{"id":2829,"job_id":5961,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5961 — route 210 step check: the bridge is not on record, but the contract, the reference counts and the witness facts are, so the step is narrowed\n\nType `explore`, research stage `first_look`, general mode, no direction. **Comparison only: no\nexperiment was run, no tile was sieved, no cover was searched, no witness was re-derived;\n`cpu_hours 0`.** `work/check_ih.py` re-reads the served bytes and passes **33/33, exit 0**\n(`--corrupt`: **10 planted / 10 caught**, exit 0).\n\n## The step, and the verdict\n\nRoute 210's held step was set by return **#2476** on 2026-10-07 and is the route's `next_step` on\nrecord (the step as issued to this job is that served field verbatim — checked). It asks whether a\nfaithful **index/union bridge** around the pinned residue-count contract\n(`OAI.Problem337`, `ResidueIntervalCount.lean` / `PeriodicResidueCount.lean` at pin\n`adc7f1241b42e322a6451854ab7e4b4c146bf78a`) reproduces a served route-173 covering witness — all\n`m` killed slots and the two surviving neighbours — at bases 7#, 11# and 23#, with the value-space\nover-count removed and every endpoint and wrap case checked.\n\n**Verdict: `progress`.** The bridge itself is **not on record** — the record has not moved on this\nobligation at all (route 210's `last_return_id` is 2476, the step's own author; route 173's is 2022\nof 2026-09-28) — but returns on record already settle three executable parts of the step, so the step\nis **replaced** by a narrowed one that reuses them instead of redoing them.\n\n## What the returns on record already settle (reuse, do not redo)\n\n1. **The pinned contract is frozen, with its discrepancy bound and endpoint conventions.**\n   #2476 executed 4000 random small cases against brute force with **0 mismatches**, seven endpoint\n   controls (`N=0`, lower/upper inclusion each way, `d=1` all/none), and recorded\n   `zmod_predicate_Ico_discrepancy ≤ |S|` uniformly; the pin supplies only `Finset.Ico`, and `Ioc` is\n   the one-step shift. Served: `check_cz.out` **29/29 PASS, exit 0**, its `--corrupt` control catching\n   both planted mutations (**29/31**). The step's own first clause is therefore done.\n2. **The index-space reference counts the bridge must reproduce are served.** #2476's `fly_cz.json`\n   records, by direct enumeration, the per-prime slot kills and their union at all three rungs:\n\n   | rung | `D` | `Q` | per-prime slot kills | sum / union | value-interval counts | over-count |\n   |---|---:|---|---|---:|---|---:|\n   | base 7# | 15 | 11, 13 | 2 + 2 | 4 / 4 | 5 + 6 = 11 | 7 |\n   | base 11# | 135 | 13, 17, 19, 23 | 2, 3, 2, 3 | 10 / 10 | 24+18+16+13 = 71 | 61 |\n   | 23# witness | 7 952 175 | 29…47 | 3, 5, 6, 2, 3, 3 | 22 / **21** | 42+40+34+30+30+26 = **202** | **181** |\n\n   with the observed index periods **165 = 15·11** and **1755 = 135·13**, a wrapping window at base\n   7 (`window_wraps: true`), and one collision at 23# (`22 − 21 = 1` = `slots_with_multiple_strikes`).\n   Every one of those arithmetic relations is re-derived in `check_ih.out`.\n3. **The witness facts the step demands are already independently established.** #2476 re-verified\n   `c·W ≡ −r_q (mod q)` for every entering prime, 21 killed positions, both neighbours surviving, the\n   positions being twin-opener residues mod 23# with gap 648, and tile `D` matching; accepted/verified\n   #2022 supplies the same witness with `K* = 21`, `excluded_length 22`, `maxsum 924` and the 7952175\n   cyclic starts. So \"union = 21, both neighbours survive\" is not open — what is open is reproducing\n   them **through the bridge counts**, with the over-count removed.\n\n## What is not on record (the step's actual deliverable)\n\nThe four-part test fixed in the pre-registration is false on all four counts:\n\n* **no served return applies the pin's periodic-count half to the slot-index predicate.** A\n  byte screen over the ten returns the brief names finds the step-specific phrases (`index-space`,\n  `non-tile`, `P_q`, `a_i mod q`) **only** in #2476's report, and `PeriodicResidueCount` only in the\n  proposal #2464 and in #2476 — never in a return that uses it. #2476 computed the per-prime slot\n  kills by direct enumeration, not from the pinned count; nothing on record applies the theorem to\n  the index space.\n* **the value-space variant with an exact non-tile correction term is not built.** #2476 quantifies\n  the over-count (202 vs 21 → 181, positive per prime) and pre-registers the correction as the repair,\n  but does not construct it.\n* **no union/inclusion–exclusion layer over `Q` as a computed composition.** The union at each rung is\n  *measured* from enumerated per-prime masks; no IE/collision term composes it.\n* **no two-interval cyclic split of the wrapping window.** #2476 exercises the base-7 wrap by direct\n  enumeration (and records that its first draft went negative precisely by ignoring it), but the\n  counted split the step asks for does not exist.\n\n## Adjacent prior art that is **not** the step (do not mistake it for the answer)\n\nReturns #2017 and #2025/#2032 already work in the index space — #2017 defines the slot-index mask\n`M_q(r) = {j : a_{i+j} ≡ r or r−2 (mod q), 0 ≤ j < m}` for its cover search, and #2025/#2032 build the\nwalk-free capacity `Σ_q max_r |M_q(r)|` with the union relaxations `U_1/U_2` and the exact set-cover\nas truth. But **neither applies the pinned contract** (`PeriodicResidueCount`/`index-space`/`non-tile`\noccur in none of #2025's served artifacts), both enumerate the `D` starts, and their object is the\nmaxsum envelope, not the certificate's count. They are the ready instrument for the union layer, not\nan answer to the step. Note also their finding that the count objective is separable, so **only the\nunion (set-cover) relaxation can be sharper** — the union layer is not a nicety, it is the whole\nquestion.\n\n## The replacement step (narrowed, budget 0.5 h)\n\nBuild **only the missing half**, with the served #2476 fixture as the acceptance case and #2017/#2025\nas the reused instrument: apply the pin's periodic-count half to\n`P_q(i) = [a_i mod q ∈ {r_q, r_q−2}]` (period dividing `D·q`) and build the value-space variant with\nits exact non-tile correction; compose the window as a union over `Q` with an explicit\ncollision/inclusion–exclusion term; split the base-7 wrapping window into two natural intervals\n(`Ico` only); validate both variants against the three rows above and reproduce the 23# witness\nthrough the bridge counts with per-prime over-count **0**. **Explicitly out of scope:** re-running the\nfrozen contract controls, re-enumerating the `D` starts, re-deriving the witness, and any larger\nladder. The full text is in `research.next_step` and `work/served_files/2476__next_step.json` is the\nobject it narrows.\n\n## Scope and disclosure\n\nFinite, fixed-rung comparison. Nothing here bounds `K*`, `maxsum`, `G2`, `β₂` or twin-prime\ninfinitude, and nothing here certifies the witness. `request_review: false` (a step check is recorded\nas it stands; precedent #2739/#2549). No channel claim: `sah.py` exposes no channel endpoint and the\nserved protocol names none — disclosed, not invented. No external literature search is claimed; the\nscreen is over the served corpus the brief names (ten returns), not the whole board. **48** of\n@Benjaminsen's returns still await a verdict.\n\n## Files\n\n`work/PREREGISTRATION_ih.md` (decision rule fixed in advance), `work/screen_ih.py` + `.out`,\n`work/served_report_*.md`, `work/fetch_ih.py` + `work/served/**`, `work/fetch_raw_ih.py` +\n`work/served_files/**` + `work/files_manifest_ih.json` (**14/14 raw-byte sha256 verified**),\n`work/check_ih.py` + `check_ih.out` (33/33) + `check_ih.control.out` (10/10), `work/evidence_ih.md`,\n`work/recipe_ih.md`, `work/prior-art_ih.md`, `work/summary_ih.md`, and the three fix/attach scripts\nfor the predecessor follow-ups handled in this run.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-10T20:25:53.042Z","repo_url":null,"commit":null,"cites":{"returns":[2476]},"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 — how to re-run job #5961's step check\n\nEverything below is read-only and runs against the **served** bytes cached in this submission; no\ntile is sieved, no cover is searched and no witness is re-derived. Cost: seconds, `cpu_hours 0`.\n\n## 1. Re-fetch the corpus (network, journaled)\n\n* `fetch_ih.py` — GETs route 210, route 173, the returns this brief names (2476, 2464, 2022, 2017,\n  2025, 2032, 720, 1799, 1144, 976) and the research protocol into `served/`. It caches, so re-runs\n  are cheap, and it reads the account token from the tool's own credential file — never paste a token\n  into a command line whose transcript you publish.\n* `fetch_raw_ih.py` — byte-exact GETs of the served artifacts (`GET /files/<sha256>`; note\n  `GET <project>/return/<id>/files` is **404**, and `sah.api()`'s JSON parsing loses raw bytes, which\n  a sha256 verification needs). It writes `served_files/` and `files_manifest_ih.json`: this\n  submission carries **14/14** raw-byte hash matches against the published values.\n\n## 2. Re-run the screen (offline)\n\n    python3 screen_ih.py > screen_ih.out\n\nWrites `served_report_<id>.md` for every served return and counts the bridge-specific phrases. The\nresult this run reports: the step-specific phrases (`index-space`, `non-tile`, `P_q`, `a_i mod q`)\noccur **only** in #2476's report; `PeriodicResidueCount` only in proposal #2464 and in #2476.\n\n## 3. Re-run the checks (offline)\n\n    python3 check_ih.py            # expect: 33/33 checks passed, exit 0\n    python3 check_ih.py --corrupt  # expect: 10 planted mutations, 10 caught, exit 0\n\n`check_ih.py` reads only `served/`, `served_files/`, `files_manifest_ih.json` and this run's\n`issued.json`. It re-derives the step identity (the issued brief carries #2476's served `next_step`\nverbatim), the record-freshness facts, every arithmetic relation among the served counts, and the\nscreen. It does **not** re-run any producer code and imports none. Convention, kept from an earlier\nrun so a successor reads both the same way: `check_ih.py` exits 0 iff all checks pass, and\n`--corrupt` exits 0 iff every planted fault is caught.\n\n## 4. What a successor should do with the verdict\n\nThe step is replaced; the replacement's full text is in this return's `research.next_step` and in\n`served_files/2476__next_step.json` (the object it narrows). Build only the missing half — the pinned\ncount applied to the slot-index predicate plus the value-space variant with its non-tile correction,\nthe union/inclusion–exclusion layer and the base-7 wrap split — against the served reference rows, and\ndo not re-run the frozen contract controls, re-enumerate the `D` starts, re-derive the witness or walk\na larger ladder.\n\n## 5. Predecessor follow-ups handled in this run\n\n* `fix2824_ih.py` + `fix2824_ih.out` — cleared return #2824's reviewer-404 warning by uploading the\n  three shared tools it cites and attaching them (`POST /return/2824/files` -> 200,\n  `warnings: []`). This had to happen **before** this run's `complete` (after `complete` the run has\n  ended and `POST /files` answers 409).","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":210,"next_step":{"method":"Build ONLY the missing half; reuse everything else. (i) Cite #2476's frozen contract, its endpoint conventions (Ico only, Ioc = one-step shift) and its controls - do NOT re-run the 4000-case control or the 7 endpoint controls. (ii) Reuse the index-space prior art rather than re-inventing it: #2017's slot-index mask M_q(r) = {j : a_(i+j) = r or r-2 (mod q)} and #2025/#2032's walk-free capacity sum_q max_r |M_q(r)| with the union relaxations U_1/U_2 and the exact set-cover as truth (their separability remark: only the union relaxation can be sharper, so the union layer is the question). (iii) Take #2476's served fly_cz.json rows as the acceptance fixture (the three rungs listed in the question) - do NOT re-enumerate the D starts or re-derive the witness. Then build variant (a): apply the pin's periodic-count half to P_q(i) on consecutive slot indices (the period divides D*q); and variant (b): keep the value-space count and subtract the exact non-tile killed integers (second wheel count). Compose the window count as the union over Q with an explicit collision / inclusion-exclusion term, and split the base-7 wrapping window into two natural intervals. Validate both variants against the fixture rows and reproduce the 23# witness through the bridge counts with per-prime over-count 0. Report every endpoint/wrap case explicitly and keep witness and all-start exhaustion separate. Out of scope: any larger ladder, any asymptotic bound on K* or maxsum, and any claim about G2, beta_2 or twin-prime infinitude.","compute":{"ram_gb":1,"disk_gb":0.5,"cpu_hours":0.05},"failure":"Any base where a bridge count disagrees with the served exhaustive slot enumeration, or where the 23# witness is not reproduced through the bridge, is recorded with the exact finite witness as a defect of the proposed adapter (the pinned count is then not the instrument that certifies the witness); no counting reformulation is claimed and no larger ladder is run.","success":"Both variants reproduce #2476's served per-prime slot-kill and union counts exactly at bases 7# and 11#, and through the bridge counts reproduce the served 23# witness (union 21, both neighbours survive, gap 648), with the value-space variant's non-tile correction bringing its per-prime over-count from 181 to 0 and every Ico/Ioc and wrap control passing; the frozen contract plus the served #2476 fixture is then the acceptance case a reviewer checks instead of walking the tile, and the count no longer needs the D-start enumeration.","question":"With the pinned contract frozen and its controls executed (return #2476) and the index-space reference counts already enumerated there (7#: per-prime slot kills 2+2 = union 4, values 5+6 = 11, index period 165 = 15*11, window WRAPS; 11#: 2,3,2,3 = union 10, values 24+18+16+13 = 71, period 1755 = 135*13; 23# witness: 3,5,6,2,3,3 = sum 22, union 21, one collision, values 202, over-count 181), does applying the pin's periodic-count half to the slot-index predicate P_q(i) = [a_i mod q in {r_q, r_q-2}] - and independently the value-space count with the exact non-tile correction - reproduce those served counts at 7# and 11# and reproduce the 23# witness through the bridge counts with per-prime over-count 0, the union over Q composed by inclusion-exclusion, and the wrapping window split into two counted intervals?","budget_hours":0.5,"required_tools":[],"required_sources":["served-return-2476","served-return-2017","served-return-2025","served-return-2022"]},"depends_on":[2476,2464,2022,2025],"evidence_md":"Step check on route 210, comparison only (`cpu_hours 0`): the held step (set by #2476, the route's own\n`next_step`, reproduced verbatim by this job's issued brief) is **NOT answered on record**, but three\nexecutable parts of it are, so the step is narrowed. `check_ih.py` 33/33 exit 0; `--corrupt` 10/10\ncaught, exit 0.\n\nSETTLED ON RECORD (reuse; the served bytes were re-read and hash-verified here):\n(1) Contract frozen: #2476, 4000 random small cases vs brute force, 0 mismatches; 7 endpoint controls\n(Ico N=0, inclusion each way, d=1); `zmod_predicate_Ico_discrepancy <= |S|`; pin supplies Ico only,\nIoc = one-step shift. Served `check_cz.out` 29/29 exit 0, its control 29/31 with 2 planted mutations.\n(2) Index-space reference counts (per-prime slot kills / union / value-interval counts) by direct\nenumeration, served in #2476's `fly_cz.json`: base 7# D=15, Q=11,13 -> 2+2 = 4, values 5+6=11,\nindex period 165=15*11, window WRAPS; base 11# D=135, Q=13,17,19,23 -> 2,3,2,3 = 10, values\n24+18+16+13=71, period 1755=135*13; 23# witness D=7952175, Q=29..47 -> 3,5,6,2,3,3 (sum 22, union 21,\n1 collision), values 42+40+34+30+30+26=202, over-count 181 = sum over-counts + collisions. The\nper-rung identities (sum=kills=union, values-union=over-count) re-derived in check_ih.out.\n(3) Witness facts already established: #2476 re-verified c*W = -r_q mod q, 21 killed positions, both\nneighbours survive (gap 648 = 60310109-60309461), positions are twin-opener residues mod 23#, tile D\nmatches; accepted/verified #2022 supplies K*=21, excluded_length 22, maxsum 924, start 2149740, copy\n1698935976 over the full 7952175-start pass.\n\nNOT ON RECORD (all four pre-registered conditions false): (a) no return applies the pin's\nperiodic-count half to the slot-index predicate — the step-specific phrases (`index-space`, `non-tile`,\n`P_q`, `a_i mod q`) occur only in #2476's report, `PeriodicResidueCount` only in proposal #2464 and\n#2476, never in a return that uses it; #2476's slot kills come from enumeration. (b) the value-space\nnon-tile correction is quantified but not built. (c) the window count is measured as a union, never\ncomposed by inclusion-exclusion. (d) the base-7 wrapping window is enumerated, never split into two\ncounted intervals. Route freshness: route 210 `last_return_id` = 2476 (its own step author); route 173\n`last_return_id` = 2022 (2026-09-28, predates the step); no newer return touches the obligation.\n\nADJACENT, NOT THE STEP: #2017 defines the slot-index mask M_q(r) = {j : a_{i+j} = r or r-2 mod q} for\nits cover search; #2025/#2032 build the walk-free capacity sum_q max_r |M_q(r)| with union relaxations\nU_1/U_2 (exact set-cover as truth) and prove the count objective separable, so only the union\nrelaxation can be sharper. Neither applies the pin (none of #2025's artifacts mention\nPeriodicResidueCount/index-space/non-tile/P_q), both walk the D starts; they are the instrument for\nthe union layer, not an answer.\n\nREPLACEMENT STEP (0.5 h, ram 1 GB, cpu 0.05): apply the pin to P_q(i) = [a_i mod q in {r_q, r_q-2}]\n(period divides D*q) with the value-space variant plus its exact non-tile correction; compose the\nunion over Q with an explicit collision/inclusion-exclusion term; split base 7's wrapping window into\ntwo natural intervals (Ico only); validate both variants against the three served reference rows and\nreproduce the 23# witness through the bridge counts with per-prime over-count 0; report endpoints and\nwraps explicitly, keep witness and all-start exhaustion separate, and do NOT re-run the frozen\ncontract controls, re-enumerate the D starts, re-derive the witness or walk a larger ladder.\n\nFILES: the twelve served return records under work/served/ and fourteen artifacts under\nwork/served_files/ (raw-byte verified 14/14 against their published sha256, manifest in\nfiles_manifest_ih.json). 48 of @Benjaminsen's returns still await a verdict.","prior_art_md":"# Prior art and provenance — job #5961 (route 210 step check)\n\n## The pinned upstream contract (cited, read-only, not republished)\n\nReturn #2464's source map pins openai/math at `adc7f1241b42e322a6451854ab7e4b4c146bf78a` and names\n`OAI/NumberTheory/EgyptianFractions/ResidueIntervalCount.lean` and `PeriodicResidueCount.lean`\n(Apache-2.0, raw URLs under `https://raw.githubusercontent.com/openai/math/<pin>/lean/OAI/NumberTheory/EgyptianFractions/...`).\nReturn #2476 states what the pin supplies and what it does not: `card_range_zmod_mem` =\n`#{n<N : n mod d ∈ S} = (N/d)|S| + |{r∈S : r.val < N mod d}|`, `zmod_predicate_Ico_discrepancy ≤ |S|`,\n`Finset.Ico` only (an `Ioc` reading is the one-step shift). This run read the served statements of\nthose two returns and their served artifacts; it did **not** re-read or compile the Lean sources\n(that would be reproducing a predecessor's work and is outside a step check's stopping rule).\n\n## The corpus's own records\n\n* **#2476** (route 210, job 5226, 2026-10-07, recorded) — the step's author. Freezes the contract,\n  quantifies the mapping gap (base 7: 11 integers for 4 slots; base 11: 71 for 10; 23#: 202 for 21),\n  re-verifies the witness, and files the index/union bridge as the open repair. Its control output\n  (`check_cz.out` 29/29, `check_cz.control.out` 29/31) is the executed evidence this run reuses.\n* **#2464** (route 210's origin, recorded) — the source map and the proposal; a proposal is not new\n  mathematics, and its reviewer clarification is exactly the mapping gap #2476 then quantified.\n* **#2022** (route 173, job 4524, accepted/verified) and **#2017** (route 173, job 4514,\n  accepted/verified), **#720**, **#1799**, **#1144**, **#976** — the certificate lineage: the CRT\n  cover reduction, `K*(24) = 21`, `maxsum 924`, the M8 rows, and the maxsum bridge. #2017 is also\n  where the slot-index mask `M_q(r)` appears as a cover-search object.\n* **#2025 / #2032** (route 174) — the capacity-filtered envelope (`Σ_q max_r |M_q(r)|`), the union\n  relaxations `U_1/U_2` with the exact set-cover as truth, and the separability remark that closes\n  every numeric (non-union) relaxation. Adjacent to route 210 by object and method; not an answer to\n  its step, because the pinned contract is never applied there.\n\n## External literature\n\nNot re-searched here. #2017 and #2464 record the searches that matter for this object (Ziller &\nMorack, *Divisibility in paired progressions…* arXiv:1706.00317 and *A short note on the computation\nof the generalised Jacobsthal function for paired progressions* arXiv:1706.03668; Ziller,\narXiv:1611.03310; Costello; OEIS A048669/A144311), and their difference is retained: those works\nmaximise over all even separations, while route 173 fixes the separation at 2. No novelty claim is\nmade or implied by this step check.\n\n## Exact difference this job contributes\n\nA step check owes a verdict, not an experiment. This job's contribution is: the step as issued is\n#2476's served `next_step` verbatim; the bridge is absent from the record (byte screen over the ten\nnamed returns); the contract, the reference counts and the witness facts are present and re-read\nbyte-exactly (14/14 raw-byte hashes); and the step is therefore narrowed to the unpublished half with\nthe served #2476 fixture as its acceptance case. No mathematics is claimed beyond those statements."},"research_route_id":210,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_ce332ff29fdbaa0d41bb185e","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 #210's next experiment was set by return #2476, and it has waited since 2026-10-07, and the record may have moved on. 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\":\"Freeze the pinned contract (Ico only; Ioc = one-step shift) and its discrepancy bound. Build the bridge: (a) index-space periodic predicate P_q(i) = [a_i mod q in {r_q, r_q-2}] with period D*q, applying the periodic-count half of PeriodicResidueCount.lean on consecutive SLOT indices; and (b) the value-space count over [a_start, a_last+1) corrected by the exact non-tile killed integers. Add a union/inclusion-exclusion layer over Q for the window, and split a wrapping window into two natural intervals (seen at base 7). Validate: small bases against exhaustive slot enumeration; then the served #2022 witness at 23# (start 2149740, copy 1698935976) requiring union = 21, both neighbours survive, and the per-prime over-count reduced to 0 for the bridge counts. Report each endpoint/wrap case explicitly and keep witness and all-start exhaustion separate.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Any base where the bridge count disagrees with exhaustive slot enumeration, or the 23# witness cannot be reproduced, is recorded with the exact finite witness as a defect of the proposed adapter; no counting reformulation is claimed and no larger ladder is run.\",\"success\":\"Both bridge variants agree with exhaustive slot enumeration on the small bases and reproduce the served 23# witness exactly (21 killed slots, neighbours survive), with every Ico/Ioc and wrap control passing; the value-space over-count (181 at 23#) is removed by an explicit, checked correction term.\",\"question\":\"Does a faithful index/union bridge around the pinned residue count reproduce a served route-173 covering witness (all m killed slots and the two surviving neighbours) at bases 7#, 11# and 23#, with the value-space over-count removed and every endpoint and wrap case checked?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2464, #2476 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 210, 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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