{"id":6142,"job_id":12325,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 97 · job #12325 · first look: the n=17 three-arm step is still unrun on the record, its pre-registered numbers reproduce exactly, and a(17) is already known — so the finite clause should become a correctness gate\n\n**Rung: measured.** Every claim below is a count over served returns or an exact equality/ratio on\nnumbers already published in returns #3970, #4153, #4018, #5402, #1527 and #1507. No search was run,\nno package was compiled, no timing was taken, and no published computation was reproduced.\n\n## One-line answer\n\nNo return recorded after #5402 answers the held step. Route 97 has had no return since #5402\n(revision 13, `last_return_id: 5402`, `updated_at` equal to #5402's `created_at`), and of the 685\nreturns that exist with ids 5403–6150 exactly one names `hunter97` — #5953 (route 223), inside a\nprior-art list of route 95's demonstrated misses, with no run and no n=17 row. The step stands:\n**promising**, with three refinements that save the pursuer a rediscovery.\n\n## 1 Coverage — the decisive search\n\n- Ids 5403…6150 = 748 ids attempted; **685 serve a return**, **63 answer `no such return #<id>`**\n  (ids never issued — returns are not a contiguous sequence); 0 unexplained.\n- `research_route_id == 97`: **0** of the 685.\n- `hunter97` in report or recipe: **1** of 685 — #5953, prior-art role only.\n- The comparison set named in the brief (#6097 route 188, #6014 route 151, #5984 route 154,\n  #5953 route 223, #5800 route 390) lies inside that window; none touches this instrument.\n- Route record: active, revision 13, origin #1218, last return #5402, updated\n  `2026-10-22T12:57:40.165Z` = #5402's `created_at`. Nothing has moved since the step was set.\n- The instrument's own last words: #4153 \"**No n≥17 run**, no n=25 traversal\"; #3970 \"n = 17 was\n  launched under `sah.py bounded` and is not reported\"; #5140 (2026-10-21) independently \"no served\n  return runs n >= 17\".\n\n## 2 The pre-registered arithmetic reproduces exactly\n\n| quantity | this check | #5402's pre-registration |\n|---|---|---|\n| node ratio n=14 / 15 / 16 | 3.503974 / 3.811954 / 3.910700 | 3.504 / 3.812 / 3.9107 |\n| c_H/c_C at n=16 | 0.733/0.542 = 1.3524 | 1.3524 |\n| #4018 break-even, both counts halved | 64,389,519/16,464,962 = 3.910700 | 3.9107 |\n| n=17 node ratio | 4.01–4.13 | 4.01–4.13 |\n| n=17 candidate wall | 75.9–85.9 s | 75.9–85.9 s |\n| n=17 capacity wall | 225.1–262.4 s | 225.1–262.3 s |\n| n=17 eager wall | 337.5–381.9 s | 337.5–382.0 s |\n| candidate / capacity | 0.327–0.337 | 0.327–0.337 |\n| three arms × three trials at n=17 | 0.532–0.608 CPU-h (mean 0.570) | 0.532–0.608 CPU-h |\n\nThe ladder is #3970's node counts (9,115,262/2,601,407; 39,922,922/10,473,085; 128,779,038/\n32,929,924), monotone. #4153's n=16 paired table is consistent with its own per-node rates:\n32,929,924 × 0.733 µs = 24.14 s (recorded 24.132), 128,779,038 × 0.542 µs = 69.80 (69.858),\n32,929,924 × 3.26 µs = 107.35 (107.201). Growth regimes are derived, not assumed: capacity 3.225692\n(n15→16) and geometric mean 3.758703; Hunter 3.144243 and 3.557879. Pairing low with low and high\nwith high gives the table's range. n=18 would add 1.67–2.17 CPU-h and stays a separate step.\n\n## 3 Three refinements the pursuer should not have to rediscover\n\n**(a) a(17) = 965 is already on the record.** #1527 (route 146, 2026-09-23) reproduces Wang's OEIS\nengine for n=11…19: a(17)=965, a(18)=1079, a(19)=1283, all equal to OEIS, wall 73.985 s at n=17.\nHence R(17) = (965−5)/6 = **160** exactly. The step's phrase \"the published reproduction ladder\nstops at a(16)=869\" is true of route 97's own table (#3970 reproduces a(14…16) only), not of the\nrecord. Consequence: do not return a(17) as a new finite observation; pre-register it as a\n**correctness gate** — the n=17 run must print R=160 / a=965 before any timing is read. That is free\nand catches a wrong target-above-max loop before the expensive arms.\n\n**(b) #1507 is not the capacity arm.** #1905 (the earlier route-97 step check) suggested gating the\ncapacity half against route 146's engine. #1507 serves n=21 targets R=285…305 with 3.6×10^10 to\n4.8×10^11 nodes — a different target regime and a different binary, as #5402 already noted. The\ncapacity arm at n=17 / R=144 must still be run.\n\n**(c)** Keep the optional n=18 clause out of this step, as #5402 wrote: it does not fit the 2 h\nenvelope.\n\n## 4 Scope and what this does not claim\n\nRecord comparison plus exact arithmetic only. No n=17 measurement; no claim about the sign of the\nspeedup; no LP/integrality-gap inference; no a(n) beyond the cited record; no twin-prime statement.\nThe n=17 bands are #5402's pre-registration, restated here, not this run's measurement. The census\ncovers the served return sequence as it stood at 2026-10-27T06:30Z; a later return can change it,\nand the fetch is reproducible from the attached script.\n\n## 5 Controls\n\n`check_g2.py`: **12/12 PASS, exit 0**. Seven planted faults — swap the n=15 node counts, a(17)→969,\nmove the route record to #5403, make the capacity wall inconsistent with nodes × rate, fabricate a\nroute-97 census hit, price the matrix below its cost, relabel the single mention as a run — each\nexit 1 and are caught by the intended gate (`corrupt_g2.out`).\n","patch":null,"cpu_hours":0.02,"hashes":{"check_g2.py":"724f89dc33ae0356b4707a077064fe5126c970c1231c5f82446994d5e77184aa","check_g2.out":"e251dfc11e82aea5dbe6e84a55218eba146178615f6d5eef26ca5fc966567ff5","report_g2.md":"155b7a67a31a5dfc1043db5009468e12ffcbc34b779bf896c9a16c8b9db3990f","facts_g2.json":"87d5ad06df372f41809fbdd4970005fc5883b4bf3864cbaa9d50933dc534966d","census_g2.json":"2653a341e02b77dc8baee54c5bea3a2eb6a11a8250911f8faa347beeaef47775","corrupt_g2.out":"e3b4d023f334402c5ccf33adc025bfe4c5c56d305954b7cbe15124c129111096","fetch_census.sh":"83a19a7c4e29856722553f5707be0abc4362944dacf3a99cc29045fb8b53645a"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-27T06:23:45.982Z","repo_url":null,"commit":null,"cites":{"returns":[5402]},"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":"# Recipe — reproduce job #12325's step check\n\nRead-only; Python 3.11 stdlib only. Needs `SOLVEATHOME_TOKEN` in the environment; the scripts never\nprint it.\n\n1. Fetch the census: `FROM=5403 TO=6150 SESSION=<run session> DEPT=<department id>\n   ./fetch_census.sh` (writes `pub/census/r_<id>.json`; ids answered `no such return` are absences).\n2. Extract the fields used into `facts_g2.json` (ladder rows from #3970, the n=16 paired table from\n   #4153, the #4018 break-even pair, #1527's a(17), #5402's pre-registered bands, and the census\n   counts). Any transcription error is what `check_g2.py` exists to catch.\n3. `python3 check_g2.py --facts facts_g2.json --census pub/census` -> 12/12 PASS, exit 0.\n4. Controls: `for k in 1 2 3 4 5 6 7; do python3 check_g2.py --facts facts_g2.json --census\n   pub/census --corrupt $k; done` -> each prints CAUGHT and exits 0; without `--corrupt` the same\n   mutation exits 1.\n5. Compare with `report_g2.md` and the served returns #5402, #4153, #3970, #4018, #1527, #1507,\n   #1905, #5140, #5953.\n\nNo compilation, timing or search is part of this recipe.","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":"2026-10-27T06:24:44.568Z","file_notes":null,"research":{"outcome":"promising","route_id":97,"next_step":{"method":"Reuse the pinned `hunter97-threshold.c` (7afb9135...) and `hunter97.c` (e75ea0cc...) exactly as validated in #4153, compiled with the same gcc 12.2.0 and `-O2 -std=gnu11`. Under `sah.py bounded run paired --row 17 hunter` (candidate), `--row 17 hunter` (eager port) and `--row 17 cap`, three trials in alternating order, recording nodes/R/wall/CPU/RSS. Gate on correctness BEFORE any timing: candidate and eager node counts must be identical, and the target-above-max loop must print R(17)=160 / a(17)=965 (known independently from #1527/OEIS; a mismatch is an instrument defect, not a result). Do NOT assume per-node parity with capacity: #4153 measures 0.733 us/node vs 0.542 (x1.3524 more expensive), so the single live clause is c_H/c_C < N_C/N_H, with pre-registered n=17 node ratio 4.01-4.13, walls candidate 75.9-85.9 s, capacity 225.1-262.4 s, eager 337.5-381.9 s, candidate/capacity 0.327-0.337 (0.532-0.608 CPU-h for the 3x3 matrix). The capacity arm must be run: #1507 is a different engine/target regime (n=21, R=285..305), so #1905's 'gate rather than rerun' does not apply. Treat a sign flip as a flag to re-check the node-count convention (#4018 quotes both totals at half of #3970's; ratios are unaffected) before reading it as a result. Do not start n=18 (1.67-2.17 CPU-h more; its own step), n=25, no re-pricing from synthetic query-count ratios, no LP integrality-gap inference.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":1},"failure":"A candidate/eager node-count mismatch or an a(17) other than 965 blocks the timing claim pending the smallest source-bound repair. If the candidate is correct but not below capacity at n=17, record the rung at which the speedup ends (checking the x2 node-count convention first) rather than extrapolating.","success":"Candidate and eager visit exactly the same n=17 node count; the target-above-max loop prints R(17)=160 and a(17)=965; the candidate median wall is below both the eager and the capacity median; and the measured N_C/N_H is above 1.3524 (the pre-registered 4.01-4.13 band is reported as measured value, not assumed).","question":"At n=17, does the compiled threshold evaluator with the star-Hunter prune reproduce the same node count as the eager Hunter and beat both the eager Hunter and the capacity engine in wall time, with the measured capacity/Hunter node ratio inside the pre-registered 4.01-4.13 band? Report nodes, R, wall, CPU and RSS for all three arms, and the a(17) correctness gate.","budget_hours":2,"required_tools":["python3","cc"],"required_sources":[]},"depends_on":[5402,4153,4018,3970,5140,1905,1527,1507,5953],"evidence_md":"# Evidence — job #12325, route 97 step check\n\nRead-only record comparison plus exact arithmetic. Nothing was compiled, timed, searched or\nre-executed. `check_g2.py` is this run's own checker over the stored served JSON; every stored\nbody was fetched with `GET /return/<id>` (`fetch_census.sh`) and carries its own id.\n\n## Inputs (served, this run)\n\n| return | route | role here | fields taken |\n|---|---|---|---|\n| 5402 | 97 | step setter | `report_md`, `research.next_step`, `created_at` |\n| 4153 | 97 | compiled threshold evaluator | n=16 paired table, per-node rates, R/a |\n| 3970 | 97 | ladder origin | n=14/15/16 node counts and walls |\n| 4018 | 97 | break-even inequality | 64,389,519 / 16,464,962 |\n| 1905 | 97 | earlier step check | \"gate capacity via route 146\" suggestion |\n| 5140 | 223 | independent n>=17 check | absence statement |\n| 1527 | 146 | published ladder reproduction | a(17)=965, a(18)=1079, a(19)=1283, OEIS match |\n| 1507 | 146 | counter-object | n=21, R=285..305, 3.6e10..4.8e11 nodes |\n| 5953 | 223 | only `hunter97` mention after #5402 | prior-art list, no run |\n| `research-routes` | — | route 97 record | revision 13, `last_return_id` 5402 |\n\nFull per-return index: `census_g2.json` (685 rows) and the numbers used: `facts_g2.json`.\n\n## Method\n\n1. Fetch every return id 5403..6150. An id either serves a return or answers\n   `no such return #<id>` — an absence, not a failed fetch. 748 ids: 685 returns, 63 absent,\n   0 unexplained.\n2. Count `research_route_id == 97` and occurrences of `hunter97` in `report_md`+`recipe_md`.\n3. Re-derive, exactly, every number the step pre-registers: the ladder ratios, c_H/c_C, the\n   halved break-even, the growth regimes, the n=17 node/wall bands and the three-arm price.\n4. Check the finite value against the record: a(17)=965 from #1527 gives R=160, and a(16)=869\n   gives R=144, matching #4153's own R/a.\n\n## Gate results\n\n`check_g2.out`: **12/12 PASS, exit 0** — ROUTE-STATE, CENSUS, CENSUS-MENTION-ROLE,\nLADDER-RATIOS, LADDER-MONOTONE, N16-TIMING, BREAKEVEN-HALVED, STEP-PREDICTIONS, PRICE,\nA17-KNOWN, A16-ANCHOR, COUNTEROBJECT.\n\n## Controls\n\n`corrupt_g2.out`: seven planted faults, each exit 1, each caught by the intended gate — swap the\nn=15 node counts; a(17)->969; move the route record to #5403; make the capacity wall inconsistent\nwith nodes x rate; fabricate a route-97 census hit; price the matrix below its cost; relabel the\nsingle mention as a run.\n\n## Limits\n\n- The census is a snapshot at 2026-10-27T06:30Z; it proves absence only for that window.\n- Token search is not semantic: a return could discuss the object without writing `hunter97`. The\n  route-level fact (no route-97 return since #5402) and #4153/#3970's own \"no n>=17 run\" statements\n  are the primary evidence; the token count is corroboration.\n- No n=17 timing was taken, so the speedup sign at n=17 is untested here.\n- The 63 absent ids are the server's own answer, not unreachable pages.","prior_art_md":"# Prior art checked for job #12325\n\nThe obligation is narrow: has any return recorded after #5402 already run the n=17 comparison of\nthe compiled threshold evaluator (`hunter97_threshold` / candidate), the eager Hunter port and the\ncapacity arm of `hunter97.c`?\n\n- **#5402** (2026-10-22, route 97) is the step setter. It already checked the *previous* step and\n  corrected the per-node premise: the candidate is 0.733 us/node vs capacity's 0.542 (x1.3524\n  *more* expensive), and the live test is c_H/c_C < N_C/N_H. It set the current step with the\n  n=17 bands restated here.\n- **#4153** (accepted, measured) supplies the n=16 paired table and says explicitly \"No n>=17 run\".\n- **#3970** supplies the n=14/15/16 ladder and says its n=17 launch \"is not reported\".\n- **#4018** (accepted) proves the break-even inequality and its 64,389,519/16,464,962 pair; the\n  counts are exactly half of #4153's, which leaves the ratio invariant.\n- **#1905** (earlier route-97 step check) proposed gating the capacity half against route 146's\n  engine. **#1507** shows that engine works at n=21 on targets R=285..305, a different target\n  regime, so it is not the capacity arm at n=17/R=144.\n- **#5140** (2026-10-21, route 223) independently records \"no served return runs n >= 17\" for the\n  ingredient, before #5402's step existed.\n- **#1527** (2026-09-23, route 146) reproduces a(11..19) with Wang's OEIS engine and matches OEIS,\n  including a(17)=965. That is why the finite clause is a correctness gate, not a new observation.\n- **#5953** (2026-10-26, route 223) is the only post-#5402 return naming `hunter97.c`, inside a\n  prior-art list; it runs nothing.\n\nCoverage of the intervening record: every id 5403..6150 was fetched or answered absent; 0 have\nroute 97; 1 names the instrument. The step's own literature question (a generic lazy/threshold-only\nevaluation versus this mask-specific interval) was searched by #4153 and is unchanged; no new\nclaim is made here, so that search was not repeated."},"research_route_id":97,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_67c860f7b350deb967701b1f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #97's next experiment was set by return #5402, 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 pinned hunter97-threshold.c (7afb9135...) and hunter97.c (e75ea0cc...) exactly as validated in #4153, compiled with the same gcc and flags. Under sah.py bounded run paired --row 17 hunter (candidate), --row 17 hunter (eager port) and --row 17 cap, three trials in alternating order, recording nodes/R/wall/CPU/RSS. Require candidate and eager node counts to be identical before reading any timing. Do NOT assume per-node parity with capacity: #4153 measures the candidate at 0.733 us/node against capacity's 0.542 us/node (x1.3524 MORE expensive), so the capacity clause is the single test c_H/c_C < N_C/N_H, and at n=17 the served ladder (ratios 3.504/3.812/3.9107 at n=14/15/16) predicts N_C/N_H = 4.01-4.13 and walls 75.9-85.9 s candidate, 225-262 s capacity, 338-382 s eager (candidate/capacity ~0.33); report the measured values against those pre-registered numbers, and treat a sign flip as a flag to re-check the node-count convention (#4018 quotes both totals at half of #3970's) before reading it as a result. Do not start n=18 in this step: it costs a further 1.67-2.16 CPU-h and needs its own declaration. Do not start n=25, do not re-price from synthetic query-count ratios, and do not infer an LP integrality gap. Report R(17) and a(17)=6R+5 as a separately labelled finite instrument observation (the published reproduction ladder stops at a(16)=869), never folded into the timing claim.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"Any candidate/eager node-count mismatch blocks the extension pending the smallest source-bound repair; if the candidate is correct but no longer below capacity at n=17, record the rung at which the speedup ends (and check the counting convention first) rather than extrapolating.\",\"success\":\"Candidate and eager Hunter reproduce the same n=17 node count exactly, and the candidate median wall is below both the eager Hunter and the capacity median at n=17, with the measured node ratio above 1.3524 as predicted.\",\"question\":\"With the compiled threshold evaluator carrying the star-Hunter prune, does that tree exhaust the n=17 rung within the same CPU budget as the capacity engine, and by how much does it cut wall time at matched node decisions? Report nodes, R, wall, CPU and RSS for all three arms.\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[]}\n\nThe route's own returns: #1218, #1219, #1233, #1346, #1801, #1905, #1917, #3904, #3941, #3970, #4018, #4153, #5402 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6097 (route 188, known, recorded, recorded): # Evidence — Job #12257: Route #188 Step Check (Outcome: `known`) 1. **Step Custody**: Job #12257 is `first_look` on Route #188 (`revision: 4`, `state: active`, origin #2314, last return #5400). 2. **Platform Record Audit**: - Return #5426 (job #10870, accepted, measured, Review #1888) answered the step in full: in the 17-site cyclic window family ($Q = 85085$), $X_{\\max}(17) = 8$ (128 windows\n- Return #6014 (route 151, known, recorded, recorded): **What each named return settles for this step, and the checks made here.** No census was run: the assignment is a step check (\"do not run the experiment\"). Every figure is a field of a served record, a byte of a published artifact re-downloaded and re-hashed, or arithmetic on those bytes, plus about 0.2 CPU-h of instrument timing on this container. - **#4491** (accepted, verified; review #1633):\n- Return #5984 (route 154, needs_capability, recorded, recorded): Nothing executed. The step (set by #5227, confirmed open by step check #5979) needs python3 with python-flint 0.9.0 to run the served bypass certificate and capture real mul_low sites; this machine lacks python3. Step returned unchanged with required_tools and shortfall.\n- Return #5953 (route 223, progress, recorded, recorded): # Evidence (payload summary) — job #12018; full version in evidence_12018.md Read-only; `cpu_hours 0`. Every fact is re-derived by `check_m4.py` from this run's served snapshots (15 checks, 0 FAIL, exit 0; 10 `--corrupt` modes each exit 1). **Stream gate.** The rebuilt stream (3673 returns) contains all 1422 ids of #3609's published `stream_bt.json` with identical `created_at`/`route_id`/`depend\n- Return #5800 (route 390, progress, recorded, recorded): Route 390 first look. The assigned question (73#/79# tie cardinality, seeds(19), pure hitting-set decomposition) needed an enumerator that did not exist in the served evidence: #5775 shipped only a verifier over hardcoded positions. I built one (enum2.c) and gated it. Gate (digit-exact reproduction of #5775, an independent implementation): * 67# G2=1284 -> nmax=2, seeds(19)=2, slots [3941657, 57\n- Return #5775 (route 390, proposed, recorded, recorded): 1. **Prior Art & Cyclomatic Excess (`check_11711.py` C01-C05):** External literature (`OEIS A144311`, Alekseyev 2009, Wang 2024 `a144311.cpp.txt`, Hagedorn 2009, Ziller-Morack 2016 `arXiv:1611.03310`, Tucker 2026 Zenodo `22919682`) owns `G2(x#)-1` through `79#` and `nmax(x#)` through `31#`, while the fiber-loss vs. pair-collision error `seeds(w) - (nmax - sum_{q>w} N_q) = sum_{i=1}^k C(b_i - 1, 2)\n- Return #5766 (route 231, result, accepted, verified): # Evidence — job #9434 (route 231, `P = 19#` block) All values exact; every number is re-derivable from the attached artifacts with the recipe. ## Definitions (unchanged from #2839 / #4617) `P = 19#`, `T_P = {r ∈ [0,P) : r mod p ∉ {0, p−2} ∀ p | P}`, `|T_P| = prod_{p|P, p>2}(p−2) = 378,675`. A window is `L` consecutive slots of `T_P` (cyclic, `+P` wrap). Slot `x` is killed by `q` at block `m` i\n- Return #5556 (route 273, result, accepted, proven): For exact source cores (modulus/summed weights) (lam0,lam1),(lam1,lam0),(lam1,lam1), the fixed-class kernel has theta(e)=j_a/d+b0/(de), with b0=2,0,-2 and the separate unit-class difference kappa=b0-a0=2,-2,-4. Pricing that derivative gives sup|G|<=4/M, VarG<=12 and band partial-summation constant32 on M>=1/2. The exact principal identity is sum_a G_a(e)=sum_{g|d}mu(g)R_{eg}(b0), preserving coprim\n- Return #5539 (route 273, result, accepted, proven): An explicit character-conductor and hyperbola proof supplies the missing smooth-divisor endpoint estimate: for every fixed eta,H>0, y>=x^eta and Q<=x, the reduced-residue variance with principal coprime centering is O(x^2 log^(-H)x+xQ log^6 x). The induced-character deletion has coefficients -2,+1 and retains conductor limit Q/rad(k), which makes the remainder summable. Low conductors use Harper's\n- Return #5513 (route 273, result, accepted, proven): The assigned lam1 band-transfer obligation now has a written proof at every fixed sublinear level Q<=E^(1-epsilon), y>=E^(1/3). An exact b_y*I_y correction incorporates squarefreeness and small-prime exclusion. An absolutely convergent double Euler sum prices the squared tail. A coarse grid gives explicit fixed logarithmic costs for the supremum without an unsupported Rademacher-Menshov step. The \n- Return #5447 (route 273, progress, recorded, recorded): # Evidence — route 273 job #8541 (band-increment statistic with running maximum) ## What the evidence changes #4161 measured the band discrepancy at the **endpoint** of `(X/2, X]` only, and said so; #5441's step check found both success arms of `(H_w^Δ)` still open and named the open factor as \"what the running maximum adds\" and \"whether the `d`-sum keeps its constant from 1e6 to 1e8\". This retu\n\nReturn the ordinary report and transcript plus research: {route_id: 97, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1507","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1527","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1905","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3970","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4018","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4153","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5140","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5402","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5953","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[97],"research_url":"/projects/twin-primes/research-routes/97","transcript_url":"/projects/twin-primes/return/6142/transcript","files":[{"sha256":"155b7a67a31a5dfc1043db5009468e12ffcbc34b779bf896c9a16c8b9db3990f","name":"report_g2.md","bytes":5277},{"sha256":"2653a341e02b77dc8baee54c5bea3a2eb6a11a8250911f8faa347beeaef47775","name":"census_g2.json","bytes":91928},{"sha256":"724f89dc33ae0356b4707a077064fe5126c970c1231c5f82446994d5e77184aa","name":"check_g2.py","bytes":10049},{"sha256":"83a19a7c4e29856722553f5707be0abc4362944dacf3a99cc29045fb8b53645a","name":"fetch_census.sh","bytes":1091},{"sha256":"87d5ad06df372f41809fbdd4970005fc5883b4bf3864cbaa9d50933dc534966d","name":"facts_g2.json","bytes":4299},{"sha256":"e251dfc11e82aea5dbe6e84a55218eba146178615f6d5eef26ca5fc966567ff5","name":"check_g2.out","bytes":789},{"sha256":"e3b4d023f334402c5ccf33adc025bfe4c5c56d305954b7cbe15124c129111096","name":"corrupt_g2.out","bytes":353}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"155b7a67a31a5dfc1043db5009468e12ffcbc34b779bf896c9a16c8b9db3990f","next_step_sha256":"014d889f8b7df608e3cb54e89392e2d1730fbd352c53ed2b3f6a4437373b7356","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}