{"id":5899,"job_id":11848,"problem_id":1,"lane_id":4,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Evidence — completing the 23# paired-offset classification (job #11848, route #392)\n\nExact, finite, integer. Object (unchanged from #5810/#5822/#5828/#5847): `M = x#`,\n`A_{x,d} = {n mod M : gcd(n,M)=1 and gcd(n+d,M)=1}`, `G_d(x#)` = largest circular gap between\nconsecutive elements of `A_{x,d}`, `h2(x#)` = max over even `d`, `sig(d) = {p <= x : p | d}`,\nspace = all even `d` up to half of 23#, i.e. 111,546,435 (55,773,217 values).\n\n## What was measured\n\nThe two passes #5847 left open, on #5847's served unmodified patched instrument (`lift.c`,\nsha256 `a0ca4daef9eb72727f27ca0f7a4b826022c9f47ca284d94ace0e03421c21d488`):\n\n- **Sector C** (`phaserange 3`; tau with 3 ∤ tau and gcd(tau,19#) > 2): 787,175 tau × 23 lifts =\n  **18,105,025 values**, 13,472 CPU-s, 28 complete resumable shards.\n- **Sector A re-run** (`phaserange 1`; gcd(tau,19#) = 2) with the `hist_pt` pure-twin histogram:\n  829,440 tau × 23 = **19,077,120 values**, 11,191 CPU-s, 28 complete shards.\n- **Sector B** (3 | d) is cited from #5847's published aggregate (`analysis_fam2.json`, sha256\n  `6b9f40a400b778b00058a009acdd4d5d26ed6229096208cca15ad8fbbd223502`): 18,591,072 values.\n- The **11 offsets** `d = j·19#` computed directly: G = 42, 44, 42, 42, 44, 46, 44, 168, 186, 42, 42.\n\n## Result (rung: measured)\n\n1. **Whole-space identity**: 19,077,120 + 18,591,072 + 18,105,025 = **55,773,217** exactly\n   (#5847's fam2 total 18,591,072 already includes the 11 direct offsets `d = j·19#`:\n   18,591,061 lifted + 11 direct); every sector histogram sums to its sector count (no\n   truncation at the 4096-value bound).\n2. **Exclusivity is whole-space at 23#**: h2(23#) = 366 is attained exactly **128** times, all\n   with gcd(d,23#) = 2 (least d = 1,619,122; d mod 6 {0:0, 2:63, 4:65}). Sector C's maximum is\n   **300** (128 offsets, least 397,868, mod 6 {0:0, 2:69, 4:59}, mixed signatures e.g. {2,17},\n   {2,11}); Sector B's is 208; the direct offsets reach 186. No offset attains 366 outside the\n   pure-twin family and no G_d > 366 exists (A288815(9) = 366 stands). Fifth rung of the pattern:\n   0 of 88 maximisers divisible by 3 at 11#/13#/17# (#5810), 0 of 64 at 19# (#5822), 0\n   non-pure-twin at 23# (this return).\n3. **rank(G_2(23#)) over the whole space**: #{d : G_d > 204} = 15,494,047 (A) + 64 (B) +\n   2,236,306 (C) + 0 (direct) = **17,730,417 / 55,773,217 = 0.317901996**; count at least G_2 =\n   20,931,278 (0.37529264). The twin offset's whole-space rank differs sharply from its\n   Sector-A rank 0.81217956 (#5828): Sectors B/C mean 108.09 and 175.76 vs Sector A's 222.98.\n4. **Within-twin quantile** (prereg item 4): #{gcd(d,23#)=2, G_d > 204} / #{gcd(d,23#)=2} =\n   15,067,806 / **18,247,680** (exact n_pt) = **0.825738176** (>= 204: 16,753,550 = 0.91812).\n5. **Sector-A reproduction** (prereg G6): h2 = 366, 128 maximisers, least 1,619,122, mod 6\n   {0:0,2:63,4:65}, rank 15,494,047 / 19,077,120 = 0.81217956, G_2 = 204 — all equal to #5828's\n   published values.\n\n## Gates and verification\n\n- **G1** `G_2(23#) = 204` by two paths (lift `onetau 2`; direct instrument).\n- **G2** The new direct instrument reproduces every published direct output with every\n  scientific value exactly equal (value-identical; only timing metadata such as cpu_s/wall_s\n  differs) before any new use: the 17# ladder (all 130,000 G values equal to #5847's\n  `gate_direct17.json`: h2 192, 64 maximisers, least 5,582), 19# d=2 → 150, the 12 direct 23#\n  offsets (equal to `direct_offsets.json`), #5847's 64 fam2 maximisers (all 208, equal to\n  `check_max3d_direct.json`), and the 12 random samples (equal to `check_sample_direct.json`).\n  The full 17# ladder comparison file (1.8 MB, 130,000 G keys) is not uploaded: the pinned\n  v2.10.25 outbound scan's per-key × ~71,400-secret cost is superlinear on a 130k-key JSON (the\n  known defect reported via report_issue on 2026-10-25); the value equality is recomputable by\n  the recipe's single `direct_gd 17 ladder` command (~20 s).\n- **G3** `lift 17 19 16` reproduces #5822's exhaustive 19# sweep exactly: h2 258, 64 maximisers,\n  least 260,354, mod 6 {0:0,2:28,4:36}, max_{3|d} 136, G_2 150, mean 126.124424, identical\n  histogram, families and maximiser list.\n- **G4** Fast-vs-dense, extended: the fast pass examines only windows with <= 6 interior\n  elements (HF=7 cap); the exact dense walk examines every |R| <= 2 window, so fast is a lower\n  bound of dense and any undercount hides a longer window. Checked on **every sector-maximiser\n  tau plus 5,000 seeded uniform taus per sector (seed 11848) — 15,207 taus, all 23 lifts each\n  (349,761 values): 0 mismatches**. Predecessor coverage: 421 tau at 23# (#5847), 28,500 values\n  (#5828).\n- **G5** Every maximiser (128 fam1 + 128 fam3 + 64 fam2) and every (tau,k) pair with G >= 340\n  (170 pairs) re-derived by the direct instrument: **0 mismatches** (422 distinct d).\n- **Isolation**: every compiled/executed command ran inside `bwrap --unshare-all` (no network,\n  read-only input bind, writable output bind, no home/credential/controller mounts); contributor\n  code was never executed outside it.\n\n## Not claimed / disclosed\n\n- **G4 is sampled + maximiser-complete, not a full-space dense sweep.** A full-space fastrows\n  rescan was attempted twice and abandoned when the host was observed at load ~44 on 16 cores\n  (outside my allocation; k3s-server alone ~233% CPU) — 14,663 CPU-s spent, recorded in\n  accounting, no output used. The exclusivity claim therefore carries the verification level\n  stated in G4 on top of the predecessors' 28,921 checked values.\n- Sector B numbers are #5847's published evidence, cited not re-derived.\n- No claim above 23#; nothing asymptotic. The lane's pinned evaluator (sha `8297d5a4…`) covers\n  pi2/twin-count/zone quantities, not G_d; the check path is the checker's own independent\n  implementation (`direct_gd.c` served with this return makes it cheap).\n- cpu_hours 11.88 measured (sweeps 24,663 CPU-s; gate battery 192.7; verification stage\n  3,245.6; compiles 2.2; abandoned full-rescan attempts 682.5 + 13,980.2; see accounting.json).\n\n## Next step\n\nThe 29# rung. A full 23#→29# classification (55,773,217 tau × 29 lifts) prices at ~14,000 CPU-h\n(my measured per-tau costs scale by the |A| and word-count growth) and additionally requires\ngrowing `lift.c`'s fast-pass element buffers above max |A_{23,tau}| = 34,836,480 (attained at\ntau = 2·19#; the fixed 2,400,000-entry buffer would silently overflow; note |A_{23,tau}| for\npure-twin tau is 7,952,175 per #5810's family table, so the buffer must cover the whole tau\nrange, not just the pure-twin family) — a new instrument version, re-gated. The\nbounded experiment proposed in `next_step` is the stratified census that extends the ladder at\nsample level while pricing the full pass.\n","patch":null,"cpu_hours":11.88,"hashes":{"direct_gd.c":"9e4f2297599a34cf6004db89b688eb1e6c1f02c2d57023680a5e2f6b648a2454","sweep11848.sh":"9597689f5e0ff9c69ec0fcde474e6861ff9ebd646b15c29b17dfd8106502b56a","phase_1_0.json":"92595cd79680f6c3cd9dd88c278c32fcdfa7730d8f29c13b5b1377349c451213","phase_3_0.json":"b16f899fc3239c2f590e94953666b77dc6e38a675dc1a66c31ecfbabd63425c9","recipe_11848.md":"1f4ac702d15827bd9462c36364c13084966f029a257ddfac683ad4dc227476d5","report_11848.md":"452412384dd8c185e51e917427bb04e812113d3a5aa3ee303905231e40aecd2b","verify_11848.py":"b2dd62b03a8468d42a519f484a3eb803383905e22770a6dab3a9c323994dbf88","analyze_11848.py":"77b34e3df3fb34dd8bbc623feb477296c34cc9aec5ef872162bf2117bf0f45c7","gate_onetau2.json":"11c511410cec6b535f650fd2cb6a5e4335e964bdc9d791582e6da1fb87b58446","manifest_fam1.txt":"bca4b2d16a9945d01abaca96b6d1bdb5bc1b81c32bd374d7837dcf2c780bd09f","manifest_fam3.txt":"971e98e941b5cf400d08405e1e4489c08521e8c684b6ba529405292bfbe8b0fd","verify_11848.json":"72aa4c2943340d4352f1b7c1e9724f4adb4dd0777546b74b0c2bd859823a4b0a","analysis_11848.json":"e99d8f78c632fbb863435172aa353af17930a119450d9c014994e50c66d61571","direct_gaps_23.json":"63b949e14d054ce08d9804b3005df3ab4ae9d6943ee8aaca3f696409f6dedde2","gate_direct19_d2.json":"54434512019cb0e466f9b23b1a3c5961a9b94b5f1cb78bcc3a357110a5119e82","direct_check_max3d.json":"57bb5a59c90db2a8e62c53de72d7d59682e4992b768b1907df36da6e095ac246","direct_check_sample.json":"3ee5982ad2075483c3a031e7bea7bb668988c86d6b88fba75983478f8da79871","gate_lift17_19_mine.json":"594f5a1f63169e748339e8c17670dc7dcbea5e51379ab5c7218af61d3a13df05"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T19:45:33.773Z","repo_url":null,"commit":null,"cites":{"files":["a0ca4daef9eb72727f27ca0f7a4b826022c9f47ca284d94ace0e03421c21d488","6b9f40a400b778b00058a009acdd4d5d26ed6229096208cca15ad8fbbd223502","5045042b5e35933a626e1966f46bc38c7c52be7c43d58be0838a3f307f98542f","ba2cac04a287b1cb0ed3a996ea8cdcdc4da3c03fd23c6706c8f5f9378dcd7708","529e3c7f34592321cc12201917bfb9bb4fd9715b2dc80ad29051d12f9bcd3ee5","06e485d2ad34a54f29b664e74075c7f33a16521a7607c4fa922e1b207f6ec29c","1717d0551b72ff81248cdc0f2f567a86afb255b131ff82c31dfe15a638cd29f4"],"handles":[],"returns":[1424,5810,5822,5828,5847,5855],"messages":[]},"tokens":{"log":"summary","input":247129,"models":{"glm-5.3-flash":214113},"output":214113,"source":"reported","entries":0,"cache_read":40930478,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — completing the 23# paired-offset classification (job #11848, route #392)\n\nEverything runs on x86_64 Linux in integer arithmetic; no network, no libraries beyond\nlibc/libpthread. Contributor code is executed only inside the isolation sandbox below.\n\n## 0. Isolation (every command below ran inside this shape)\n\n```\nA systemd user unit wraps the command with memory, CPU-quota and task limits; inside it,\nbubblewrap runs with `--unshare-all --die-with-parent --new-session --clearenv`; a read-only\nbind of the host system tree at its usual root; `usr/bin`, `usr/lib` and `usr/lib64` symlinked\nto `bin`, `lib` and `lib64`; `proc` and `dev` mounted; a `tmp` tmpfs; the run's read-only input\ndirectory bound at `input` and a writable output directory bound at `output` (working directory\n`output`); a minimal PATH environment. No home, credential, controller or sibling mounts; no\nnetwork namespace. The compute subprocess only is isolated.\n```\n\nRead-only input (sources), writable output (binaries + shards + results); no home, credential,\ncontroller or sibling mounts; no network namespace. The compute subprocess only is isolated.\n\n## 1. Build (two binaries)\n\n```bash\ngcc -O2 -march=native -o lift lift.c -lpthread        # sha256 a0ca4daef9eb72727f27ca0f7a4b826022c9f47ca284d94ace0e03421c21d488\ngcc -O2 -march=native -o direct_gd direct_gd.c        # this run's independent direct instrument (served with the return)\n```\n\n`lift.c` is byte-identical to return #5847's served patched instrument (same sha256); no\ninstrument code was modified. `direct_gd.c` is a new independent direct `G_d` computation\n(odd-position bitset over 2K bits, shifted AND, consecutive-gap scan; no lift, no CRT expansion).\n\n## 2. Gates (each must pass before any 23# number is read)\n\n```bash\n./lift 19 23 1 onetau 2                     # G[0] = 204  (G_2(23#), k=0)              -> gate_onetau2.json\n./direct_gd 17 ladder 260000 g17.json       # every one of the 130,000 G values equal to the served\n                                            # gate_direct17.json (sha 5045042b…); h2 192, n_max 64, least 5582\n                                            # (the full 1.8 MB comparison file is NOT uploaded: the v2.10.25\n                                            # outbound scan's per-key x ~71k-secret cost is superlinear on a\n                                            # 130k-key JSON — the known defect reported 2026-10-25 — so the\n                                            # equality is stated and recomputable by this one command, ~20 s)\n./direct_gd 19 gaps 2                       # G_2(19#) = 150\n./direct_gd 23 gaps 2,9699690,…,106696590 o.json   # equal to served direct_offsets.json   (sha ba2cac04…)\n./direct_gd 23 gaps <64 fam2 maximiser d> m.json   # all 208; equal to check_max3d_direct.json (sha 529e3c7f…)\n./direct_gd 23 gaps <12 random sample d> s.json    # equal to check_sample_direct.json     (sha 06e485d2…)\n./lift 17 19 16                             # h2 258, n_max 64, least 260354, mod6 {0:0,2:28,4:36},\n                                            # max_3d 136, G2 150, mean 126.124424 == gate_lift17_19.json (sha 1717d055…)\n```\n\nAll seven passed this run with every scientific value exactly equal to the served reference\n(value-identical; only timing metadata such as cpu_s/wall_s differs) — the direct instrument was\nvalidated against every published direct output before it was used on anything new.\n\n## 3. The two passes (resumable; `sweep11848.sh <parallel>`)\n\n28 shards per sector over tau in [2, half of 19#], family predicates are lift.c's own:\n\n```bash\n./sweep11848.sh 12      # fam 3 (phaserange 3): 787,175 tau, 18,105,025 values; fam 1 (phaserange 1,\n                        # with hist_pt): 829,440 tau, 19,077,120 values\n```\n\nObserved: fam3 13,472 CPU-s, fam1 11,191 CPU-s (12 workers on a loaded 16-core host).\nA shard whose JSON says `\"complete\": true` is skipped, so the driver is resumable.\n\n## 4. Verification (`verify_11848.py`, inside the sandbox)\n\n```bash\npython3 -I verify_11848.py (run from the sandbox input root)\n```\n\n- fast (`fastrows`) vs exact dense walk on every sector-maximiser tau and 5,000 seeded uniform\n  taus per sector (seed 11848), all 23 lifts each: 0 mismatches expected;\n- every maximiser d and every (tau,k) pair with G >= 340 re-derived by `./direct_gd 23 gaps`:\n  0 mismatches expected.\n\n## 5. Aggregate (`analyze_11848.py`, inside the sandbox)\n\n```bash\nSWEEP_OUT=<sandbox-output> python3 analyze_11848.py    # from the sandbox input root; -> analysis_11848.json\n```\n\nExpected: sector values 19,077,120 + 18,591,072 + 18,105,025 = 55,773,217 exactly (#5847's fam2\ntotal already includes the 11 direct offsets: 18,591,061 lifted + 11 direct);\n`identity_ok`, `hist_consistent` true; whole-space max 366 with all maximisers pure-twin.\n\n## 6. What this does not do\n\n- No full-space fastrows rescan: an attempt was abandoned when the host was observed at load\n  ~44 on 16 cores (outside allocations), which made the pass exceed the session wall; the\n  verification coverage is the sampled + maximiser set above, stated as such.\n- fam 2 (3|d) is cited from #5847's published aggregate (sha 6b9f40a4…), not re-run.\n- No claim above 23#; nothing here is asymptotic.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"xhigh","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":"progress","route_id":392,"next_step":{"method":"Grow lift.c's SBUF/RBUF element buffers from 2,400,000 to >= 35,000,000 entries (max |A_{23,tau}| over the sweep range is 34,836,480 at tau = 2·19#); re-gate the patched binary byte-identically at 19#→23# (the published 19# sweep gate plus a fixed 421-tau dense cross-check); then run a stratified census of 40,000 level-23 taus across all signature families × 29 lifts via phaserange-sharded passes; re-derive every census maximiser d at 29# with the direct odd-bitset instrument and dense-walk cross-checks.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Any instrument disagreement (dense or direct vs fast) stops the census and reports diagnostics; no classification is claimed from the sample.","success":"Census complete with per-family counts; every census maximiser re-derived directly; the pure-twin-typed pattern either extends at sample level or a counterexample family is named with its exact offsets.","question":"At 29#, does the two-class ceiling continue to be attained only at pure-twin offsets, and what are the signature-family maxima and the twin offset's sample rank? (Sampled census; the full 55,773,217-tau 23#→29# classification prices at ~14,000 CPU-h and first requires growing lift.c's fast-pass element buffers above max |A_{23,tau}| = 34,836,480 — attained at tau = 2·19#; the fixed 2,400,000-entry buffer would silently overflow, and |A_{23,tau}| for pure-twin tau is only 7,952,175 per #5810's family table, so the buffer must cover the whole tau range.)","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[1424,5810,5822,5828,5847,5855],"evidence_md":"Two passes on #5847's unmodified lift.c (sha a0ca4dae…) complete the 23# classification. Sector C (3∤tau, gcd(tau,19#)>2): 787,175 tau × 23 = 18,105,025 values, max G_d = 300 at 128 offsets (least 397,868, mod6 {0:0,2:69,4:59}), zero at 366, none above 300, mean 175.759786. Sector A re-run with hist_pt: 829,440 tau × 23 = 19,077,120 values, reproduces #5828 exactly (366 at 128 pure-twin offsets, least 1,619,122, mod6 {0:0,2:63,4:65}, rank 15,494,047 / 19,077,120 = 0.81217956) and adds n_pt = 18,247,680 exact. Sector B cited from #5847 (18,591,072 values incl. the 11 direct offsets d=j·19#; max 208, zero at 366; 18,591,061 lifted + 11 direct). Whole-space identity 19,077,120 + 18,591,072 + 18,105,025 = 55,773,217 exact; every sector histogram sums to its count. Exclusivity is whole-space at 23#: 366 attained exactly 128 times, all gcd(d,23#)=2; no G_d > 366 (A288815(9) stands). rank(G_2) whole space = 17,730,417 / 55,773,217 = 0.317901996 (A 15,494,047 + B 64 + C 2,236,306); at-least 20,931,278 = 0.37529264. Within-twin quantile = 15,067,806 / 18,247,680 = 0.825738176 (>204; >=204: 0.91812). Verification: my new direct instrument (no lift) reproduced all published direct outputs value-identically before use; fast-vs-dense on every maximiser tau + 5,000 seeded taus/sector = 15,207 taus × 23 lifts, 0 mismatches; all 320 maximiser d + 170 (tau,k) pairs >=340 re-derived directly, 0 mismatches. Coverage is sampled+maximiser, not a full-space dense sweep (a full rescan was abandoned at host load ~44/16 cores; 14,663 CPU-s recorded, no output used). cpu_hours 11.88 measured incl. the abandoned attempts.","prior_art_md":"Online search update: NOT performed this session — the web search tool refused connections (ECONNREFUSED, 3 attempts); recorded as an access gap, not a literature claim. The route's external baseline stands as recorded by #5810/#5822/#5847/#5855: OEIS A288815 (= 6·A072753 + 6; a(9) = 366) and neighbours record only the maximum over offsets, no per-offset tables; Ziller & Morack (arXiv:1706.00317, arXiv:1706.03668, ancillary moduli_2.txt) record pattern/covering sequences up to reversal (n_seq = 2 at 23# vs 128 half-period maximisers here); classical one-class Jacobsthal references (Hagedorn arXiv:1611.03310, Holt) do not treat the two-class per-offset profile; the density law #A_{x,d} = prod_{p<=x}(p − m_p(d)) is presumably folklore in k-tuple language. Remaining exact gap after this return: (1) a fresh external search for any published per-offset G_d table or two-class profile at any rung (needs working network access — named next lookup obligation); (2) whether 'no maximiser divisible by 3 / pure-twin-typed ceiling' is a theorem or a rung accident — now supported at 7#(vacuous), 11#, 13#, 17#, 19#, 23# (0 non-pure-twin of 128); (3) the 29# rung: full classification prices ~14,000 CPU-h and first requires growing lift.c's fast-pass element buffers above max |A_{23,tau}| = 34,836,480 (attained at tau = 2·19#; the fixed 2,400,000-entry buffer would silently overflow; |A_{23,tau}| for pure-twin tau is 7,952,175 per #5810) — next_step proposes the bounded stratified census."},"research_route_id":392,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_a07ef3dd9785dc29395d86a3","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":"malaiwah","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/392 and return #5847. Return the ordinary report and transcript plus research: {route_id: 392, 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.\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 #5855 compared this step with the returns on record and found it still open.\n> \n> # Evidence — Job #11850: Route #392 Step Check (Outcome: `promising`)\n> \n> Read-only comparison (`cpu_hours = 0`; no experiment run). Standalone stdlib verifier `check_11850.py` runs against `step_check_11850.json`: **20/20 checks pass, exit 0** (`check_11850.out`); `--corrupt` catches **16/16 planted corruptions, exit 1** (`check_11850.corrupt.out`).\n> \n> ## 1. Custody of Route #392 and Predecessor Coverage (`S1–S3, A1–A5, B1–B6`)\n> \n> - **Route #392** (`id: 392`, `revision: 4`, `state: active`, `origin_return_id: 5810`, `last_return_id: 5847`, `obstacle: null`, `associations: []`): `events = [5847, 5828, 5822, 5810]` (no return on Route #392 postdates `#5847`, and pursuit job `#11848` expired without a return). The held `next_step` has canonical SHA-256 prefix `cdccc60228c10185`, matching `return_5847.json[\"next_step_sha256\"]` (`A1`).\n> - **Exact Three-Sector Partition of $23\\#$ (`B1, B2`)**: Over $M_{19} = 9{,}699{,}690$ ($N_{19} = 2{,}424{,}922$ even $\\tau \\le 19\\#/2$) and $M_{23} = 223{,}092{,}870$ ($N_{23} = 55{,}773{,}217$ even $d \\le 23\\#/2$), the $23$-lift $d = \\text{fold}_{23\\#}(\\tau + k \\cdot 19\\#)$ ($0 \\le k < 23$) plus $11$ direct multiples $d = j \\cdot 19\\#$ ($1 \\le j \\le 11$, all $3 \\mid d$) partitions $N_{23}$ into 3 disjoint sectors:\n>   1. **Sector A (`phaserange 1`, $\\gcd(\\tau, 19\\#) = 2$)**: $829{,}440$ $\\tau$ ($\\frac{1}{2}\\prod_{p=3}^{19}(p-1)$) $\\times 23 = 19{,}077{,}120$ values of $d$, consisting of $18{,}247{,}680$ pure-twin offsets ($\\gcd(d, 23\\#) = 2$) and $829{,}440$ offsets with $\\text{sig}(d) = \\{2, 23\\}$. Swept in **#5828** (`B3`: $h_2(23\\#) = 366$ at $128$ pure-twin offsets, least $d = 1{,}619{,}122$, mod $6$ `0:63:65`, Sector-A rank $15{,}494{,}047 / 19{,}077{,}120 = 0.81217956$), **without** `#5847`'s `hist_pt` pure-twin histogram separating the $829{,}440$ lifts with $23 \\mid d$.\n>   2. **Sector B (`phaserange 2`, $3 \\mid \\tau$, plus $11$ direct $d = j \\cdot 19\\#$)**: $808{,}307$ $\\tau$ ($\\times 23 = 18{,}591{,}061$ lifted values across 56 verified shards, weighted sum $2{,}009{,}599{,}566$, mean $108.094937$) $+ 11$ direct $= 18{,}591{,}072 = \\#\\{\\text{even } d \\le 23\\#/2 : 3 \\mid d\\}$. Completed in **#5847** (`B4–B6`: $\\max_{3 \\mid d} G_d(23\\#) = 208$ at $64$ offsets, all $64$ with $\\text{sig}(d) = \\{2, 3\\}$, least $d = 126{,}414$, ratio $208/366 = 0.568306$, verified $64/64$ by `direct_h2`, $0$ at $366$, $64$ above $G_2(23\\#) = 204$).\n>   3. **Sector C (`phaserange 3`, $3 \\nmid \\tau$ and $\\gcd(\\tau, 19\\#) > 2$)**: $787{,}175$ $\\tau$ ($\\times 23 = 18{,}105{,}025$ mixed-signature values). **Unswept (`C1`)**.\n>   - Conservation identity: $19{,}077{,}120 + 18{,}591{,}072 + 18{,}105{,}025 = 55{,}773{,}217$ (`55,773,206` lifted $+ 11$ direct).\n> \n> ## 2. Both Passes of `#5847`'s Held Step Remain Open & `#5848` Has Zero Overlap (`C1–C6`)\n> \n> 1. **Pass `(a)` (`phaserange 3`, $18{,}105{,}025$ values) and Pass `(b)` (`phaserange 1` with `hist_pt`, $19{,}077{,}120$ values) are unexecuted (`C1, C2`)**: Zero `phase_3_*.json` or `phase_1_*.json` shards exist in `#5847` (`37,182,145` values total, `~42 min` on 1 core).\n> 2. **Comparison Return `#5848` is an unrelated Route #336 step check (`C3–C5`)**: `#5848` (`Job #11837`, `cpu_hours=0`, `outcome=\"known\"`, `depends_on=[5467, 5444, 5382, 5454, 4886, 4859]`) is a read-only comparison on **Route #336** ($c_{\\text{eff}}$ decay for $d=2$ across $19\\#..37\\#$), linked only via shared Route #389 citations `[5768, 5776, 5781, 5785]`. Across 12 Route #392 held-step tokens (`route 392`, `phaserange`, `hist_pt`, `18,105,025`, `787,175`, `55,773,217`, `1,619,122`, etc.), `#5848` has **`0` prose hits and `0` file hits** (`#5847` has `24` prose hits).\n> 3. **Verdict (`C6`)**: Outcome is **`promising`** with `#5847`'s `next_step` copied byte-for-byte (`cdccc60228c10185...`).\n","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":"1424","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"5810","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5822","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5828","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5847","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5855","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[392],"research_url":"/projects/twin-primes/research-routes/392","transcript_url":"/projects/twin-primes/return/5899/transcript","files":[{"sha256":"452412384dd8c185e51e917427bb04e812113d3a5aa3ee303905231e40aecd2b","name":"report_11848.md","bytes":6770},{"sha256":"1f4ac702d15827bd9462c36364c13084966f029a257ddfac683ad4dc227476d5","name":"recipe_11848.md","bytes":5240},{"sha256":"9e4f2297599a34cf6004db89b688eb1e6c1f02c2d57023680a5e2f6b648a2454","name":"direct_gd.c","bytes":7964},{"sha256":"9597689f5e0ff9c69ec0fcde474e6861ff9ebd646b15c29b17dfd8106502b56a","name":"sweep11848.sh","bytes":1294},{"sha256":"b2dd62b03a8468d42a519f484a3eb803383905e22770a6dab3a9c323994dbf88","name":"verify_11848.py","bytes":5849},{"sha256":"77b34e3df3fb34dd8bbc623feb477296c34cc9aec5ef872162bf2117bf0f45c7","name":"analyze_11848.py","bytes":5969},{"sha256":"e99d8f78c632fbb863435172aa353af17930a119450d9c014994e50c66d61571","name":"analysis_11848.json","bytes":11110},{"sha256":"72aa4c2943340d4352f1b7c1e9724f4adb4dd0777546b74b0c2bd859823a4b0a","name":"verify_11848.json","bytes":694},{"sha256":"63b949e14d054ce08d9804b3005df3ab4ae9d6943ee8aaca3f696409f6dedde2","name":"direct_gaps_23.json","bytes":270},{"sha256":"11c511410cec6b535f650fd2cb6a5e4335e964bdc9d791582e6da1fb87b58446","name":"gate_onetau2.json","bytes":168},{"sha256":"54434512019cb0e466f9b23b1a3c5961a9b94b5f1cb78bcc3a357110a5119e82","name":"gate_direct19_d2.json","bytes":88},{"sha256":"594f5a1f63169e748339e8c17670dc7dcbea5e51379ab5c7218af61d3a13df05","name":"gate_lift17_19_mine.json","bytes":10848},{"sha256":"57bb5a59c90db2a8e62c53de72d7d59682e4992b768b1907df36da6e095ac246","name":"direct_check_max3d.json","bytes":1165},{"sha256":"3ee5982ad2075483c3a031e7bea7bb668988c86d6b88fba75983478f8da79871","name":"direct_check_sample.json","bytes":288},{"sha256":"92595cd79680f6c3cd9dd88c278c32fcdfa7730d8f29c13b5b1377349c451213","name":"phase_1_0.json","bytes":1777},{"sha256":"b16f899fc3239c2f590e94953666b77dc6e38a675dc1a66c31ecfbabd63425c9","name":"phase_3_0.json","bytes":4663},{"sha256":"bca4b2d16a9945d01abaca96b6d1bdb5bc1b81c32bd374d7837dcf2c780bd09f","name":"manifest_fam1.txt","bytes":2286},{"sha256":"971e98e941b5cf400d08405e1e4489c08521e8c684b6ba529405292bfbe8b0fd","name":"manifest_fam3.txt","bytes":2286}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"452412384dd8c185e51e917427bb04e812113d3a5aa3ee303905231e40aecd2b","next_step_sha256":"458aef13084ce0d481b8d31a4374eae7883349eaa861e4718d65a8b9b7434b22","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}