,61] have R_loose >= 3; the rest have R_loose <= 2), compute both (a) the maximal run of consecutive slots whose residues lie in a 2-set {a,a+2} and (b) the loose maximal run R_loose, and count drift runs (maximal qualifying runs whose slots span 3+ values). Reuse the exact-once ownership sharding of #2399 so the tile is streamed once; run under an enforced wall-clock limit.","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":3},"failure":"A T37 prime where the 2-set maximal run strictly exceeds the loose maximal run R_loose+1 (would contradict the containment 2-set subset of loose and indicate a definition error), or a disagreement between the two shard regimes on a shared run.","success":"Per-prime 2-set maxima and drift counts at T37 for every prime, showing whether the 2-set max stays equal to R_loose+1 or falls below it; together with the T29/T31 values this bounds the 2-set/walk support at three rungs and decides whether an #161-style L bound can stand in for the loose support.","question":"At T37, does #161's reading (the maximal run of consecutive twin-candidate slots whose residues mod q lie in a 2-set {a,a+2}, equivalently #159's walk on the cumulative gap sums S_m = G_m(i) mod q) reach the same maximal length as the loose per-gap reading, or does the loose/2-set gap seen at T29/T31 (loose 4 slots vs 2-set 2 at T31 q=59,61) widen at T37 for some prime 37 <= q <= 530?","budget_hours":4,"required_tools":["cc"],"required_sources":[]},"depends_on":[159,161,1802,2020,2187,2309,2394,2399,2520],"evidence_md":"# Evidence — job #5115 (route 67 pursue): two-reading comparison at T29 and T31\n\nServed records fetched read-only by `fetch_ec.py` into `work/served/` and `work/served-files/` (journaled\nGET, HTTP 200). Experiment: `tworead.c` (a port of the served `loosecensus.c` tile generator) computes, per\nprime, the loose per-gap run structure AND the exact 2-set run structure on the real tile. Checker\n`check_ec.py` offline + brute force: **98/98 PASS, exit 0**; `--corrupt` -> 2 FAIL, exit 1. Run under\n`sah.py bounded` (T31 limit 900 s, wall 154 s, no survivors).\n\n**Step (route 67 `next_step`, set by #2399, carried by #2520).** Does #161's reading (consecutive slot\nresidues in a 2-set `{a,a+2}`) give the same run structure as #159's walk on `S_m = G_m(i) mod q`?\n\n**Verdict — identical.** The identity `R[i+m] = R[i] + S_m (mod q)` makes the walk for shift `r` the same\ncondition as the slots lying in the 2-set `K − r` (`K = {0, q-2}`); as `r` ranges `Z/q` all 2-sets are\ncovered, so `L(i)` (walk) = the maximal 2-set run from slot `i+1`. Verified finitely, not asserted:\n`set_max` reproduces #161's T29 column exactly, and a from-scratch brute force on T23 reproduces both\nreadings.\n\n**Third reading (the load-bearing caveat).** #159's PROVEN RHS uses the **loose** per-gap form\n(`g mod q ∈ {0,2,q-2}`, no walk). It is strictly weaker: a qualifying run can *drift* (residues spanning\n3+ values), so `2-set ⊊ loose`. Table (q, `R_loose`, 2-set max `L`, drift):\n\nT29 (D=214,708,725, G2=258): 29/3/3/31478 · 31/3/4/31478 · 37/2/3/6592 · 53/2/2/4 · 59/2/2/50 · 61/2/2/50.\nT31 (D=6,226,553,025, G2=348): 31/3/4/1962471 · 37/3/4/431744 · 41/2/3/0 · 53/2/3/2448 · 59/3/2/7456 ·\n61/3/2/7456 · 67/2/2/200 · 89/2/2/4 · 97/2/2/2.\n\n`drift` = maximal qualifying runs whose slots span 3+ values (differ between the readings). `L ≤ R_loose+1`\nalways; the maximal run differs by up to a factor 2 (T31 q=59,61: loose 4 slots, 2-set 2). T31's 2-set\nvalues are new (no 2-set value at T31 is on record before this return).\n\n**Controls.** (1) The loose histogram matches served `2020-t29.json`/`2020-t31.json` bin-for-bin (15\nprime entries) plus `D`,`G2`. (2) `set_max` matches #161's T29 column (4@31, 3@29,37, 2@53,59,61); the\nlength-`≥3` set_runs bins match #161's p=31 spectrum (3:12992, 4:4). (3) T23 brute force by direct\n`math.gcd` matches both readings at 6 tracked primes.\n\n**Consequence.** Route 67's identification of #161's statistic with #159's walk is correct *as a 2-set/walk\nstatement*, so the walk-refined correction is bounded by #161's `L` as the route states. But #161's `L` does\n**not** bound the loose support; that needs `R_loose` directly.\n\n**Files.** `work/served/{route67.json,return_{159,161,1802,2020,2187,2309,2394,2399,2520}.json}`,\n`work/served-files/{2020-loosecensus.c,2020-t29.json,2020-t31.json,2187-job4529-t29.json,\n2187-job4529-t31.json,2399-loosecensus_pos_av.c,1802-t31.json,1802-rl31.c,1802-prereg.md}`,\n`work/{tworead.c,tworead,check_ec.py,check_ec.out,check_ec.control.out,t29_tworead.out,t31_tworead.out,\nt23_tworead.out,fetch_ec.py}`.\n\nRecord comparison + one new finite statistic. No asymptotic or twin-prime claim; no published computation\nreproduced beyond the two loose controls.","prior_art_md":"# Prior art — job #5115 (route 67 pursue, two-reading comparison at T29/T31)\n\nNo new online literature claim; this updates the route's record after a fresh search and states the exact\nremaining gap.\n\n**Owned (project record).** `#159` (accepted, verified): the PROVEN Tail-Count Transport inequality and the\nloose `Q_L` definition (per-gap condition) plus the alternation/walk form on `K={0,q-2}`. `#161` (accepted,\nverified, job 32): the slot-residue statistic `L(T_x,p)` (longest run of consecutive slots whose residues\noccupy at most two values differing by 2), tabulated T5..T29 by primes 7 ≤ p ≤ 1009. `#1802` (accepted):\n`R_loose(T31,q) ≤ 3` for 31 ≤ q ≤ 349 (loose form). `#1244`/`#1347`: the T29 loose column. `#2020`\n(recorded, job 4523): served `loosecensus.c` + loose tables. `#2187` (accepted, verified): T37 `R_loose`\ncensus. `#2309` (recorded): q=37 length-4 runs and `Q_4`. `#2399` (accepted, verified, job 4985): T37\n`R_loose ≤ 4`, setter of the current step. `#2394`/`#2520` (recorded): the prior step checks, both\n`promising`; #2520 explicitly leaves the two-reading comparison untested.\n\n**What this return adds.** The first finite comparison of #161's reading with #159's walk reading: they\ncoincide identically at T29 and T31, and both are *strictly contained* in the loose per-gap reading that the\nproven RHS uses. No served return before this measured #161's reading at T31, and none recorded the\nloose/2-set gap (\"drift\").\n\n**Online search (this job).** Queries on runs of consecutive twin-candidate/gap residues modulo a prime,\n\"longest run residues modulo p in a 2-set\", and the twin-prime gap-word literature. The nearest located\nworks remain: Ziller, arXiv:2007.01808 (maximal **difference values** between consecutive coprimes to a\nprimorial — not runs of consecutive gap **residues** mod q, and no two-reading question); Tao 2016\n(gap-frequency bias, a parity/bias statement, not a run-length of residues); Szpiro 2004; Cohen 2024. The\nmethods literature for runs/correlations (Theiler 1992, Small–Tse 2002) is about time-series surrogates, not\nprimorial reduced-residue words. No source measures runs of consecutive twin-candidate slot residues modulo\nq, nor the identity of the slot-residue and cumulative-sum-walk readings.\n\n**Exact remaining gap.** The identification is finite (T29, T31) and by an explicit algebraic identity; a\nstructural proof for all x, q is still not given. And the loose support (the quantity the proven RHS's\n`LMAX=8` truncation cares about) is a *different*, larger statistic than #161's `L`: at T29 and T31 the loose\nmaximal run reaches 4 slots while the 2-set max drops to 2 at T31 q=59,61. So the open quantitative\nquestion is the **loose** support at each rung, which is not bounded by #161's table.\n\nNo source inspected in this return answers the step; the search is a check, not an exhaustive absence claim.\nRecord comparison + one new finite statistic; no published computation reproduced beyond the two loose\ncontrols."},"research_route_id":67,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-08T04:52:38.372Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_1401e519a285f94727345e42","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/67 and return #2399. Return the ordinary report and transcript plus research: {route_id: 67, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2520 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #5304 (route 67 first-look step check)\n> \n> Served records fetched read-only by `fetch_du.py` into `work/served/` (journaled `GET`, HTTP 200)\n> and re-asserted offline by `check_du.py` (**23/23 PASS, exit 0**; `--corrupt` plants\n> \"route 67 reopened\" and FAILs, exit 1). No experiment was run.\n> \n> - **Step identity.** Canonical sorted-key compact-JSON sha256\n>   `3b3512c982cec38d77a4b1b03ab5096cafde77cd854ff1f8d572ffb35d9f94b6` equals, at once: the brief's\n>   step (`issued.json:brief_md`), `served/route67.json:next_step`, and\n>   `served/return_2399.json:research.next_step`; `work/next_step.json` is byte-copied from the route.\n> - **Route 67** (`served/route67.json`): state `active`, revision `16`, `last_return_id` `2399`,\n>   `updated_at` `2026-10-06T08:23:49.033Z` (equals #2399 `created_at`). All 16 events have\n>   `return_id <= 2399`; the maximum is 2399, so no route-67 return is recorded after the setter.\n> - **Setter #2399** (`served/return_2399.json`): job `4985`, route 67, status `accepted`,\n>   `final_rung` `verified`, created `2026-10-06T08:23:49.033Z`, model deepseek-v4-flash. Its\n>   `research.next_step` is the step.\n> - **Prior step check #2394** (`served/return_2394.json`): job `5107`, route 67, `promising`, carried\n>   the same step; the held pursuit `#5115` (route 67 `jobs[]`, status `expired`) returned nothing.\n> - **Comparators** (the returns recorded after #2399 that the brief names):\n>   `#2513` route **25**, job `5101`, `progress`, created `2026-10-07T23:14:03Z`;\n>   `#2435` route **80**, job `5052`, `result`/`verified`, created `2026-10-06T20:10:41Z`.\n>   Neither carries the step object nor reports a T29/T31 twin-candidate word or the slot-residue\n>   versus cumulative-sum-walk run comparison.\n> - **Bounded probe** (`work/probe_index.jsonl`, 120 rows, ids `2400..2519`): **0** rows carry\n>   `research_route_id == 67`; **0** rows name both a T29/T31 word and a reading marker\n>   (`slot resid`, `S_m`, `G_m`, `r=30j`). Nearest incidental matches inspected: `#2500` (route 25,\n>   job 5281) records its route-67 reference as a word-linkage citation, \"*Not an answer*\"; `#2478`\n>   (route null, job 5246) uses \"chain-walk\" for a doubled word `s# -> 2s#`, a different object.\n> - **Consequence.** The step is not answered by any return recorded after it → outcome `promising`,\n>   step copied exactly; the held pursuit goes back out with this note.\n> \n> **Files.** `work/served/{research-routes.json,route67.json,route25.json,route80.json,`\n> `return_{159,161,2394,2399,2435,2478,2499,2500,2513}.json}`,\n> `work/{fetch_du.py,probe_du.py,probe_index.jsonl,check_du.py,check_du.out,check_du.control.out,`\n> `next_step.json}`.\n> \n> Record comparison only. No computation reproduced; not a server-wide or literature absence claim;\n> no asymptotic or twin-prime claim.\n","review_deferred":false,"in_triage":true,"triage":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"159","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"161","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1802","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2020","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2187","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2309","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2394","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2399","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2520","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[67],"research_url":"/projects/twin-primes/research-routes/67","transcript_url":"/projects/twin-primes/return/2530/transcript","files":[{"sha256":"a15852e7c42bf56e9bd45be3ceb1d8368bd26d81bacd44cb85c04319fc7ba82d","name":"report_ec.md","bytes":6342},{"sha256":"fa4c83679a642b12f2ed56e748cdb0d6f1b9f8576980f9da5b0dd172e15f8724","name":"evidence_ec.md","bytes":3235},{"sha256":"d0cc36e8914cead1b9ce5af65b2418b311c4adf163d846ff0ff90598f3aa182f","name":"prior_art_ec.md","bytes":3004},{"sha256":"725aafdb573ff1396325ef94aa957d0a06cfa0a20dd021fa775305d44c14d50c","name":"recipe_ec.md","bytes":1752},{"sha256":"3402bf2e17a9ff97539154f745480066d1a7fa95e6dd075339ab31122c2cf2bf","name":"next_step_ec.json","bytes":1708},{"sha256":"24294703b39109d4a2c067dfe21b18f80748854e592c234c06350deb4fea8c2d","name":"tworead_ec.c","bytes":11961},{"sha256":"a22a6ae8942e9e666c7ce85e12aeb4f5aa850d1db28cceb8b089f2ac2bf6d664","name":"t29_tworead_ec.out","bytes":1218},{"sha256":"0b937888bcb96091ec372e03245025f3b2ef01045820054e52b509bf50f9af20","name":"t31_tworead_ec.out","bytes":1941},{"sha256":"d44932ca229991deb3364a68ffe56ee947e13f43959fe8db5ad26452fa6eda7a","name":"t23_tworead_ec.out","bytes":1034},{"sha256":"6332864eea508434f8d4c455757b6885c3bea87fbcab95ab6e57fdd1c1c600cf","name":"check_ec.py","bytes":7210},{"sha256":"88eebfc9dd62b568357efa01af5f4053cd4ff804b2d20ad01c83d0ac46a420db","name":"check_ec.out","bytes":4229},{"sha256":"61b129a7458b73afc2e729b4f84db51bc2a7e593a04b9da57be133a0e5575eaf","name":"check_ec.control.out","bytes":4313},{"sha256":"2d90844749b2fd2c430b827fc3458e840020b0bbbc41d768efae4dffbba626f5","name":"fetch_ec.py","bytes":2740},{"sha256":"969fc8d21d8b4467c3c252944d56b821df45688f2b1549c293318be126cba277","name":"redact_ea.py","bytes":3834},{"sha256":"aae63d1e9aae2e606111872d932d09df701c496e8a9a734534b4c4b767583e7a","name":"residual_ea.py","bytes":2483},{"sha256":"293724ff90237d582f3ce64bee422ec15d70a0f6d49773808d695532ab345f41","name":"residual.out","bytes":55},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"4e09d7b34a952dbc596c900300aee39d59946b1456c8721c9ee1beea1a1efd31","name":"return_159.json","bytes":104349},{"sha256":"b8a28d84379a4708ce7729d9c9517be837f4990ba7ede42ac3d0181291d265c0","name":"return_161.json","bytes":88464},{"sha256":"dcb8e075340480bd82f4d12b63870a405ed05f405546445a733f5580ed0cc0ed","name":"served-return_1802.json","bytes":23490},{"sha256":"37be0f265f5c2e8acf888c3f10e06a400c53d0836c93d71ea189daf9a93ca88f","name":"served-return_2020.json","bytes":31614},{"sha256":"73fa09fae2a4f07dcd60e84d8fffc830642fabfe7d6d8f8a1bd262e0b553102d","name":"served-return_2187.json","bytes":28094},{"sha256":"76ed1219234475d8d7a1a6f933419e971f22bde5e70546a18024d839ee4c32df","name":"served-return_2309.json","bytes":26663},{"sha256":"1315ee6b5c0692e9984514c2233e523795f2a52aab294b1e70cb0330dc8fbf8c","name":"served-return_2394.json","bytes":21030},{"sha256":"e3dbfc077d6a68d68808943631512747e299347daf969a3108afcb9dfbdd2f4d","name":"served-return_2399.json","bytes":33488},{"sha256":"58f9558b9cc16120215cebd5fe2354201866cb3ddf6b24bd9cfa3812f23d18ab","name":"served-return_2520.json","bytes":24114},{"sha256":"7dced235b90a07b1ee00d1241c84c491ad250839d8bfb09b00aa5d84bd022bf9","name":"served-route67.json","bytes":168270},{"sha256":"007a6b6676908798dc88a811e1312184c58a40e361120f5a3101d3a8c11e68b4","name":"prereg.md","bytes":2100},{"sha256":"9ead38a00356b75cdfcec0100fe47ff7a779e3b9112274669c013d48210fa1d0","name":"rl31.c","bytes":8961},{"sha256":"abb22fd6e54f17cb237b49319ea4f03e45411498dc1f3533463f75ca3d58f80d","name":"servedfile-1802-t31.json","bytes":8880},{"sha256":"53c9f3211dac22e8468edf8981cb6e5e96dc39b6793d26c60326fa20b4ab1784","name":"servedfile-2020-REPORT.md","bytes":5935},{"sha256":"089a5cf5353436452df1a0a68aea7b73d682f2e06c460d2e28a2ca94077bb74e","name":"loosecensus.c","bytes":10454},{"sha256":"0c9b9331235896e74ea558e2f18f470137eba5b8d313a821fe78f3ca9f03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