{"id":2878,"job_id":6049,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 185 step check — the held step is PARTLY answered: one further boundary constant (the #1976 divisor family) is genuinely uncovered\n\n**CLAIM.** Route 185's held step (set by **#2509**, revision 6) is **not** answered as written and is\n**not** open as written either: three of the four boundary constants its question names already carry\nregister verdicts on record — the tail `R±1/2` (five typed rows of the served `check_af.json`), the\nsmooth-APS `(H_w)` prefix (`#1983 → S`) and the PrimeGaps186 cell law (`#2074 → L`) — while the\nfourth, the **#1976 divisor family**, is typed nowhere. So the outcome is **`progress`**: the held\npursuit is replaced by one that adds exactly the uncovered row and the register-format emission,\ninstead of re-emitting verdicts the register already holds.\n\n**(1) Step identity, read from the served records.** Route 185 (`research-routes/185`, GET 200):\n`state` active, `revision` **6**, `last_return_id` **2509**, events `[2509, 2504, 2489, 2378, 2297,\n2288]`; its `next_step` equals the brief's step object exactly (method 1420 chars, sha256\n`90bbd191fd3fd507…`). No return was recorded after the setter on the route. Route 182 — the ledger\nthe step extends — is `revision` **2**, `last_return_id` **2257**, unchanged since 2026-10-04, and its\nown queued step is the `zone-tail-02.js` class-null consumer edge that our step excludes by name.\n\n**(2) What is already on record (the part of the step the register answers).** The predicate and its\nimplementation are served with the route's pursuit return: `check_af.py`, sha256 `bb53ace359b9e0b4…`\n(identical in #2297 and #2509), beside `check_af.json` whose **five tail rows are typed** — `R_shell`\nL, `R_bin` L, `R_band` S, `classNull` S, and `R + 1/2` L carrying the corrected `5/2` and `3`. #2509\nadds the four rows of its pursuit return, naming `#1983 → S`, `#2074 → L`, `#2013 → S`, `#1973 → S`.\nThe collapse test is run and reported: #2297 — *\"The collapse test fails for every S row (`R_band`,\n`classNull`, `#1983`, `#2013`, `#1973`).\"* Three of the four constants the question names are\ntherefore already decided, with units and opposing-domain values.\n\n**(3) What the register still lacks: the #1976 divisor family.** #2288 (the route's origin, rung\n`verified`) resolved the pair and asked for the missing field — *\"the register needs a typed\ndivisor/population field, not only a convention field\"* — while #2297 only re-verified the arithmetic\n(`82 = 246/3`, reused `check_y.py`, 13/13) and typed no row. Its population is the four-run word\n`60+126+60` (word sum 246 over `L−1 = 3` internal gaps); its two conventions are the served\n`82 = 246/(L−1)` (#1976) and the stored `123/2 = 246/L` (#2254's Check B); and its offset lives on the\ndivisor axis, which is exactly the unit question the predicate needs — `2 × (82 − 123/2) = 41` in the\nmean's own unit but not a half-unit move on the divisor axis. That is the one row to decide.\n\n**(4) Why the returns recorded after the setter do not answer it.** #2728 (route 204, job 5689, the\nlatest linked-route return) states it in writing: *\"route 182's register still lacks typed rows for\n#2013, #1973 and #2074 and the subtype column (#2509's finding), and #2509's own route 185 next step\n(the corpus sweep) carries the register-completeness obligation.\"* #2540 (route 226) quotes the held\nstep only as declared raw material; #2545 (route 226) cites route 185's typing rather than extending\nit; #2527 (route 222) puts the half-unit axis out of scope; #2511 (route 219) quotes #2297's collapse\nresult; #2539/#2538 (route 207), #2567/#2563 (route 230) and #2515 (route 222) carry no register row.\nA masked vocabulary scan (every `next_step` field replaced by a placeholder — the trap this folder\nrecorded for route 200) finds the step's own core phrases **only inside quoted steps**: count 0\noutside them in every fetched return. A route-level census of all **254** routes shows the axis\nvocabulary on route 185 only (29 hits), plus route 182's title/contribution.\n\n**THE REPLACEMENT STEP (narrowed to what is uncovered).** Add the **#1976 divisor family** row: state\nits population, its offset and its own unit (the mean's own unit against the divisor axis) and the\nopposing-domain value, apply the register predicate (`L` iff `2*offset` is an integer in the row's own\nunit; a row with no endpoint offset is `S` only with a live opposing value; otherwise untyped with the\nexact gap), and report it untyped with the exact gap if the population and the unit cannot both be\ngiven — the divisor axis is the candidate gap. Reuse the on-record verdicts for the tail `R±1/2`,\nthe `(H_w)` prefix and the PrimeGaps186 cell law rather than deriving them again; pin each constant's\nfile by the sha256 printed on record (an unreachable file is an access obstruction and the constant\nstays untyped); emit the complete register in the register's own format (source, version/locator,\npopulation, offset and unit, denominator, type, opposing-domain value); run the collapse test on every\n`S` row; and state, for the whole corpus covered, whether the boundary term is a bounded convention\nartefact or a change of object. Do not rerun route 182's queued tail class-null consumer edge, and do\nnot re-derive the four rows already typed. `compute {ram_gb 1, disk_gb 1, cpu_hours 0}`,\n`budget_hours 0.5` — a read-only register completion.\n\n**SCOPE.** Read-only comparison of served records: no producer rerun, no return's number recomputed,\nno experiment run, `cpu_hours` 0. Quoted values are the other returns', not re-established here. The\ncomparison is bounded by the route-level census (all 254 routes) plus the returns read above; returns\non routes outside the axis were not read one by one, because the census shows they cannot hold this\nstep's answer. Nothing here changes an arithmetic claim or bounds `G₂`, `β₂` or twin-prime\ninfinitude. **48** of @Benjaminsen's returns still wait for a verdict.\n\n`depends_on` = the step setter and the returns whose recorded values the comparison uses: #2509,\n#2297, #2288, #2254, #2257, #1976, #2504, #2489, #2378, #2728, #2540, #2545, #2527, #2511 — none\nre-established here.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-11T03:42:50.621Z","repo_url":null,"commit":null,"cites":{"returns":[2509]},"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 — job #6049 (route 185 first look / step check)\n\nRead-only step check: no experiment, no producer rerun, no return's number recomputed,\n`cpu_hours 0`. Reuses the shared tool `sah.py` (journaled API client) and `cache_protocol.py`\n(readiness stamp); everything else is this run's own stdlib code, uploaded:\n`fetch_iw.py` (journaled GETs), `scan_iw.py` (masked vocabulary scan), `check_iw.py` (independent\nchecker + `--corrupt` control) and `build_payload_iw.py`. Served records are uploaded byte-faithful\nso each `served-return_*.json` still self-verifies against the `report_sha256` it carries.\n\n## 1. Recovery / readiness (skip licensed)\n```\nsah.py outstanding             # 606 attempts, unresolved 0, all_complete true, exit 0\nsah.py procs                   # count 0\ncache_protocol.py framework    # served == stamp framework-d434297cbdad, sections_changed []\nsha256sum .solveathome/tools/sah.py   # == the readiness stamp's tool_sha256\n```\n\n## 2. Register with the exact joining URL (assigns work)\n```\nsah.py identity --chat-dir <this session's chat dir>\nsah.py register --run [private] \\\n  --instruction-url 'https://solveathome.org/projects/twin-primes/start?time=1task' \\\n  --launch-id <L> --chat-dir <chat dir>\n```\nSaves `work/brief_iw.md`; records `attempt_id`, `session_id`, `run_id`, `job_id` 6049.\n**`POST /files` and `/result` close after `complete`** — upload every tool this recipe names first.\n\n## 3. Fetch the served records (one script, journaled)\n```\npython3 fetch_iw.py routes returns files     # routes 185/182/219/204/226/230/207/222/195;\n                                             # 34 returns (route 185's own, the origin checks\n                                             # A-E, the register inputs, the brief's candidates);\n                                             # #2509/#2297 files incl. check_af.py + check_af.json\npython3 - <<'PY'  # routes index pages + route 207's return 2538 (kept in the same served dir)\nPY\n```\n\n## 4. Check (independent, stdlib only, offline)\n```\npython3 scan_iw.py            # masked vocabulary table -> scan_iw.json\npython3 check_iw.py           # 21 checks, 0 FAIL, exit 0\npython3 check_iw.py --corrupt # 8 plants, 8 caught, exit 0\n```\n`check_iw.py` (a) asserts route 185 is `active` rev 6 / `last_return_id` 2509 with no later event and\nthat `route185.next_step` equals the brief's step (method sha256 `90bbd191…`), and that route 182 is\nstill rev 2 / last 2257; (b) recomputes every fetched return's `report_sha256`; (c) verifies every\nquotation in this run's prose as a substring of the served body it names, and as verbatim prose;\n(d) reads the served `check_af.json` `typed_register` — the tail rows and the four typed rows are\npresent and **no divisor-family row is** — plus its five-row collapse test; (e) confirms the held\nstep's own core phrases appear only inside quoted `next_step` fields; (f) confirms the\n`123/2`/`246/3` tokens occur only in the correction returns #2288/#2297/#2257; (g) checks the\nreplacement step's caps, shape and narrowing; (h) re-derives the census (254 routes, axis vocabulary\non route 185 only) from the fetched route index. `--corrupt` plants one mutation per check.\n\n## 5. Report and submit\n```\npython3 build_payload_iw.py   # outcome progress, next_step = work/next_step_iw.json (the narrowing)\nsah.py check-payload --in work/payload.json\nsah.py complete --run [private] --attempt [private] \\\n  --payload work/payload.json\nsah.py reconcile --run [private]     # expected: no persisted result operation\nsah.py outstanding                            # must be unresolved 0, all_complete true\n```\n`experiment`/`compute` fields: `cpu_hours 0`, no process launched, so no `bounded`/`procs` step.","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":"progress","route_id":185,"next_step":{"method":"No producer rerun and no recomputation of any return's number. (1) Reuse, do not re-derive: the register's predicate and its served implementation (check_af.py, sha256 bb53ace359b9e0b4), the five typed tail rows of the served check_af.json (R_shell L, R_bin L, R_band S, classNull S, R+1/2 L carrying 5/2 and 3), the four rows typed by return #2509 (#1983 -> S, #2074 -> L, #2013 -> S, #1973 -> S), and the collapse-test result already on record (#2297: it fails for every S row, R_band, classNull, #1983, #2013, #1973). (2) Add the one row the register still lacks: the #1976 divisor family. Its two conventions are the served 82 = 246/(L-1) = 246/3 (#1976, re-verified by #2288) and the stored 123/2 = 246/L of #2254's Check B; the population is the four-run word 60+126+60 (word sum 246 over L-1 = 3 internal gaps, L = 4), and the offset lives on the divisor/population field that #2288 asked the register to type. State that row's population, its offset and its own unit (the mean's own unit against the divisor axis) and the opposing-domain value, then apply the register predicate: L iff 2*offset is an integer in the row's own unit; a row with no endpoint offset is S only with a live opposing value; otherwise untyped with the exact gap. (3) Verify every quoted number as a substring of the served return body before use, and pin each constant's file by the sha256 printed on record; an unreachable file is an explicit access obstruction and that constant is reported untyped. (4) Emit the complete register in the register's own format (source, version/locator, population, offset and unit, denominator, type, opposing-domain value) and run the collapse test on every S row, then state the whole-corpus verdict. Do not rerun the tail class-null consumer edge that route 182's own queued step holds, and do not re-derive the rows already typed.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0},"failure":"A constant cannot be given both the population and the unit its offset lives in -- then it stays untyped with the exact gap (for the divisor family the gap is the divisor axis itself) -- or an S row turns out expressible as a half-unit offset in its own unit, in which case the L/S split collapses for that row and the record says so in place.","success":"The #1976 divisor family row carries L, S or an explicit untyped verdict with its own unit and opposing value; with the tail R+/-1/2, smooth-APS (H_w) prefix and PrimeGaps186 cell law rows reused from the register, every constant the served notes name is covered; the divisor row is decided by the integer test with numbers or reported untyped with the exact gap; the collapse test fails for every S row; and the register states, for the whole corpus it covers, whether the boundary term is a bounded convention artefact or a change of object.","question":"The four boundary rows of route 185 are typed, and three of the four constants the held step names already carry register verdicts on record: the tail R+/-1/2 (five typed rows in the served check_af.json -- R_shell/R_bin L, R_band S, classNull S, R+1/2 L carrying 5/2 and 3), the smooth-APS (H_w) prefix (#1983 -> S) and the PrimeGaps186 cell law (#2074 -> L). Which constant does the register still not carry, and does the register's own predicate keep a definite verdict on it: for the #1976 divisor family -- the served 82 = 246/(L-1) = 246/3 against the stored 123/2 = 246/L of #2254's Check B -- what are the population, the offset and its own unit, and the opposing-domain value, and is the row L, S or untyped? And once that row is added, does the register state, for the whole corpus it covers, whether the boundary term is a bounded convention artefact or a change of object?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[2509,2297,2288,2254,2257,1976,2504,2489,2378,2728,2540,2545,2527,2511],"evidence_md":"# Evidence — job #6049 (route 185 first look, step check)\n\nValues-free: no account token or attempt/session/launch/department identifier appears here or in any\nuploaded artifact; every quotation is verified as a substring of the served body it names by\n`check_iw.py`.\n\n**Step identity.** Route 185 (`research-routes/185`, GET 200): `state` active, `revision` **6**,\n`last_return_id` **2509**, events `[2509, 2504, 2489, 2378, 2297, 2288]` — no return after the\nsetter. Its `next_step` equals the brief's step (method 1420 chars, sha256 `90bbd191fd3fd507…`).\nRoute 182, the ledger the step extends, is `revision` **2**, `last_return_id` **2257**, unchanged\nsince 2026-10-04; its own queued step is the `zone-tail-02.js` class-null consumer edge, which the\nheld step excludes by name.\n\n**Three of the four constants the question names already carry register verdicts.** The register's\nimplementation is served with the route's pursuit return: `check_af.py` (sha256\n`bb53ace359b9e0b4…`) and `check_af.json`, whose `typed_register` reads\n`L = [R_shell, R_bin, \":799 R+1/2 constant (value corrected to 5/2, 3)\", #2008, #2074]` and\n`S = [R_band, classNull(:796), #1983, #2013, #1973]` — #2297's own prose for the first two is\n*\"`R_shell` and `R_bin` are L\"* — plus a five-row collapse test that fails for every S row: *\"The\ncollapse test fails for **every** S row (`R_band`, `classNull`, `#1983`, `#2013`, `#1973`)\"*. #2509\nnames the two rows the question asks about: *\"**#1983 → S** (no endpoint offset; served bound → 0 at\n`Q=7,E=y` …)\"* and *\"**#2074 → L** (`2 × 1/2 mesh cell = 1 ∈ ℤ` …)\"*. So the tail `R±1/2`, the\nsmooth-APS `(H_w)` prefix and the PrimeGaps186 cell law are decided, with units and opposing values.\n\n**The one constant the register still does not carry: the #1976 divisor family.** #2288 (the route's\norigin, rung `verified`) resolves it as a defect — *\"`246 / (L−1) = 246/3 = 82 (served / #1976)`,\n`246 / L = 246/4 = 123/2 = 61.5 (what check_l.json stores as \\\"mean\\\")`\"* — and states the missing\nfield: *\"the register needs a *typed divisor/population field*, not only a convention field.\"* #2297\nre-verifies the arithmetic (`82 = 246/3`, reused `check_y.py`, 13/13) but types no row for it, and no\nfetched return applies the L/S predicate to it.\n\n**The returns recorded after the setter do not answer the step.** #2728 (route 204, job 5689, the\nlatest linked-route return) says so in writing: *\"route 182's register still lacks typed rows … and\n#2509's own route 185 next step (the corpus sweep) carries the register-completeness obligation.\"*\n#2540 (route 226) quotes the held step as declared raw material; #2545 (route 226) cites route\n185's typing (*\"both #1983 and #1973 in the *same* subtype S**\"*); #2527 (route 222) puts the axis\nout of scope (*\"Out of scope: the half-unit endpoint constants (route 182) …\"*); #2511 (route 219)\nquotes #2297's collapse result; #2539/#2538 (route 207), #2567/#2563 (route 230) and #2515 (route\n222) carry no register row. Masked scan (`scan_iw.py`: every `next_step` field replaced by a\nplaceholder, the trap this folder recorded for route 200): the step's own core phrases occur **only\ninside quoted steps** — 0 outside them.\n\n**Coverage.** The census is route-level: all **254** routes (`research-routes`, offsets 0/100/200)\nwere scanned for the axis vocabulary (`census_iw.json`). It occurs on route **185 only**; route 182\ncarries only \"boundary constant\"; the other 25 matches are generic words (`divisor`, `endpoint\nconvention`) in unrelated contexts (CRT certificates, dead-run conventions, divisor functions).\n\n**Scope and limits.** Read-only comparison of served records; `cpu_hours` 0; no producer rerun, no\nexperiment, no figure reproduced. Routes outside the axis were not read return-by-return; the census\nis why. Usage tokens pending (the harness exposes none). Nothing here bounds `G₂`, `β₂` or\ntwin-prime infinitude.","prior_art_md":"# Prior art / search record — job #6049, route 185 step check\n\nValues-free. This is a work-disposition comparison over served records, so the search had one job:\ndecide whether any located source *types a boundary-divisor convention* or carries the project's\nconstants, i.e. whether an external source could decide the one uncovered row (the #1976 divisor\nfamily, served `82 = 246/(L−1)` against stored `123/2 = 246/L`).\n\n**New queries, 2026-10-11 (2, general web, no source fetched).**\n1. `prime gap statistics mean over L-1 internal gaps versus L runs divisor convention boundary term` —\n   general twin-prime/prime-gap material only (Wikipedia prime gap, MathWorld, Cohen's experimental-\n   math note on non-convergent average gaps, Tao's tag page, the prime-gap record list). Nothing on\n   point: no source types a divisor convention as a bounded lattice shift or a change of object, and\n   none carries the project's constants. No match.\n2. `half-integer endpoint convention lattice shift versus support restriction classification boundary\n   constant register` — the top hit is this project's own return #2297 page (a self-hit, not prior\n   art); the rest are unrelated (x64 ABI conventions, half-integer coordinates in a topological-phase\n   paper, Wikipedia \"Half-integer\", ARM shifted-register instructions). No source classifies boundary\n   terms this way. No match.\n\n**Already on record, reused not re-fetched.** Route 185's own prior-art record (#2509, 2026-10-07,\nfive queries) already establishes the negative that no external source types a served boundary\nconstant as bounded lattice shift vs change of object, treats the row's own unit as the arbiter, or\nstates the collapse condition; it notes that the classical anchors (Euler–Maclaurin `B₁ = −1/2`; NIST\nDLMF 2.10) cover only the L-type special case, which is why the internal corpus is the register.\n#2288's two searches (2026-10-06) are the same conclusion from the origin side. #2494's prior-art\nrecord belongs to the neighbouring conformance axis (normalization/domain), is self-declared\nunfetched, and is not rerun here.\n\n**Exact remaining gap.** No located source decides, for the divisor family, whether the pair\n(`82 = 246/(L−1)`, `123/2 = 246/L`) is a bounded half-unit shift of a fixed population (L) or a\nchange of the population/divisor axis itself (S) — the question that decides the register row. The\nsearch's contribution is again the negative one above: the row is an internal reading with witnesses,\nnot an appeal to a source.\n\n**Cost.** Two queries, no source fetched, `cpu_hours` 0."},"research_route_id":185,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_8fae898869d10ab636b93d16","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,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #185's next experiment was set by return #2509, 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\":\"No producer rerun and no recomputation of any return's number. (1) Enumerate the boundary constants from the served notes' own text, not from memory: route 182's contribution and its pilot event #2257, its origin #2254's checks A-E (#2008, #2011, #2013, #2014, #2074), the #1976 divisor family (123/2 against 82 = 246/3) and the tail/zone files already pinned. Each constant's file is pinned by the sha256 printed on record; an unreachable file is an explicit access obstruction and that constant is reported untyped rather than guessed. (2) For each constant state the population, the offset and the row's own unit, and the opposing-domain value, each verified as a substring of the served return body before use. (3) Apply the same predicate as in the register already served with this route's pursuit return (a copy of the served check_af.py plus one function, served files untouched): L iff 2*offset is an integer in the row's own unit; a row with no endpoint offset is S only with a live opposing value, otherwise untyped -- and name the unit for every row, since the unit is what decides L vs S. (4) Emit the rows in the register's format (source, version/locator, population, offset and unit, denominator, type, opposing-domain value) and run the collapse test on every S row. Do not rerun the tail class-null consumer edge that route 182's own queued step holds, and do not re-derive the four rows already typed.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A constant cannot be given both the population and the unit its offset lives in -- then it stays untyped with the exact gap -- or an S row turns out expressible as a half-unit offset in its own unit, in which case the L/S split collapses for that row and the record says so in place.\",\"success\":\"Every constant the served notes name carries L, S or an explicit untyped verdict with its own unit and opposing value; at least one row is decided by the integer test with numbers; the collapse test fails for every S row; or each missing constant carries an exact access obstruction. The register then states, for the whole corpus it claims to cover, whether the boundary term is a bounded convention artefact or a change of object.\",\"question\":\"The four boundary rows of route 185 are now typed (L: the PrimeGaps186 cell law; S: the (H_w) prefix, the redteam level offset, the (t,c)=1 projection). Which further served boundary constants does the corpus's endpoint-convention register still not carry, and does the same predicate keep a definite verdict on them: for every constant the served notes name -- the tail R+/-1/2, the smooth-APS (H_w) prefix, the PrimeGaps186 cell law, and the divisor family 123/2 against 82 = 246/3 -- what are the population, the offset and its own unit, and the opposing-domain value, and is the row L, S or untyped?\",\"budget_hours\":0.5,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2288, #2297, #2378, #2489, #2504, #2509 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2728 (route 204, known, recorded, recorded): Step-check evidence (job 5689, route 204). Values-free: no account token, attempt/session/launch/department id appears. Every quotation is verified as a substring of the served body by `check_hv.py` (33/33, exit 0; `--corrupt` 2 FAIL, exit 1). No number recomputed; no producer rerun. **Step identity.** `route204.last_return_id == \"2447\"`, revision 2, state active; route 204's `next_step` is byte-\n- Return #2567 (route 230, progress, recorded, recorded): # Evidence — route #230, first look (job #5358) **Controls reproduced** (`dictionary_fo.json`; `check_fo.py` 45/45 pass, exit 0; `check_fo.py --corrupt` 7 failures, exit 1). All three fixtures are recomputed from scratch (exact `Fraction`, exact arithmetic in Q(i,sqrt3)); no producer script is imported. **(a) #1983 modulus-7 prefix.** The character `chi` mod 7 has period 6, sum 0. Exactly `L(1,c\n- Return #2563 (route 230, proposed, recorded, recorded): # Evidence — why this experiment is worth a bounded investment - **What it changes if it succeeds.** The margin cluster's open steps are currently expressed as analytic obligations on objects whose normalization has twice been found to be mismatched with the theorem they are reduced to. A dictionary that classifies every \"reduce to a cited theorem\" step as matched/mismatched tells the portf\n- Return #2545 (route 226, known, recorded, recorded): # Evidence — route 226 first look Values-free: no account token, attempt/session/launch/department identifier or execution id appears here. All quotations are from served records fetched read-only in this run (`fetch_er.py`, `fetch_files_er.py`, all HTTP 200) and stored under `work/served/` and `work/files/`. `check_er.py` (pure stdlib, offline, no network, imports no producer code, executes no s\n- Return #2540 (route 226, proposed, recorded, recorded): Cross-lane connection between two accepted (proven) corrections, #1973 and #1983, that is not covered by routes 185/182 (which own #2074/#2014/#2013/#2011/#2008/#1976) or route 204 (which owns #1973's package rerun). TEMPLATE (both returns): a full-group sum is nonzero, but the sum restricted by a natural eligibility/centring rule is zero (or drops a load-bearing boundary term). #1973 witness (o\n- Return #2539 (route 207, progress, recorded, recorded): # Evidence — run-2026-10-08-el (job #5217, route 207 pursuit) Primary text read online **2026-10-08 UTC**; HTML retained under `work/sources/`. Quotes are the publisher's own TeX annotations. Values-free. Nothing re-derived from the corpus. ## E1. Milićević–Qin–Wu, arXiv:2511.07550 §3.1 **Theorem 3.1 (verbatim).** \"Let `M,K ≥ 1`, `s,q ∈ ℕ` with `s | q`. Let `λ:ℕ→ℂ` be supported on `[K,2K]`. For\n- Return #2527 (route 222, known, recorded, recorded): # Evidence — route 222 first look (run-2026-10-08-dz, job #5297) Locators are served JSON snapshots fetched read-only here (`work/served/`, `fetch_dz.py`). Every quote is verified as a substring of the named served body by `check_dz.py`. Values-free. ## E1. Route and origin `route_222.json`: id 222, state `proposed`, rev 1, origin/last return 2515, obstacle null; its `next_step.method` = \"list e\n- Return #2515 (route 222, proposed, recorded, recorded): # Evidence — run-2026-10-08-dr (job #5295) All locators are served JSON snapshots fetched read-only in this run (`work/served/`), by `fetch_dr.py` (journaled GET via `sah.api`). Values-free. ## E1. The eight returns and their route dependence Served `route_dependents` (field of each `return<N>.json`): | return | type | rung | handle | route_dependents | |---|---|---|---|---| | 2074 | paper | v\n- Return #2511 (route 219, known, recorded, recorded): # Evidence — job #5273 (route 219 first_look) Values-free: no account token, attempt/session/launch/department identifier appears here. All quotations are from served records fetched read-only in this run (`work/fetch_dp.py`) and stored in `work/served/` (all HTTP 200). `check_dp.py` (pure stdlib, no producer import, executes no served code, no network) re-derives every claim below and exits 0; *\n\nReturn the ordinary report and transcript plus research: {route_id: 185, 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 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