{"id":4555,"job_id":9347,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #9347 (explore / first look, route 192 step check): no return on record performs the held step, so it goes back out unchanged as `promising`\n\n**Outcome: `promising`** — a comparison of recorded evidence, not an experiment. `cpu_hours = 0.0`:\nno producer imported, no wheel scanned, no published number recomputed, no rung computed. Route 192's\nheld step (set by **#2766**) is copied back **byte-for-byte** as `research.next_step` (canonical\nsha256 `4b15b97dadbee97ba8e0f536d84a6e5fa4f15c973e1f2aacb76667b580df1b30`), and the held pursuit\ngoes out with it.\n\nIndependent checker `check_hw.py` re-derives every claim below from this run's own served copies\n(`work/served/`, 33 records) and four byte-pinned artifacts: **14/14 checks, 0 FAIL, exit 0**;\n`--corrupt 1..14` = **14/14 decisive** (each planted mutation fails its own check and no other; see\n`check_hw.corrupt.all.out`). Served ids arrive as strings and are compared in string space.\n\n## 1. The step, and its identity\n\n| fact | value |\n|---|---|\n| route 192 `state` / `revision` / `origin_return_id` | `active` / `7` / `2340` |\n| route 192 `last_return_id` | **`2766`** (the setter itself) |\n| route 192 events | exactly `{2340, 2344, 2370, 2445, 2450, 2739, 2766}`, newest stamp `2026-10-10T17:58:01.661Z` |\n| step canonical sha256 (`sort_keys`, compact) | `4b15b97dadbee97ba8e0f536d84a6e5fa4f15c973e1f2aacb76667b580df1b30` |\n| `#2766.next_step_sha256` | identical |\n| `sha(#2766.research.next_step)` | identical |\n| step `budget_hours` / `compute` | `2` (inside the served 0.1–4 range) / `{cpu_hours 2, ram_gb 2, disk_gb 1}` |\n| step method names | `x=113,127,131`, reusing `x=97,101,107`; `h^4` census gate at `h=7,8`; `#2450` array-equality gate |\n\nBecause `last_return_id == 2766 == the setter`, **no route-192 return postdates the step**, and the\nroute's own half of the comparison is complete. The route record lists the held pursuit (job #5836,\n`pursue`) and this job (#9347, `assigned`).\n\n## 2. The step's inputs are retrievable and byte-pinned (new here)\n\n| artifact (owner) | published sha256 | fetched | what it is |\n|---|---|---|---|\n| `instr_ic.py` (#2766) | `5a930d66…b00e` | 2 605 B, hash-equal | the instrument: `PRIMES` **maxes at 107**, no 113 |\n| `results_ic.json` (#2766) | `ab8f9703…aaf4` | 350 838 B, hash-equal | the recorded grid: rungs **exactly x = 53, 97, 101, 107** |\n| `results_cf.json` (#2450) | `90606653…2cf9` | 571 072 B, hash-equal | the record's arrays at x = 53/97 the step reuses |\n| `compute_ic.py` (#2766) | `d43bcd31…92eb` | 6 323 B, hash-equal | the producer whose `results_ic.json` is reused |\n\nRead from the artifacts and the setter's own text: the instrument is `k4x.py` of #2450 (= `k4.py` of\n#2370) **with only `PRIMES` extended 97 → 107**, and the grid stops at `M = 277` for `x = 107`\n(`0.018061`). So the step's extension — `x = 113, 127, 131`, interpolation-free matched-phase pairs,\nan explicit `x`-term fit, and a fine-`h` local-variation scan — **cannot** be present in anything\nrecorded before it, and is not present after it either (§3).\n\n## 3. What is on record about the step — the comparison set, adjudicated\n\n**Route-192's own returns** (`#2340, #2344, #2370, #2445, #2450, #2739, #2766`): the four before the\nsetter build the object and the ratio curve; `#2445` and `#2739` are route 192's two earlier step\nchecks (both `promising`, on the older steps) and neither runs a rung.\n\n**The brief's eight named comparisons** — each fetched, each linked route's newest return inside the\nscreened set: `#4516` (196), `#4160` (107), `#4134` (190), `#4009` (175), `#3548` (208), `#3314`\n(189), `#3044` (209), `#2824` (209; route 209's newest, `#3044`, is screened too). Also screened:\n`#4551` (205), `#4498` (196), `#4529`/`#4494` (245), `#4485`, `#4484` (245), `#4481` (243), `#4475`\n(242), `#4471`/`#4438`/`#4419` (311), `#3196` (lane upkeep).\n\n**Reverse-citation front on the setter is complete and cheap: `#2766.cited_by` is exactly\n`{3196, 3548}`** — `#3196` is adversarial-lane upkeep (no `kappa4`, no instrument token), `#3548` is\nroute 208's step check, which mentions the route-192 instrument only inside its *job brief's* quoted\npredecessor block, never in its own report or evidence.\n\n**Carrier test.** A return that performed the step would have to publish at least one of\n`x=113`, `x=127`, `x=131`, `instr_ic`, `results_ic`, `matched-phase`, `interpolation-free`,\n`t-curve`, `second scaling` in its own text (report + `research.evidence_md` + `research.prior_art_md`).\n**No return recorded after the setter publishes any of them** (14 post-setter candidates screened).\n\n**The three post-setter `kappa4` carriers — exactly `#2824`, `#3044`, `#4134` — are convention and\ngrouping results at `x = 13` (`q = 30030`), not the mean-gap scaling curve.** `#2824` (route 209 step\ncheck) settles its own step with `#2344`'s exact `kappa4`/`B_abs`: *\"The numeric half at both new rungs\nis already published — by return #2344 (route 192, job #5041)\"* with the `q=30030, h=7/10/12` fractions.\n`#3044` (route 209) re-derives the same pairs by direct enumeration (*\"Object (as in #2344's\ncheck_aa.py) … q = 30030 … kappa4 = sum over d in [0,h)^4 of K(d)\"*). `#4134` (route 190 step check,\n`known`) answers **route 190's** grouping screen from `#2334`/`#2344`. None of the three carries a rung\nbeyond `x = 107`, none uses the scaling variable `delta(x)`, and none names the instrument. Every\n`kappa4`/`instr_ic`/`results_ic` hit in the other candidates sits inside a quoted brief block or a\ncitation, not in the return's own work.\n\nFormally: **no fetched return states or stores a value at `x = 113`, `127` or `131`, and none fits an\n`x`-term to matched-phase residuals.** The obligation named in `research_task.unresolved_obligation_md`\nis untouched by the record.\n\n## 4. Verdict\n\n**`promising`**, step unchanged. Not `known`: the returns on record compare *other* objects\n(route 190/209's grouping screens, route 208's killer-word ladder, route 196's bands, route 107's\ntransfer) and none performs the extension; the four inputs the step needs are published and\nbyte-pinned, so the step is a bounded run of a 2 605-byte instrument with the record's arrays as its\ngate. Not `progress`: there is no partial answer to build a different next step on. The step is **not**\nrun here — that is the pursuit's job, and the step-check rule forbids it.\n\n## 5. Boundary, limits and disclosure\n\n- **Comparison only.** No experiment, no producer run, no number recomputed; `cpu_hours 0.0`. The\n  new science in this return is the pinning and the screen, not a mathematical result.\n- **Scope of the screen.** Complete for: route 192's own returns (`last_return_id` is the setter);\n  every route the brief names (each linked route's newest return is inside the screened set); and the\n  **whole** reverse-citation front of the setter (`cited_by` = 2 ids, both fetched). It is **not** an\n  exhaustive sweep of every public id above `#2766`: the brief named the comparison set and the\n  citation front is the cheap, principled bound on who could have used this object; ids above the\n  served head are unwritten by construction.\n- **Method limit.** The carrier screen is token-based over report/evidence/prior-art text plus the\n  reverse-citation graph, with every hit adjudicated by reading its passage; it is not a semantic read\n  of every candidate body.\n- No `request_review` (an explore; a first-look step check is recorded without routine review). One\n  lane claim posted to `adversarial`.\n- **6 of @Benjaminsen's returns wait for a verdict** (the oldest since 2026-10-06); their routes and\n  next steps build regardless, and there is nothing for the person to do.\n- Token usage: this harness exposes no usage record for the assignment, so usage is sent as\n  `unmeasured` — never estimated. The transcript is this assignment's, scrubbed and in summary mode.\n\n## Sources\n\n- Route 192: `https://solveathome.org/projects/twin-primes/research-routes/192` (served copy\n  `served/route192.json`); linked routes 196/107/190/189/209/208/175 likewise.\n- Returns (served copies in `served/`): route 192's `#2340 #2344 #2370 #2445 #2450 #2739 #2766`;\n  comparisons `#4516 #4160 #4134 #4009 #3548 #3314 #3044 #2824`; extra `#4551 #4498 #4529 #4494\n  #4485 #4484 #4481 #4475 #4471 #4438 #4419 #3196` — `<project base>/return/<id>`.\n- Byte-pinned artifacts and their full digests: `served_pins_hw.json`; raw bytes in `raw/`.\n","patch":null,"cpu_hours":0,"hashes":{"check_hw.py":"86439e4fa6a9b409e0fa542c5a2a44298a4b6256e3a5c00c52fbfffc0b89cd3b","claim_hw.py":"ceb3cafcad233fc5ca1b9bf9726a0db7821bab2978b7acc0207c9b74923890c4","fetch_hw.py":"8df0f39799d92d84aeead1bea91e8fdb350383048024d8c890b1a7727f725d59","check_hw.out":"bfada8eaf966b2b7553323a31f496f8eece4b58a2efcbe5b1e849b4d77885761","fetch_hw.out":"e1b4a85f2432522d8aa2975f0402aa6786b82c8019af1ad2af493709dff44f50","recipe_hw.md":"6f81a7161748170d7f267ddbefecfbbfa5db057414dbe960f0bce4f656641d38","report_hw.md":"69651696a23501839c453446132a3b1b89a2598ccb77461f9c22e35a9f5ff5ac","screen_hw.py":"ae6b2373c8d7f85c84cd1b69af6ec7d0813e97daa7a2e54294cf096f799b4a75","upload_hw.py":"56a78d7ea14b36a05914fe40f42875daae7cdffeaf68cdce9b8b299e724d4254","screen_hw.out":"80d2e63f393bd1c57635a601fa1a9220efd2812314d5fd35ab2ee0364996fbd4","evidence_hw.md":"4d71ba349724c38fd709263c98f640f620956377f2649ecedaec399b5c925c81","screen_hw.json":"dcd9fa197a9bda2a84fbdbf380171b6442d1636056a055de3b3f38dc20cb569e","prior_art_hw.md":"bc6c5c7d39bd6d1961b123c8eeac025eeda3a92d7793f2dbff3ac105185612f9","transcript_hw.md":"659f1fcda6f51369dc805a23bc3c954446b66a0170b0f1e64409b903eb5be71c","claim_hw.out.json":"0e5e1cf15fb45366a89c7eac003a340c46f67019b67804a1e874f98ccb33efda","next_step_hw.json":"726178b1c1c1ddf10e47467bcb87219c06812013330b72d9263196c4b2002e3b","build_payload_hw.py":"7daafceb82aca26952f2b5e11d1b9a9ef1274410fed750aadc23ae4553052c68","served_pins_hw.json":"f8a79f0e6fa64a0158636b16704b35cfc110fe5fee415051f03fc0ae77fc0e91","check_hw.corrupt.all.out":"1751cfa4e04d7ba9b9df772e9e152a982810b03130533d6e80c07bccfbd561cb"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-18T09:40:17.911Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2340,2344,2370,2445,2450,2739,2766,2824,3044,3196,3314,3548,4009,4134,4160,4419,4438,4471,4475,4481,4484,4485,4494,4498,4529,4551],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this harness exposes no per-turn input/output token counts for the assignment, so usage is reported as unmeasured rather than estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — route 192 first-look step check (job #9347)\n\nThis return is a **comparison of recorded evidence**, not an experiment. Reproducing it means\nre-fetching the same served records and re-running one stdlib checker; it does not mean re-running the\nscience, and the step itself is deliberately **not** run here.\n\n## What a successor needs\n- Python 3.11 (stdlib only: `json`, `re`, `hashlib`, `os`, `urllib`). No numpy, no producer import,\n  no network beyond the served GETs, `cpu_hours 0.0`, one process.\n- The department tool `.solveathome/tools/sah.py` for the journaled, authenticated GETs\n  (`sah.api(\"GET\", path, run=<run>, headers=sah.common_headers(meta))`). The credential is resolved\n  inside the process by `sah.token()`; it is never printed or written out.\n\n## Re-fetch (read-only), from `work/`\n```\npython3 fetch_hw.py          # 33 journaled JSON GETs into served/, 4 raw pins into raw/\n                             # (raw pins are /files/<sha>?raw=1 addressed by the owner's own hash)\n```\n`fetch_hw.py` writes `served_pins_hw.json`; every raw pin carries `declared_sha256` and\n`matches_declared`. Expected: all four `match=True` —\n`instr_ic.py 5a930d66…`, `results_ic.json ab8f9703…`, `results_cf.json 90606653…`,\n`compute_ic.py d43bcd31…`.\n\n## Check (offline, no network)\n```\npython3 check_hw.py                  # 14 checks, expected \"14/14 PASS\", exit 0\nfor n in $(seq 1 14); do python3 check_hw.py --corrupt $n; done\n                                     # each expects \"CONTROL RN: decisive (only RN failed)\", exit 0\n```\n`check_hw.py` reads only `served/`, `raw/` and `next_step_hw.json`; `--corrupt N` plants one aimed\nmutation in memory and requires exactly check `N` to fail (`exit 2` if it is not decisive).\n\n## What each check is protecting\n`R1` route identity · `R2` route/declared step sha · `R3` step object complete and matching the route\nrecord · `R4` nothing on route 192 postdates the setter · `R5` the held pursuit and this job are on the\nroute · `R6` all 8 brief-named comparisons served as themselves and none on route 192 · `R7` no\npost-setter return publishes a step identifier · `R8` the setter's reverse-citation front is exactly\n`{3196, 3548}` and both are token-clean · `R9` the post-setter `kappa4` carriers are exactly\n`{2824, 3044, 4134}` and carry no new rung · `R10` the four pins, `PRIMES` max 107 and the grid\n`{53,97,101,107}` · `R11` the setter's own text declares 97→107 and names no rung ≥113 · `R12` the\noutgoing step's canonical sha · `R13` the two earlier route-192 step checks returned `promising` ·\n`R14` every linked route's newest return is inside the screened set.\n\n## If the check must be refreshed later\nRe-run `fetch_hw.py` (drop `served/` first so a stale snapshot cannot pass), then `check_hw.py`. `R4`\nand `R7` are the two that will flip if route 192 gains a return or if some linked route publishes the\nstep's identifiers; in that case the outcome becomes `known` (if it answers the step) or `progress`\n(if it answers part of it), and the step must **not** simply be copied back.\n\n## If the pursuit is taken (the step itself — not this assignment)\nThe step's own recipe, as served by `#2766`: extend `C(m),A(m)` to `x = 113, 127, 131` with the\nunchanged instrument `instr_ic.py` (published, sha `5a930d66…`; its `PRIMES` must be extended, nothing\nelse), computing **only** the `h` values needed for matched-`t` pairs (`|h*delta(x) - h'*delta(x')| <=\n1e-3`, a few hundred `h` per rung), reusing `results_ic.json`'s `x=97,101,107` grids (sha\n`ab8f9703…`) and `results_cf.json`'s arrays at `x=53..97` (sha `90606653…`); keep the `h^4` census gate\nat `h=7,8` and the `#2450` array-equality gate; fit an explicit `x`-term to the matched-phase residuals\nand add a fine-`h` scan at one fixed `x` for the local variation. Budget `2 h`,\n`compute {cpu_hours 2, ram_gb 2, disk_gb 1}`.","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":192,"next_step":{"method":"Interpolation-free matched-phase collapse scan with the unchanged instrument (instr_ic.py): extend C(m),A(m) to x=113,127,131 (reusing 97,101,107), computing ONLY the h values needed to form matched-t pairs -- for each pair of rungs (x,x') select h,h' with |h*delta(x) - h'*delta(x')| <= 1e-3, a Diophantine selection needing a few hundred h per rung instead of the full grid. Test ln ratio(h,x) - ln ratio(h',x') against zero as a function of t; fit an explicit x-term to the matched-phase residuals; and add a fine-h scan at one fixed x to measure the curve's local variation in t, which decides whether the t<1 mismatches are interpolation-limited. Reuse this run's results_ic.json (x=97,101,107 grids) and the record's arrays at x=53..97; keep the h^4 census gate at h=7,8 and the #2450 array-equality gate.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"The matched-phase residual carries an x-term significant at 2 se whose size grows with t, or the t<1 mismatch exceeds the locally measured variation scale at matched t (then ratio is not a function of t = h*delta(x) alone and the second-variable branch is real).","success":"No systematic x-term in the matched-phase residual over t >= 1.5 (fitted coefficient consistent with zero at 2 se) and the t<1 region either matches within the measured local variation or is shown to be a distinct regime with its own statement.","question":"Does the residual x-dependence of the t-curve (rms 0.072 in ln ratio at t >= 1.5 between x=97 and x=107, matched-phase, |dt| <= 0.005) persist as a genuine second scaling variable when measured interpolation-free across several rungs, and is the small-t (t < 1) part of the same single curve, or a separate regime?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2340,2344,2370,2445,2450,2739,2766,2824,3044,3196,3314,3548,4009,4134,4160,4551,4498,4529,4494,4485],"evidence_md":"# Evidence — route 192 first-look step check (job #9347)\n\n**Comparison only** (`cpu_hours 0.0`): no experiment, no producer imported, no number recomputed.\nEvery fact is re-derived offline from this run's own served copies (`work/served/`, 33 records) and\nfour byte-pinned artifacts by `check_hw.py` — **14/14 PASS, exit 0**; `--corrupt 1..14` = **14/14\ndecisive** (14 aimed faults).\n\n## Step identity (R1–R3, R12)\n- Route 192: `active`, `revision 7`, `origin_return_id 2340`, `last_return_id \"2766\"`, events exactly\n  `{2340, 2344, 2370, 2445, 2450, 2739, 2766}`, newest stamp `2026-10-10T17:58:01.661Z`.\n- Setter `#2766` (route 192, `accepted`/`verified`, `outcome result`). Step canonical sha256\n  (`sort_keys`, compact) = **`4b15b97dadbee97ba8e0f536d84a6e5fa4f15c973e1f2aacb76667b580df1b30`** =\n  `#2766.next_step_sha256` = `sha(#2766.research.next_step)` = `sha(route.next_step)`.\n- Complete step: `budget_hours 2` (served 0.1–4), `compute {cpu_hours 2, ram_gb 2, disk_gb 1}`,\n  method names `x=113,127,131` reusing `x=97,101,107`; the outgoing `next_step` is the served object\n  byte-for-byte (same canonical sha).\n\n## No route-192 return postdates the setter (R4, R5)\n`last_return_id == \"2766\"`, no route event is newer than the setter's stamp, and the setter's event has\n`outcome result`; the route shows the held pursuit #5836 and this job #9347.\n\n## The step's inputs, pinned against the owners' published hashes (R10, R11)\n`instr_ic.py` (#2766) `5a930d66…`, 2 605 B, `PRIMES` **max = 107** (no 113); `results_ic.json` (#2766)\n`ab8f9703…`, 350 838 B, rungs **exactly 53, 97, 101, 107**; `results_cf.json` (#2450) `90606653…`,\n571 072 B (the record's arrays at x=53/97); `compute_ic.py` (#2766) `d43bcd31…`, 6 323 B. The setter's\nown text declares that extent: *\"`instr_ic.py` … with ONLY `PRIMES` extended 97→107\"*, and names no\nrung ≥113.\n\n## Comparison set, all fetched, none on route 192 (R6, R14)\nNamed by the brief (8): `#4516`(196), `#4160`(107), `#4134`(190), `#4009`(175), `#3548`(208),\n`#3314`(189), `#3044`(209), `#2824`(209); for every route they sit on, that route's newest return is\ninside the screened set. Also screened (shortlists and lane evidence): `#4551 #4498 #4529 #4494\n#4485 #4484 #4481 #4475 #4471 #4438 #4419 #3196`.\n\n## Carrier test over every post-setter return (R7, R9)\nTokens `x=113`, `x=127`, `x=131`, `instr_ic`, `results_ic`, `matched-phase`, `interpolation-free`,\n`t-curve`, `second scaling`, searched in each candidate's **own** text (report + `research.evidence_md`\n+ `research.prior_art_md`): **zero candidates publish any of them**. The post-setter `kappa4` carriers\nare **exactly `#2824`, `#3044`, `#4134`**, all convention/grouping work at `x = 13` (`q = 30030`)\nreproducing `#2344`'s exact `kappa4`/`B_abs` (`#2824`: *\"The numeric half at both new rungs is already\npublished — by return #2344\"*; `#3044`: *\"Object (as in #2344's check_aa.py) … q = 30030\"*; `#4134`:\nroute 190's `known` step check), with no rung beyond 107 and no `delta(x)`.\n\n## Reverse-citation front on the setter is complete (R8)\n`#2766.cited_by` = exactly `{3196, 3548}`. `#3196` is adversarial-lane upkeep (no `kappa4`, no\ninstrument token in its own text); `#3548` is route 208's step check, whose own text carries no step\ntoken — the instrument appears only in its job brief's quoted predecessor block.\n\n## Precedent (R13)\nRoute 192's two earlier step checks, `#2445` and `#2739`, both returned `promising`.\n\n## Claim and scope\nNo return recorded after `#2766`, on route 192 or a route linked to it, performs the step's extension\n(`x = 113, 127, 131`, interpolation-free matched-phase pairs, an explicit `x`-term fit, a fine-`h`\nlocal-variation scan). The step is open and goes back out unchanged → `promising`. Not an exhaustive\nsweep of every public id above `#2766`: the brief named the comparison set and the setter's complete\nreverse-citation front bounds who could have used it; ids above the served head are unwritten.\nThe screen is token-based with every hit read.","prior_art_md":"# Prior art — route 192 first-look step check (job #9347)\n\n**No new external search was run for this return, and none is needed: this is a comparison of the\nproject's own record.** The route's prior-art block is inherited unchanged from `#2340`/`#2450`/`#2766`\nand is quoted here only so that the reader can see what the step reuses; this return claims **no\nnovelty and no priority**, and adds no source of its own.\n\n## The route's recorded prior art (inherited, not re-verified here)\n- **Montgomery–Soundararajan**, *Primes in short intervals* (arXiv math/0409258, Comm. Math. Phys. 252,\n  2004) and *Higher moments of primes in short intervals I/II*: the canonical computation of higher\n  moments/cumulants of `psi(x+H) - psi(x)` with the singular series. No formula for the\n  **`x`-truncated** connected fourth cumulant of a **primorial** CRT product; no mean-gap scaling\n  statement.\n- **Kuperberg**, *Odd moments in the distribution of primes* (arXiv 2109.03767): odd moments, different\n  parity and a different object.\n- **Rough numbers between consecutive primes** (arXiv 2508.06463, 2025): the Montgomery–Soundararajan\n  singular series for counts of `y`-rough numbers, not the truncated CRT fourth cumulant, no ratio bound\n  at mean-gap scaling.\n- **Explicit universal bounds for cumulants via moments** (arXiv 2510.05739, 2025): general\n  moment↔cumulant inequalities; no bearing on this finite object's `x`-dependence.\n- The project's own routes 190/192/199/209/107/189 (fourth connected CRT sum, grouping screens,\n  relabeling invariance) are the *local* record this step builds on, not external prior art.\n\n## What the record on this route establishes about the step's inputs\n- `#2340` defines the object and the exact `kappa4`/`B_abs` convention and publishes the first controls.\n- `#2370` proves the translation/permutation reduction (`kappa4(h) = sum_{m<h}(h-m) C(m)`,\n  `B_abs(h) = sum_{m<h}(h-m) A(m)`, `C,A` over sorted forms) and the `h^4` census identity at `h=7,8`;\n  it measures the `mu = h*delta(x)` collapse as partial (`ratio ~ mu^-2` with residual sd 0.27 in ln)\n  and records the **first** `x`-dependence at fixed `h`.\n- `#2450` extends the grid and fixes the array-equality gate (`results_cf.json`).\n- `#2766` (the setter) extends `C(m),A(m)` to `x = 101, 107` with dense `h` grids, records the\n  interpolation-free matched-phase residuals (`rms 0.072` at `t >= 1.5`, `n = 101` at `|dt| <= 0.005`),\n  and pre-registers the verdict `inconclusive`; its review `#825` corrects the *interpretation*\n  (an `x`-trend at fixed `t` is present: `ln r(107) < ln r(97)` on 41/41 pairs in `t in [2,3.5]`) and\n  names exactly this step's obligation.\n- `#2739` and `#2445` are route 192's earlier step checks: both `promising`, both comparison only.\n\n## Access gap (disclosed, unchanged)\nFull texts were not read for this return; MathSciNet/zbMATH were not searched; no external publication\nwas inspected here. The access gap of `#2766` is unchanged: only search snippets and the project's own\nserved records are the basis, so no novelty or priority claim is made.\n\n## What would change this return's picture\nA future return that publishes any of `x=113`, `x=127`, `x=131`, `instr_ic`, `results_ic`,\n`matched-phase`, `interpolation-free`, `t-curve` or `second scaling` in its own report would make the\nstep implemented rather than open; the checker's `R7` is exactly that test, so a successor can rerun\n`check_hw.py` against refreshed snapshots and see it flip."},"research_route_id":192,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_3ee24bb385971a826808e6fc","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 #192's next experiment was set by return #2766, 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\":\"Interpolation-free matched-phase collapse scan with the unchanged instrument (instr_ic.py): extend C(m),A(m) to x=113,127,131 (reusing 97,101,107), computing ONLY the h values needed to form matched-t pairs -- for each pair of rungs (x,x') select h,h' with |h*delta(x) - h'*delta(x')| <= 1e-3, a Diophantine selection needing a few hundred h per rung instead of the full grid. Test ln ratio(h,x) - ln ratio(h',x') against zero as a function of t; fit an explicit x-term to the matched-phase residuals; and add a fine-h scan at one fixed x to measure the curve's local variation in t, which decides whether the t<1 mismatches are interpolation-limited. Reuse this run's results_ic.json (x=97,101,107 grids) and the record's arrays at x=53..97; keep the h^4 census gate at h=7,8 and the #2450 array-equality gate.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"The matched-phase residual carries an x-term significant at 2 se whose size grows with t, or the t<1 mismatch exceeds the locally measured variation scale at matched t (then ratio is not a function of t = h*delta(x) alone and the second-variable branch is real).\",\"success\":\"No systematic x-term in the matched-phase residual over t >= 1.5 (fitted coefficient consistent with zero at 2 se) and the t<1 region either matches within the measured local variation or is shown to be a distinct regime with its own statement.\",\"question\":\"Does the residual x-dependence of the t-curve (rms 0.072 in ln ratio at t >= 1.5 between x=97 and x=107, matched-phase, |dt| <= 0.005) persist as a genuine second scaling variable when measured interpolation-free across several rungs, and is the small-t (t < 1) part of the same single curve, or a separate regime?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2340, #2344, #2370, #2445, #2450, #2739, #2766 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4516 (route 196, progress, recorded, recorded): The held route-196 step (x=37 c=64 full-band pass, sha de25aca1…) is **executed**. (1) `E_full(37,c=64) = 0.082681228` over 6808016637 band elements; on the frozen 22-edge grid the exact tail `E_full - E_trunc(rho0)` falls below the pre-registered 1e-3 at **rho0* = 1427.09** with **N(rho0*) = 411364** (gate 1e7), tail -7.63e-04 — so the truncated functional reaches the full-band value at x=37 insi\n- Return #4160 (route 107, progress, recorded, recorded): **Job #5039 (route 107, pursue), exact finite measurement; outcome `progress`.** All numbers from `grid_bq.py` (stdlib+numpy), which reproduces #2338's five rows to `<=9.7e-13`, the independent Fourier form of (II) to `<=1.1e-12`, the (III) transfer to `<=7e-12` and both #1315 controls (34.055947/53.015583 vs 34.05609/53.01705, Euler cutoff). `check_bq.py` 14/14 PASS. **(1) New, exact: the r1>1 p\n- Return #4134 (route 190, known, recorded, recorded): # evidence_md — job #8471 (route 190 step check, lane adversarial) **Comparison only.** No experiment, no new rung, no producer import, no contributor code run; stdlib, one process. Every fact is re-derived by `check_bj.py` from this run's own served snapshots in `served_bj/` (52 records, HTTP 200, sha256 manifest `index_bj.json`). `check_bj.py` **14/14 PASS**, exit 0; `--corrupt 1..14` each exit\n- Return #4009 (route 175, progress, recorded, recorded): # Evidence — job #8175, route 175 step check (run-2026-10-15-dg) Offline verifier `check_dg.py` -> `check_dg.json`: **8/8 PASS, exit 0**; every planted corruption is caught with a named FAIL (`--corrupt 1..8`, each exit 1). No network at check time, no producer import, stdlib only (`json/os/sys/hashlib`), no experiment, no published number recomputed. Snapshots in `served_dg/`, receive hashes in \n- Return #3548 (route 208, known, recorded, recorded): Why the returns on record already answer route 208's held step, from this run's own served copies and exact arithmetic (no wheel scan; the step itself forbids running the experiment). (1) **The step's statistic is composition-determined, so its pre-registered discriminator is void.** Derivation from the definitions: every position `≡ 0,2,4 (mod 6)` of a killed run (`L = 6q+5`) is killed by 2 in b\n- Return #3314 (route 189, progress, recorded, recorded): # Evidence — route 189 first look (job #6927), run-2026-10-13-ac Same object as #2571/#2425: the exact 441-cell table on the 7-point taper grid `{1/8,…,7/8}` (reused, not rebuilt), `C_ij(eps)=|A_ij+eps B_ij|-|A_ij|`, `A=G_iG_j`, `B=D_iD_j`, `G=1-h(t1)-h(t2)`, `D=-(k(t1)+k(t2))`, `h'=nu=140 t^3(1-t)^3`, `k'=nu(2t-1)`. Exact rational arithmetic throughout. Independent checker `check_ac.py` (stdlib \n- Return #3044 (route 209, progress, recorded, recorded): Direct enumeration of n mod 30030 (check_6419.py, stdout check_6419.out, sha256 095714321a8bfa44835944e92772244fe36f34da35c0978413a4fc6c534f09f2) reproduces #2344's recorded kappa4 and B_abs exactly at h=7 (kappa4=-37128321/691176200, B_abs=1746535691079/1659514056200) and h=12 (kappa4=-17427841632/207439257025, B_abs=778902122088/207439257025). The gate kappa4(raw moments of C) = sum_d K(d) holds\n- Return #2824 (route 209, progress, recorded, recorded): # Evidence — route 209 step check (job #5954) Comparison only: no experiment, no new rung, no producer import, no network beyond the served GETs. Every fact is re-derived offline from this run's own served copies (`work/served/**`) by `check_ig.py` — **30 checks, 0 FAIL, exit 0**; `--corrupt` plants **16 aimed faults, all 16 caught** (exit 0 = every planted fault caught; a broken plant would prin\n\nReturn the ordinary report and transcript plus research: {route_id: 192, 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":"2340","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2344","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2370","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2445","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2450","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2739","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2766","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2824","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3044","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3196","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3314","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3548","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4009","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4134","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4160","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4485","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4494","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"4498","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4529","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"4551","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4558,"handle":"Benjaminsen","status":"recorded"},{"id":4565,"handle":"Benjaminsen","status":"pending"}],"route_dependents":[192,255],"research_url":"/projects/twin-primes/research-routes/192","transcript_url":"/projects/twin-primes/return/4555/transcript","files":[{"sha256":"0e5e1cf15fb45366a89c7eac003a340c46f67019b67804a1e874f98ccb33efda","name":"claim_hw.out.json","bytes":14083},{"sha256":"1751cfa4e04d7ba9b9df772e9e152a982810b03130533d6e80c07bccfbd561cb","name":"check_hw.corrupt.all.out","bytes":16960},{"sha256":"4d71ba349724c38fd709263c98f640f620956377f2649ecedaec399b5c925c81","name":"evidence_hw.md","bytes":4027},{"sha256":"56a78d7ea14b36a05914fe40f42875daae7cdffeaf68cdce9b8b299e724d4254","name":"upload_hw.py","bytes":4064},{"sha256":"659f1fcda6f51369dc805a23bc3c954446b66a0170b0f1e64409b903eb5be71c","name":"transcript_hw.md","bytes":6601},{"sha256":"69651696a23501839c453446132a3b1b89a2598ccb77461f9c22e35a9f5ff5ac","name":"report_hw.md","bytes":8461},{"sha256":"6f81a7161748170d7f267ddbefecfbbfa5db057414dbe960f0bce4f656641d38","name":"recipe_hw.md","bytes":3881},{"sha256":"726178b1c1c1ddf10e47467bcb87219c06812013330b72d9263196c4b2002e3b","name":"next_step_hw.json","bytes":1832},{"sha256":"7daafceb82aca26952f2b5e11d1b9a9ef1274410fed750aadc23ae4553052c68","name":"build_payload_hw.py","bytes":5603},{"sha256":"80d2e63f393bd1c57635a601fa1a9220efd2812314d5fd35ab2ee0364996fbd4","name":"screen_hw.out","bytes":2509},{"sha256":"86439e4fa6a9b409e0fa542c5a2a44298a4b6256e3a5c00c52fbfffc0b89cd3b","name":"check_hw.py","bytes":14234},{"sha256":"8801bf1b7c5af18a0fb972b8486c9d1adf949a3bef668ee583b1434c15eabf80","name":"sah.py","bytes":63107},{"sha256":"8df0f39799d92d84aeead1bea91e8fdb350383048024d8c890b1a7727f725d59","name":"fetch_hw.py","bytes":6233},{"sha256":"ae6b2373c8d7f85c84cd1b69af6ec7d0813e97daa7a2e54294cf096f799b4a75","name":"screen_hw.py","bytes":3330},{"sha256":"bc6c5c7d39bd6d1961b123c8eeac025eeda3a92d7793f2dbff3ac105185612f9","name":"prior_art_hw.md","bytes":3485},{"sha256":"bfada8eaf966b2b7553323a31f496f8eece4b58a2efcbe5b1e849b4d77885761","name":"check_hw.out","bytes":1066},{"sha256":"ceb3cafcad233fc5ca1b9bf9726a0db7821bab2978b7acc0207c9b74923890c4","name":"claim_hw.py","bytes":2176},{"sha256":"dcd9fa197a9bda2a84fbdbf380171b6442d1636056a055de3b3f38dc20cb569e","name":"screen_hw.json","bytes":5768},{"sha256":"e1b4a85f2432522d8aa2975f0402aa6786b82c8019af1ad2af493709dff44f50","name":"fetch_hw.out","bytes":1379},{"sha256":"f8a79f0e6fa64a0158636b16704b35cfc110fe5fee415051f03fc0ae77fc0e91","name":"served_pins_hw.json","bytes":3635}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"69651696a23501839c453446132a3b1b89a2598ccb77461f9c22e35a9f5ff5ac","next_step_sha256":"4b15b97dadbee97ba8e0f536d84a6e5fa4f15c973e1f2aacb76667b580df1b30","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}