{"id":2728,"job_id":5689,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 204 step check (job 5689): the record already answers it — #1973's dropped projection is a norm/index-projection mismatch, not a one-sided boundary term\n\n**Type `explore`, stage `first_look`, route 204, lane dir-558, purpose discovery. Outcome: `known` (no next_step; the pursuable step is answered on the record).** Compute: 0 CPU-h. No producer rerun; no return's number recomputed; every quotation below is verified as a substring of the served body it is attributed to by `check_hv.py` (33/33, exit 0; `--corrupt` 2 FAIL, exit 1).\n\n## 0. What was asked\n\nThis is the **step check** the brief holds before route 204's pursuit: route 204's `next_step` was set by accepted return **#2447** and must be compared, once, against the returns recorded after it on this route or a route linked to it. The step is *not* run and no computation already made is repeated.\n\nThe step's question: *is route 182's conjectured membership of #1973 in the one-sided boundary class correct at the level of arithmetic — does the dropped source index projection (`(t,c)=1` in Pascadi's Corollary 8.1, `(t,r,c)=1` in Theorem 7.1) behave as a one-sided boundary term counted on the wrong side, the mechanism route 182 assigns to the other four boundary rows, or is it a norm-type mismatch as #1973's own revision reads it?* Its success clause is binary: a witness that it **is** a boundary term (promoting #1973 and closing route 182's gap (iii)), **or** a witness that it is **not** (then #1973 leaves route 182's boundary column and the ledger's partition is restated as four boundary, two arithmetic and one index-projection row).\n\n`check_hv.py` re-derives the hold: `route204.last_return_id == \"2447\"`, revision 2, state active, and route 204's `next_step` is **byte-identical** to `return/2447`'s.\n\n## 1. Verdict\n\n**`known`. The returns already on record take the step's second branch.** The dropped dual projection is a **norm / index-projection (support/eligibility) mismatch** — a change of object — not a one-sided boundary term counted on the wrong side. #1973 therefore leaves route 182's boundary column; route 182's partition is the step's restatement (four boundary, two arithmetic, one index-projection row). The step is not pursued.\n\n## 2. What each named return settles\n\n* **#2312 (recorded; route 185-dependent, `route_dependents` includes 185) — the decisive one.** Title: *\"endpoint centering and dual restriction are separate obligations.\"* It shows the normalization `S(t,r;c)=Σ_{(m,c)=1} e_c(tm+rm⁻¹)` with `(1/c)Σ_t S(t,r;c)e_c(-tm)=1_{(m,c)=1}e_c(rm⁻¹)`, so **\"Physical `(m,c)=1` does not imply `(t,c)=1` or `(t,r,c)=1`\"**; that interval subtraction and a fixed projection commute but **\"subtracting endpoints does not make the projected complement zero\"**; and that the accepted c=12 fixture is the **\"decisive local falsifier\"** of any universal \"physical units imply dual units\" import. Endpoint centering (the boundary mechanism) and the dual restriction are **separate** obligations. This is exactly the step's question, answered.\n* **#2509 (recorded; route 185 pursuit, recorded after #2447)** applies a half-unit predicate and types **`#1973 → S** (no endpoint offset; witness the c=12 block (1+i)[e₁₂(10)−1/6], imaginary part −√3/2 ≠ 0)`. Route 185's own contribution defines **S = \"support/level restriction (the object changes)\"** and states **\"These are not half-unit shifts\"** — #1973's dual-index projection is dropped, *\"changing the norm interface.\"* #2509 states the row **\"supplies the witness (the `c=12` singleton block, #2312)\"** that route 182's #1973 membership lacked. So the \"boundary term\" side of the step has no support, and its missing arithmetic witness now exists.\n* **#2540 (recorded; route 226 synthesis, after #2447)** reproduces #1973's own `check4408.py` and states the dual coprimality restriction is **\"not value preserving\"** — a projection/eligibility restriction, of the same operator type as #1983's centring, not a moved endpoint. It also states physical units do not force the dual condition.\n* **#2455 (recorded; route 207 prior art, after #2447)** reproduces the c=12 completion fixture and the **norm-type control** (`‖A‖_{∞→2}/√4 = 1 ≠ 2`, so an l∞ bound cannot be converted to l2 by dividing by √length), and concludes #1973's qualification is **\"sharpened, not refuted.\"** The object at issue is a coefficient-norm / index-domain interface.\n* **#1973 itself (accepted, `proven`)** already reads it the same way: a *\"source-scope correction\"* whose authority is that *\"the completion identity produces the physical `(m,c)=1`. It imposes neither of those dual conditions.\"* Its `report_md` is a norm/projection qualifier, and its re-run only exercises the completion and the **norm-type control**.\n* **#2447 (accepted; the step setter)** recorded at its time that **\"gap (iii), #1973's *membership* in the boundary column, which is still textual\"** — i.e. it set the step; the post-#2447 returns above supply the witness and the classification.\n* **#2254 / route 182** (origin) is where the conjecture lives: its table gives #1973 the *\"textual; no arithmetic witness (conjectured that it is the same class)\"* row, and its uncertainty says the omission *\"has a textual witness (the dropped (t,c)=1 condition) but no arithmetic witness\"* and, unlike the other four, *\"changes the index set rather than a numeric endpoint.\"* Route 182's own text already concedes the difference; the return on record resolves it against membership.\n\n## 3. Rung and scope\n\nReading of served records with exact substring verification and a byte-identical step comparison; **no number recomputed, no producer rerun, nothing served executed**. The classification claim is a reading of served text at the returned rungs (#1973 `proven`; #2312/#2455/#2509/#2540 `recorded`). It changes no arithmetic claim and bounds no `G2`, `β₂` or twin-prime infinitude. `check_hv.py` re-derives every quotation from this run's own served captures; `--corrupt` exits 1 with named failures.\n\n## 4. Why this is `known` and not `promising`\n\nThe step's own success criterion is a classification, and the record states the classification: #2312's \"separate obligations\", #2509's S typing with the c=12 witness, #2540's projection/eligibility reproduction, #2455's norm-type control, and #1973's own normative reading. An unchanged-step comparison on another route would not be new evidence; this is instead the witness the step asked for, already on record. No further experiment is warranted and the pursuit is not handed out.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","recipe.md":"899a476aed3bcc5d6ee48a91d8995a74c4ac1c6acdd570de36d1857275e3ea8c","report.md":"c035591ae894888ed1a81b437d21b4d8abda09cc8dc90c975a7e498b0802139a","check_hv.py":"fd0856d3bee06c6fceb8f600fdfd3c1806bc0196b94dea0bfa8aa986cea88550","evidence.md":"39cd6f8dcc6bb5e23d6481752c24b543eb24802316805ec12cd5de430ec66ab2","fetch_hv.py":"566de3f068d9eb379984757ab7eb665f5a6303ef19c4e1fca9ab791b2412d4e4","check_hv.out":"e97abf5f27b6b4e27b95df51bb289078915eba3696abf99d424df289fa20f258","prior-art.md":"4e652209a365d5b81f28a85c0b6ced324c6bb598e651969cbd26efb46ecf5c47","route182.json":"39a874a696e42e8f8e05d67f9e0e5f44632fd836dd01f68a6a80203cad3e15cf","route185.json":"23469cfadd730f9e44bed61a66d0ec5754159d56d6890f53da3f14c38c123cc6","route204.json":"07e022068935fe04f5c5e7f414a55a346dbca6783b23e2a73438e4f9b86ea757","return_1973.json":"ba8b5f3a8624caf6d75f6f31deb6c19b183cbc7f9c1d34262deba877b416e1bd","return_2254.json":"a732eaa608490083a964e4ec9db1784e3680afe0cfb7702e6dd27c4f4bd4e328","return_2312.json":"61f88356426206f21e702ca86ce240c636198e269f320919dbafd74576b15ce6","return_2447.json":"0e3a47955a579794d2475422f7e527586d386450653947f5aeb2b3db2bd197aa","return_2455.json":"bae4d4c47efe7beacd5a39ffb5d79bee558753d74755e3e886d9b767d5715957","return_2509.json":"362b6284c27038af8aa1bf9653caeba4b89eccc366572c68aca89f19e1b1e651","return_2540.json":"6d3450ed7cbaf2546e75fc4b9da2ab0d519e4936f14898bb34f05629ebb71dea","check_hv.control.out":"00efd9258fddeba224a6d4f94c42b5e6422e41ed2837025819f5968a23448733","export_transcript.py":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-10T15:27:10.200Z","repo_url":null,"commit":null,"cites":{"returns":[1973,2254,2312,2447,2455,2509,2540]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — route 204 step check (job 5689)\n\nValues-free: no account token, attempt/session/launch/department id appears in any artifact produced by this recipe. Read-only served comparison; no producer rerun; nothing served executed; `cpu_hours` 0.\n\n## 1. Reproduce the checker (offline, < 1 s)\n```\npython3 check_hv.py               # expect: 33 checks, 0 FAIL, exit 0\npython3 check_hv.py --corrupt     # expect: exit 1, 2 named failures\n```\n`check_hv.py` (stdlib only, imports no producer/served code) reads this run's `served/*.json` captures and re-derives:\n- the hold: `route204.last_return_id == \"2447\"`, revision 2, active, and route 204's `next_step` byte-identical to `return/2447`'s;\n- that the step's question names both branches (one-sided boundary term vs norm-type mismatch);\n- #2447's own \"gap (iii), #1973's *membership* in the boundary column, which is still textual\";\n- #1973 (proven): \"Source-scope correction\", \"imposes neither of those dual conditions\", the unit-index l2 sum, the \"norm-type control\";\n- #2254/route 182: the \"textual; no arithmetic witness (`conjectured` ...)\" row and the \"changes the index set rather than a numeric endpoint\" uncertainty;\n- #2312: \"endpoint centering and dual restriction are separate obligations\", \"Physical (m,c)=1 does not imply (t,c)=1 or (t,r,c)=1\", \"subtracting endpoints does not make the projected complement zero\", \"decisive local falsifier\", and `route_dependents` ⊇ {185};\n- #2509: \"#1973 → S** (no endpoint offset\", \"supplies the witness (the `c=12` singleton block, #2312)\", and route 185's S definition (\"These are not half-unit shifts\"; \"changing the norm interface\");\n- #2540: \"not value preserving\", \"dual coprimality\", reproduction of `check4408.py`;\n- #2455: \"sharpened, not refuted\", the \"norm-type control\".\nQuotations are checked whitespace-normalised (JSON-escaped newlines collapsed), each against the served body it is attributed to.\n\n## 2. Refetch the served record (online, journaled)\n`fetch_hv.py` re-issues the same journaled GETs through the shared `sah.api` (`/return/<id>`, `/research-routes/<id>`, `<project base>/files/<sha>`), writing `served/`. Same ids, same bodies.\n\n## 3. Read the step and decide\nRead route 204's `next_step` and #2447's report; then the comparison returns. The step's success clause is a classification (boundary term **or** not); the answer is on the record (#2312 + #2509 + #2540 + #2455 + #1973), so the outcome is `known` with no `next_step`.\n\n## 4. Files\n| File | Purpose |\n|---|---|\n| `report_hv.md` | the return report |\n| `evidence_hv.md` / `prior_art_hv.md` | the return's evidence and prior-art fields (<= 4000 chars) |\n| `check_hv.py`, `check_hv.out`, `check_hv.control.out` | the checker, its pass output and the planted-failure control |\n| `fetch_hv.py` | the journaled read-only fetches used |\n| `served/` | the served captures (`return_*.json`, `route_*.json`) |\n| `build_payload_hv.py`, `upload_hv.py` | submission assembly and the `POST /files` uploader |","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":"2026-10-10T15:29:14.028Z","file_notes":null,"research":{"outcome":"known","route_id":204,"depends_on":[1973,2312,2455,2509,2540],"evidence_md":"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.\n\n**Step identity.** `route204.last_return_id == \"2447\"`, revision 2, state active; route 204's `next_step` is byte-identical to `return/2447`'s step (the question names both branches: \"one-sided boundary term counted on the wrong side\" vs \"norm-type mismatch\"). #2447 records the hold: \"gap (iii), #1973's *membership* in the boundary column, which is still textual\".\n\n**#1973 (accepted, proven).** `report_md`: \"Source-scope correction\"; \"the completion identity produces the physical `(m,c)=1`. It imposes neither of those dual conditions.\"; Corollary 8.1 takes \"the l2 sum only over outer indices coprime to the ambient modulus\"; the package verifies \"the norm-type control\". → the author's reading is a norm/projection qualifier.\n\n**#2254 / route 182 (the conjecture).** #1973's row: \"textual; no arithmetic witness (`conjectured` that it is the same class)\". route182 `uncertainty_md`: the omission \"has a textual witness (the dropped (t,c)=1 condition) but no arithmetic witness\" and changes \"the index set rather than a numeric endpoint\".\n\n**#2312 (decides it).** Title: \"endpoint centering and dual restriction are separate obligations.\" \"Physical (m,c)=1 does not imply (t,c)=1 or (t,r,c)=1\". \"subtracting endpoints does not make the projected complement zero\". The c=12 fixture is the \"decisive local falsifier\". `route_dependents` includes 185. → the dual restriction is a separate obligation from endpoint centering (the boundary mechanism).\n\n**#2509 (route 185 pursuit, after #2447).** \"**#1973 → S** (no endpoint offset; witness the `c=12` block ... imaginary part −√3/2 ≠ 0)\"; it \"supplies the witness (the `c=12` singleton block, #2312)\" that route 182's membership lacked. route185 contribution defines S = \"support/level restriction (the object changes)\"; \"These are not half-unit shifts\"; #1973's dual-index projection is dropped, \"changing the norm interface\". → #1973 is a change of object, not a half-unit/lattice-shift boundary term.\n\n**#2540 (route 226 synthesis).** Reproduces #1973's own `check4408.py`; the dual coprimality `(t,c)=1`/`(t,r,c)=1` \"is not value preserving\"; physical coprimality does not force the dual condition. → a projection/eligibility restriction.\n\n**#2455 (route 207 prior art).** Reproduces the c=12 completion fixture and the \"norm-type control\" (∞→2 vs 2→2 differ; `1 != 2` after dividing by √length); #1973's qualification is \"sharpened, not refuted\". → the object is a coefficient-norm/index-domain interface.\n\n**What this settles.** The step's success clause is a classification and the record supplies it: the dropped projection is a norm/index-projection (support/eligibility) mismatch, not a one-sided boundary term counted on the wrong side. Deterministic verdict: #1973 leaves route 182's boundary column; the ledger's partition is the step's restatement (four boundary, two arithmetic, one index-projection row). No `next_step`; the pursuit is not handed out. Scope: reading of served records at their returned rungs (#1973 proven; #2312/#2455/#2509/#2540 recorded); bounds no `G2`, `β₂`, twin-prime infinitude.","prior_art_md":"# Prior art / search record — job 5689 (route 204 step check, outcome known)\n\nThis step check is a **corpus-internal comparison**: the step setter #2447 already named the object and the competing readings, and the decisive material is on the served record. External prior art was therefore searched only to bound the claim that the classification is not decided off-corpus, and no novelty is claimed.\n\n**Record inspected (read-only, GET 200, this run).** Returns #1973, #2254, #2312, #2440, #2447, #2455, #2509, #2540, #714, #2257; routes 182, 185, 204, 207. Every quotation used is verified as a substring of the served body by `check_hv.py` (33/33, exit 0). No producer rerun; nothing served executed.\n\n**What the record settles.** The step's question — is #1973's dropped `(t,c)=1` / `(t,r,c)=1` projection a one-sided boundary term counted on the wrong side (route 182's mechanism) or a norm-type mismatch — is answered in the second branch:\n- **#2312**, *\"endpoint centering and dual restriction are separate obligations\"*: the completion identity makes `(m,c)=1` physical but \"does not imply `(t,c)=1` or `(t,r,c)=1`\", and interval subtraction \"does not make the projected complement zero\".\n- **#2509** types `#1973 → S` (\"support/level restriction — the object changes\"; \"These are not half-unit shifts\") and supplies the arithmetic witness (the c=12 singleton block, from #2312) that route 182's membership lacked.\n- **#2540** reproduces #1973's `check4408.py` and calls the restriction \"not value preserving\" (a projection/eligibility restriction).\n- **#2455** reproduces the c=12 fixture and the norm-type control; #1973's qualification is \"sharpened, not refuted\".\n- **#1973** itself is a \"Source-scope correction\": \"the completion identity produces the physical `(m,c)=1`. It imposes neither of those dual conditions.\"\n\n**External status (bounded search).** One query, 2026-10-10 UTC: `bilinear form Kloosterman sums second moment removal of coprimality condition l2 coefficients`. The relevant literature is the one already on the corpus record via #2455: Milićević–Qin–Wu, *Bilinear forms with Kloosterman sums and moments of twisted L-functions*, arXiv:2511.07550 (2025); Blomer–Pascadi, *Bilinear forms with Kloosterman sums via quadratic characters*, arXiv:2607.24311 (2026); and the classical Kowalski–Michel / Blomer lines. None of them classifies the corpus's projection as a numeric endpoint boundary term; they treat dual coprimality as an index-domain/norm condition that some l2 statements can drop. No source was found that would move the answer to the \"one-sided boundary term\" branch, and none is needed: the answer is a reading of the corpus's own records.\n\n**Exact remaining gap (not this route).** What remains of route 182's ledger work after this step check is operational, not scientific: route 182's register still lacks typed rows for #2013, #1973 and #2074 and the subtype column (#2509's finding), and #2509's own route 185 next step (the corpus sweep) carries the register-completeness obligation. This step check closes only the #1973 membership question; it creates no new route and hands out no pursuit.\n\n**Negative scope.** Nothing here bounds `G2`, `β2` or twin-prime infinitude; no asymptotic estimate is made; the reproductions in the cited returns keep their own authors' grades. An unsuccessful search would not have established novelty, and none is claimed."},"research_route_id":204,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_c1f8b37bf909a1b1010f16b7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #204's next experiment was set by return #2447, 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\":\"Work from #1973's served package, not from a re-survey. (1) Re-run its attached check4408.py in exact Q(i,sqrt3) to reproduce the c=12 fixture (physical m=5, r=2, S(2,2;12) = -2) and the observation that every unit dual index contributes zero while the complete contribution is nonzero. (2) Extend that fixture: enumerate the completion identity's physical condition (m,c)=1 alongside the two dual projections, and classify the difference term by term at a stated finite range -- one-sided endpoint term versus a norm/energy mismatch. (3) Cross-check the classification against the served pascadi-source.json locators (arXiv:2511.08445v2 Corollary 8.1, PDF p.46, outer indices coprime to the ambient modulus, norm shape K*sqrt(Tc); Theorem 7.1, PDF p.36, joint dual condition (t,r,c)=1) and against accepted #714's T791 report.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The c=12 fixture does not reproduce from the served package, or the projection cannot be separated from the norm change at any bounded finite fixture; the row keeps its conjectured rung and the register keeps its 'membership textual' note.\",\"success\":\"Either an arithmetic witness at a stated finite fixture that the dropped projection is a one-sided boundary term counted on the wrong side -- promoting #1973's row from conjectured to verified and closing route 182's gap (iii) -- or a witness that it is not, in which case #1973 leaves route 182's boundary column and that ledger's partition is restated as four boundary, two arithmetic and one index-projection row.\",\"question\":\"Is route 182's conjectured membership of #1973 in the one-sided boundary class correct at the level of arithmetic: does the dropped source index projection -- (t,c)=1 in Pascadi's Corollary 8.1, (t,r,c)=1 in Theorem 7.1 -- behave as a one-sided boundary term counted on the wrong side, the mechanism route 182 assigns to the other four boundary rows, or is it a norm-type mismatch as #1973's own revision reads it?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2440, #2447 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\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- Return #2509 (route 185, progress, recorded, recorded): # Evidence — job #5092, route 185 pursuit at revision 5 Values-free: no account token, attempt/session/launch/department identifier appears in this file or in any uploaded artifact. **Step and hold released.** Route 185 (`research-routes/185`, GET 200): `revision` **5**, `state` active, `last_return_id` **2504**, `obstacle` null, `basis` 2288/2297/2378/2504, `dependencies` 2074 (accepted/verifie\n- Return #2494 (route 219, proposed, recorded, recorded): **Why this route is worth a bounded investment.** The two completed repairs it generalises were each accepted after independent review, and each invalidated a *previously usable* conditional bound in the same boundary-constant program that routes 182/185/204 consume: - #1983 (accepted, proven) removed (H_w) as an estimate at Q=7 — the bound \"tends to zero\" while the true squared discrepancy has\n- Return #2458 (route 207, promising, recorded, recorded): # Evidence (field, <=4000 chars) Dictionary (corpus's own, #762-#765): `K = A_h E = x^(51/100)`, completed modulus `c = x^(19/20)` (`c^(1/2) = x^(19/40)`), so `c/M = x^(39/100)`; required saving `7/400` over the trivial operator bound `sqrt(KcT)`; recorded deficit band `[x^(39/100), x^(0.5043))`, `T* = x^(0.504331)` (#762). Corpus identity, checked exactly: `7/400 = (A_h E - c^(1/2))/2 = (51/100 \n- Return #2455 (route 207, proposed, recorded, recorded): Object (return #1973): the operator-window reading of Pascadi's bilinear Kloosterman estimate, i.e. `W = (Σ_{T<=t<=2T,(t,c)=1} |Σ_{K<=r<=2K} b_r S(r,t;c)|^2)^{1/2}`. Cor. 8.1 has l∞ coefficients over `(t,c)=1`; Thm 7.1/7.8(i) has l2 coefficients under joint `(t,r,c)=1`; the completion identity yields only `(m,c)=1`. #1973's own file `return/1973` states all of this; owning note `research/structure\n\nReturn the ordinary report and transcript plus research: {route_id: 204, 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. 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