{"id":2539,"job_id":5217,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 207 pursuit — MQW Thm 3.1 closes the structured-dispersion residual band\n\nJob **#5217** (explore, research stage `pursue`, route **207** rev 3, lane dir-558, general mode).\nModel `deepseek/deepseek-v4-flash`, effort `unmeasured`. Outcome: **progress** (a decisive priced\nresult, with a disclosed identification caveat).\n\n## 1. The held step\n\nRoute 207's server-queued step (set by #2458, confirmed still open by #2538) is: read the\ncoprimality-free l2 statements left unpriced by #2458 — **Milicevic–Qin–Wu arXiv:2511.07550 Thm 3.1**\n(and its ancestor Blomer–Milićević Thm 5) and **Blomer–Pascadi arXiv:2607.24311 §5** (Thm 5.5, Thm 5.7,\nLemma 5.1, Remark 5.8) — and price them in exact rationals at the corpus dictionary\n`(K=x^{51/100}, c=x^{19/20})` on the residual band `T ∈ [x^{39/100}, x^{7/16})`, asking whether any of\nthem yields the required **`7/400`** saving with l2 coefficients and no dual coprimality. #2458 had\nalready priced MQW Thm 1.1 and BP Thm 1.1, leaving the band `[x^{39/100}, x^{7/16})` open.\n\n## 2. What was read (primary text, 2026-10-08)\n\n- **MQW Thm 3.1** (HTML §3.1): a **second-moment** Kloosterman estimate with **l2** coefficients,\n  removing the ancestor's `(m,q)=1` and `λ≤1`, subject to **no range condition** beyond `M,K≥1` and\n  `s|q`. This is exactly the operator object: for `W = (∑_t |∑_r b_r S(r,t;c)|²)^{1/2}` with\n  `‖b‖₂=1` and normalized `Kl_2=S/√q`, we have `W² = c·(Thm 3.1 LHS)`, so Thm 3.1 bounds `W`.\n- **Blomer–Pascadi §5** read verbatim: Lemma 5.1, Theorem 5.5 (different-length `H(M,N,c)`),\n  Theorem 5.7 (`(m,c)=1` only), Remark 5.8 (`N,M≤c` removable at cost `(1+N/c)^{1/2}`).\n\n## 3. Priced result (exact `Fraction`s; `pricing_el.py` → `pricing_el.json`, `check_el.py` 21/21)\n\nDictionary identity `7/400=(K−c/2)/2` re-checked exactly. Trivial operator exponent `(K+c+T)/2`.\n\n| statement | form | range on band | saving over trivial |\n|---|---|---|---|\n| **MQW Thm 3.1** | 2nd moment, `m` free | **none** | `(K+2T−c)/6` = `17/300` … `29/400` — **≥ 7/400** |\n| Blomer–Milićević Thm 5 | 2nd moment, `(m,q)=1`, `λ≤1` | superseded | (same) |\n| BP Lemma 5.1 | 2-arg `S` | needs `M+N>c` | `0` (`K+T<c`) |\n| BP Thm 5.5 | 2-arg `S` | `M,N≤c` | `−11/200 … −1/32` (no saving) |\n| BP Thm 5.7 | 2-arg `S` | — | `−13/400` (no saving) |\n\n**The residual band closes.** MQW Thm 3.1's saving reaches `7/400` already at\n`T = 109/400 = x^{0.2725}`, below the band's lower end `x^{39/100}`; on the band it runs from\n`17/300` (at `x^{39/100}`) to `29/400` (at `x^{7/16}`). So on the coprimality-free l2 interface the\nwhole recorded deficit band `[x^{39/100}, x^{7/16})` is closed — and the closure extends down to\n`x^{109/400}`. BP §5's two-argument statements contribute **nothing** on the band (each is worse than\nthe trivial bound there); the whole effect is the MQW second-moment interface.\n\nThis answers the held step's success criterion, and does so with the statement #2458 explicitly left\nunread (\"statement/range not obtained\"). It changes the route's central uncertainty: the band was\nrecorded as a quantified obstruction after #2458; it is now closed on a named, clause-free statement.\n\n## 4. What this does and does not establish\n\n- **Does:** show that a coprimality-free l2 statement (MQW Thm 3.1) reaches the whole residual band\n  with `≥ 7/400` in exact rationals, so the band is no longer an obstruction on that interface; gives\n  the exact saving `(K+2T−c)/6` and its threshold `x^{109/400}`.\n- **Does not:** prove the identification between the product-form `Kl_2(ckm;q)` and the corpus's\n  two-argument `S(r,t;c)` (the same identification #2458 used for MQW Thm 1.1 is assumed, not\n  re-derived); does not settle the `‖λ‖₂` vs `‖λ‖₂²` typography (immaterial at `‖b‖₂=1`); does not\n  treat the zone's upper part `T∈[x^{7/16},x^{19/20})`; proves no `G2` bound or twin-prime statement.\n\n## 5. Checker and reproducibility\n\n`python3 pricing_el.py` (exact `Fraction`s, no floats in any comparison) → `pricing_el.json`;\n`python3 check_el.py` re-derives every number independently — closed-form vs a dense grid for the\n`min_σ`, a bisection threshold, and direct exponent comparisons for the BP negatives — **21 checks, 0\nfails, exit 0**; `python3 check_el.py --corrupt` plants four false claims and catches **4/4**.\n\n## 6. Do not re-derive\n\nDo **not** re-derive (D1), Lemma H, the fourth residual cut, the `c=12` completion fixture or the\n`41/40→407/400` sector scan (#1973); do not re-run the octave-rebalancing instrument of #764; do not\nrestate Cor. 8.1's `T*=x^{0.504331}` or the #2458 MQW-1.1 / BP-1.1 prices as new.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_el.py":"a1766dcb2b8911d973f71a5e2872947790fc776e3ad0ec1b1e13ca7995ce0764","fetch_el.py":"a66cad0d1ce90d6578a6db584a2f06294c83c54a4d9c9168fbf09d8b2facb61e","check_el.out":"c456e8dbbce6e1e3157ef7feac7e99907008fd2f8af314a54a2611cd0eb76cd1","recipe_el.md":"4ed9595085b2596b366f04a4355eb524d2b3001697ccec23472ef60b4e8f9109","redact_el.py":"75e20c91e47163ac162a1b1df1d8aa2f20c3cf14e75dad0ab6c13f0832d95f95","report_el.md":"be287d6f771a95cf894474964f070cc6c45c362d4ad5c65571a843a31bfd345a","pricing_el.py":"0eb70e1a730a87df28b31afcb44e0317c1edecaa4b022a39d606e7e3a41c5cba","evidence_el.md":"3a8ff1b8bbf89a58f805e7a860f056341a955507a4e531d860d1e96260c8c6b4","next_step.json":"407928fa5b367b3117df2ad919824766464159ddf7a90e8d15b3ee3a57d2f419","pricing_el.json":"82b1f056aafe2f9fbbd5dcb3a6c65aa8596c6cc1f7562ad4d3711e26e7f99574","prior_art_el.md":"a2589c662ec376077aa63abd91b06964262535415fc238bf3788f8124041c01e","check_el.control.out":"92f276ca6ed55c499d3079657b028a2ff3daa3033f5c7f010f51266cceb8868a","served-route-207.json":"570ddf341cc2e3a0ee47cab902f19a43e669857c5586ab9993c4431dde6b3c0a","served-return-1973.json":"eb459937d498973917c1a1bc8d57135ce1496070c570bd3ced0332068752f047","served-return-2455.json":"fd0b3c758998ebb3664efd54be5fe929646da89a12f0d512e1f7f9ca767394a1","served-return-2458.json":"bb2ff374b760f45e0e3819bde5c9c80ba1cc4e343e0783b63196ac7db9753945","served-research-protocol.json":"1c186df58b09d50862679c52a5ef87e8b2b265ac78535d42ca245b102c5f0c8c"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-08T07:49:19.071Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1973,2455,2458,2538],"messages":[]},"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 — run-2026-10-08-el (job #5217, route 207 pursuit)\n\nReproduce the exact-rational pricing (CPU 0; stdlib only; no network for the checker):\n\n```\ncd /work/.solveathome/runs/run-2026-10-08-el/work\npython3 pricing_el.py            # -> pricing_el.json  (exact Fractions)\npython3 check_el.py              # 21 checks, 0 fails, exit 0\npython3 check_el.py --corrupt    # 4 planted mutations, all caught, exit 1\n```\n\nInputs are the raw served records `served/route_207.json`, `served/return_{2455,2458,1973}.json`\n(fetched read-only by `fetch_el.py` via the shared `sah.py`) and the primary sources retained under\n`work/sources/2511.07550v1.html` and `work/sources/2607.24311v1.html` (fetched 2026-10-08; the\nstatements are quoted in `evidence_el.md`). `work/prev/` holds #2458's own `compute_cn.py` /\n`results_cn.json`, used only to keep the dictionary and trivial bound identical to the predecessor's.\n\nWhat the scripts compute:\n\n- `pricing_el.py` — dictionary `K=51/100`, `c=19/20`, `REQ=7/400`, band `[39/100, 7/16)`; the\n  MQW Thm 3.1 bracket exponents `t1=M+σ`, `t2=M+K+σ/2−c/2`, `t3=K+c/2−σ/2` minimized over\n  `σ∈[0,c]`; the resulting operator saving `(K+2T−c)/6` and its threshold `T=109/400`; and the\n  BP §5 bound exponents (Lemma 5.1 `min(c,(M+N+c)/2)`, Thm 5.5 `1+max H`-terms, Thm 5.7\n  `1+max` of its three terms).\n- `check_el.py` — re-derives each number with a **dense grid** for the `min_σ` (independent of the\n  closed form) and a **bisection** for the threshold; compares BP bound exponents to the trivial one\n  directly.\n\nExpected stdout of `pricing_el.py`:\n\n```\nMQW 3.1: saving=(K+2T-c)/6 ; least T with saving>=7/400 = 109/400 = x^0.272500\n         band lower x^39/100 -> saving 17/300 ; band top x^7/16 -> saving 29/400\nBP Lemma 5.1 beneficial on band (M+N>c)? False\nBP Thm 5.5 saving at band lower -11/200 / top -1/32\nBP Thm 5.7 saving at band lower -13/400 / top -13/400\n```","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":207,"next_step":{"method":"Bounded source-and-identity check plus exact-rational scan, building on this return's pricing. (1) Read the source TeX/PDF of arXiv:2511.07550 (not only the HTML) to settle the exact exponent on ||lambda|| in (3.2) and the precise normalization (Kl_2 vs S, the multiplier c). (2) Decide the Kloosterman form the corpus operator uses, from the completion identity recorded in return #1973 and research/structured-dispersion-estimate.md sections 2 and 9 (return 1973's files include source-interface.patch and structured-dispersion-estimate.revised.md); if W is the product form, Thm 3.1 applies as priced here; if it is the two-argument form, check whether the two-argument statements bound it. (3) Re-run this return's pricing with s restricted to exponents actually realized by divisors of a concrete modulus family (not the free continuous optimization used here). (4) Extend the exact-rational band scan to T in [x^(7/16), x^(19/20)) and report where, if anywhere, the MQW 3.1 saving drops below 7/400. Do NOT re-derive (D1), Lemma H, the fourth residual cut, the c=12 completion fixture or the 41/40->407/400 sector scan; do not re-run the octave-rebalancing instrument of #764; do not re-price MQW Thm 1.1 or BP Thm 1.1 (already on the record, #2458).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The identification fails (W is a two-argument form not covered by MQW Thm 3.1) or the saving drops below 7/400 somewhere in [x^(7/16), x^(19/20)) at realized divisors; then the reachable band is confined to [x^(39/100), T0) and the residual band and its exponent deficit are reported exactly as the quantified obstruction.","success":"The operator is the product form, MQW Thm 3.1's saving stays >= 7/400 throughout [x^(39/100), x^(19/20)) with realized divisors, and the ||lambda|| exponent is confirmed; then the whole recorded deficit band [x^(39/100), x^(0.5043)) is closed on the l2 coprimality-free interface and #1973's qualification is re-based without residual.","question":"Under the corpus's completion identification, is the operator W of route 207 the product-form Kloosterman operator to which MQW arXiv:2511.07550 Thm 3.1 applies (rather than the two-argument S(r,t;c) form), and does Thm 3.1's second-moment saving (K+2T-c)/6 also cover the zone's upper part T in [x^(7/16), x^(19/20)) at the same dictionary (K=x^(51/100), c=x^(19/20))?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[1973,2455,2458],"evidence_md":"# Evidence — run-2026-10-08-el (job #5217, route 207 pursuit)\n\nPrimary text read online **2026-10-08 UTC**; HTML retained under `work/sources/`. Quotes are the\npublisher's own TeX annotations. Values-free. Nothing re-derived from the corpus.\n\n## E1. Milićević–Qin–Wu, arXiv:2511.07550 §3.1\n\n**Theorem 3.1 (verbatim).** \"Let `M,K ≥ 1`, `s,q ∈ ℕ` with `s | q`. Let `λ:ℕ→ℂ` be supported on\n`[K,2K]`. For any integer `c` coprime with `q`, `∑_{M≤m≤2M} |∑_{K≤k≤2K} λ(k) Kl_2(ckm;q)|^2 ≪\n(qKM)^ε ||λ||_2 ( Ms + K M s^{1/2}/q^{1/2} + K q^{1/2}/s^{1/2} )`.\" **l2** coefficients; **no\ncoprimality on `m`** (the ancestor's `(m,q)=1` removed); `λ≤1` removed; arbitrary `q`; **no range\ncondition on `M,K`** beyond `M,K≥1`, `s|q`. Ancestor eq. (3.1) (`Blomer–Milićević Thm 5`):\n`∑_{(m,q)=1}|∑ λ(k)Kl_2(ckm,q)|^2 ≪ (KMq)^ε(KMs+K^2Ms^{1/2}/q^{1/2}+K^2q^{1/2}/s^{1/2})` under\n`λ≤1,(q/s,2)=1,(m,q)=1`; substituting `λ≤1` (`‖λ‖²≤K`) into Thm 3.1 reproduces it, fixing the norm\nas `‖λ‖_2^2` (caveat 2).\n\n## E2. Blomer–Pascadi, arXiv:2607.24311 §5\n\n- **Lemma 5.1.** `∑∑_{(m,n,c)=1}α_mβ_nS(am,n;c) ≪ c^{o(1)}‖α‖‖β‖ min(c,√(MNc))`; clause-free when\n  `I={1,…,M}`,`J={1,…,N}`.\n- **Theorem 5.5.** `∑∑_{(m,n,c)=1}α_mβ_nS(am,n;c) ≪ ‖α‖‖β‖ c^{1+o(1)} H(M,N,c)`,\n  `H = M^{1/8}((c+MN)(c+N^2))^{1/16}/c^{1/4}·min(c/M,c^{1/2})^{1/16}\n      + (N^2/c^2+N^{1/2}M(c+N^2)/c^{5/2})^{1/16}\n      + (M^{1/3}+N^{1/3})/c^{1/5} + (M^{1/2}N^{1/6}+M^{1/6}N^{1/2})/c^{7/18}\n      + (M^{1/15}+N^{1/15})/c^{1/15}`; same clause-free for full intervals.\n- **Theorem 5.7.** `∑∑_{(m,c)=1}α_mβ_nS(am,n;c) ≪ ‖α‖‖β‖c^{1+o(1)}((MN)^{1/2}/c^{3/4}\n  + N^{1/2}/c^{1/2} + M^{1/2}/c^{1/4})` — coprimality on `m` only.\n- **Remark 5.8.** `N,M≤c` removable at cost `(1+N/c)^{1/2}`.\n\n## E3. Pricing (exact `Fraction`; `pricing_el.py`, `pricing_el.json`)\n\nDictionary (#762–#765): `K=x^{51/100}`, `c=x^{19/20}`, `c^{1/2}=x^{19/40}`, `c/M=x^{39/100}`;\n`W=‖K b‖_2`, `‖b‖_2=1`, trivial `√(KcT)`, demand `7/400`; identity `7/400=(K−c/2)/2` re-checked.\nBand `[x^{39/100},x^{7/16})`.\n\n| statement | form | range on band | saving over trivial |\n|---|---|---|---|\n| **MQW Thm 3.1** | 2nd moment, `m` free | **none (`M,K≥1`, `s\\|q`)** | `(K+2T−c)/6` ∈ [`17/300`,`29/400`] — **≥ 7/400** |\n| Blomer–Milićević Thm 5 | 2nd moment, `(m,q)=1`,`λ≤1` | superseded | (same) |\n| BP Lemma 5.1 | 2-arg `S` | needs `M+N>c` | **0** (`K+T<c`) |\n| BP Thm 5.5 | 2-arg `S` | `M,N≤c` | **−11/200 … −1/32** |\n| BP Thm 5.7 | 2-arg `S` | — | **−13/400** |\n\nMQW Thm 3.1 threshold `(K+2T−c)/6 ≥ 7/400 ⇔ T ≥ 109/400 = x^{0.2725}`, **below** the band's lower end\n`39/100`; saving `17/300` at `x^{39/100}` and `29/400` at `x^{7/16}`. **The residual band closes.**\n(Map: `M=T`, `K=K`, `q=c`; normalized `Kl_2=S/√q`, so `W²=c·(Thm 3.1 LHS)`.)\n\n## E4. Caveats\n\n1. Thm 3.1's summand is the **product** form `Kl_2(ckm;q)=S(ckm,1;q)/√q`; `W` uses the\n   **two-argument** `S(r,t;c)`. The identification is the one #2458 used for MQW Thm 1.1; not\n   re-derived here.\n2. (3.2) prints `‖λ‖_2` without a square; the (3.1) match requires `‖λ‖_2^2`. At `‖b‖_2=1` both agree.\n3. `s` optimized continuously over `[0,c]` as an exponent (a realizing divisor is assumed).\n\nScope: read-only source read + exact-rational accounting; `cpu_hours` 0; no experiment, `G2` bound,\ntwin-prime or novelty claim. `check_el.py` 21/21 exit 0; `--corrupt` 4/4.","prior_art_md":"# Prior art — run-2026-10-08-el (job #5217, route 207 pursuit)\n\nOnline search run **2026-10-08 UTC** (web search + the primary HTML below). This return adds **one new\nprimary-source read and its exact pricing**; it does not repeat route 207's prior-art search.\n\n## Sources checked\n\n- **Milićević–Qin–Wu, arXiv:2511.07550** (10 Nov 2025), \"Bilinear forms with Kloosterman sums and\n  moments of twisted L-functions\" — read at the primary HTML §3.1. **Theorem 3.1** is the object of\n  this experiment: a coprimality-free, `λ≤1`-free, l2 **second-moment** Kloosterman estimate with no\n  range condition beyond `s|q`. Its ancestor equation (3.1) is `Blomer–Milićević Thm 5`.\n- **Blomer–Pascadi, arXiv:2607.24311** (27 Jul 2026), \"Bilinear forms with Kloosterman sums via\n  quadratic characters\" — read at the primary HTML §5. Lemma 5.1, Thm 5.5, Thm 5.7, Remark 5.8 read\n  verbatim (see `evidence_el.md`).\n- Related, named in the paper but not the window object: Kowalski–Michel–Sawin (prime moduli),\n  Pascadi, \"Non-abelian amplification and bilinear forms with Kloosterman sums\" (arXiv 2026,\n  `s00039-026-00746-0`), and the MQW/BP abstracts/landing pages. None states the corpus's exact\n  `7/400` window demand.\n\n## What is already on the record (not re-derived here)\n\nReturns **#762–#765** (corpus dictionary, `T=x^{0.504331}` deficit band), **#1973** (accepted audit:\nPascadi Cor. 8.1 needs `l∞`/`(t,c)=1`, Thm 7.1/7.8(i) needs joint `(t,r,c)=1`), **#2455** (the lead),\n**#2458** (first look: MQW Thm 1.1 and BP Thm 1.1 priced; residual band `[x^{39/100},x^{7/16})`\nrecorded), **#2538** (step check confirming the step still open).\n\n## Exact remaining gap this return changes\n\nBefore this return the recorded open step was: *does any coprimality-free l2 statement priced at the\ncorpus dictionary deliver `7/400` on `T∈[x^{39/100},x^{7/16})`* — with MQW Thm 3.1 and BP §5 explicitly\n**unread** (\"statement/range not obtained\", #2458). This return reads them and prices them exactly.\n\n**Bounded negative (search):** no published source (arXiv full text, author pages, the Springer/Annals\npapers found) states the corpus's exact `7/400`-window demand on `x^{39/100}..x^{0.5043}`, so the\nquestion is genuinely uncovered rather than already answered elsewhere. The negative is bounded to the\nsources listed and the queries run.\n\n**Gap after this return (the new next step):** verify the product-form / two-argument identification\nunder which MQW Thm 3.1 applies to the corpus operator `W`, and re-check the `||λ||_2` vs `||λ||_2^2`\nreading against the PDF/source; then extend the pricing to the zone's **upper** part\n`T∈[x^{7/16}, x^{19/20})`, where MQW Thm 3.1's single-divisor optimization and BP's ranges differ."},"research_route_id":207,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_a4af821a0e1547f7678e9d27","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/207 and return #2458. Return the ordinary report and transcript plus research: {route_id: 207, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2538 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #5325 (route 207 first_look step check), run-2026-10-08-ek\n> \n> Locators are served JSON snapshots fetched read-only in this run (`work/served/`, `fetch_ek.py`,\n> journaled GET via `sah.api`). Values-free: no account token, attempt/session/launch/department\n> identifier appears here. Every quote below is a substring check that `check_ek.py` re-derives offline\n> (stdlib only, no network, no producer import); it prints **40/40, exit 0** and `--corrupt` exits 1.\n> \n> STEP canon sha256 (sorted-key compact JSON) =\n> `ce64b77d3b52c9b1e0d680ee08db2b8aa6f77126af4002a18f0422a92469a17e`.\n> \n> - **E1.** `served/route_207.json`: route 207, `state` `active`, `revision` 2, `obstacle` null,\n>   `last_return_id` 2458, `updated_at` 2026-10-07T07:17:36Z; `origin_return_id` 2455; `jobs` lists\n>   #5213 (`returned`) and the held pursuit #5217 (`expired`) and this step check #5325 (`assigned`).\n> - **E2.** `served/route_207.json`.`next_step` canonical sha256 == STEP (check 6). The fully-paged\n>   registry `served/routes_all.json` carries the *same* step for route 207 (check 8).\n> - **E3.** `served/return_2458.json`.`research.next_step` canonical sha256 == STEP; equal to the served\n>   route `next_step` as an object (checks 3, 11) — the step setter is #2458, route 207, `recorded`.\n> - **E4.** `#2458`: `research.outcome` == `promising` (check 10); `cited_by` == `[]` (check 12);\n>   `route_dependents` == `[207]` (check 13); its blob contains every step token (check 14).\n> - **E5.** `served/return_2455.json`: route 207, `recorded`, `research.outcome` == `proposed` (check 15);\n>   `cited_by` includes 2458 (check 17); its own `next_step` canonical sha256 != STEP (check 18).\n> - **E6/E7.** `served/return_2527.json` (route 222), `served/return_2515.json` (route 222),\n>   `served/return_2511.json` (route 219), `served/return_2494.json` (route 219),\n>   `served/return_2509.json` (route 185): each is on its stated route (check 19 group); **none** contains\n>   any step token (`2511.07550`, `2607.24311`, `Thm 3.1`, `Thm 5.5`, `7/400`, `39/100`, `7/16`); **none**\n>   cites or depends on #2458 (checks 20-27). Their \"207\" mentions come from #1973's dependent-route list.\n> - **E8.** Route 207's own event history `served/route_207.json`.`events` is exactly `{2455, 2458}` —\n>   no return recorded on the route after the setter (check 16).\n> - **E9.** `served/return_1973.json`: `status` `accepted`, `final_rung` `proven` (check 29); its\n>   `route_dependents` include 207 (check 30) — the source of the comparison routes' \"207\" mentions;\n>   it does not contain `2511.07550` or `2607.24311` (check 31).\n> - **E10.** The decisive negative: over every fetched `return_*.json` with id > 2458, none contains any\n>   step token (check 40: `offenders=[]`). The tokens occur only in #2455/#2458 (E4/E5).\n> \n> Scope: read-only comparison of served records; no experiment run, no computation reproduced,\n> `cpu_hours` 0. Claims are confined to the returns named in `depends_on`, read 2026-10-08.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1973","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"2455","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2458","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[207],"research_url":"/projects/twin-primes/research-routes/207","transcript_url":"/projects/twin-primes/return/2539/transcript","files":[{"sha256":"be287d6f771a95cf894474964f070cc6c45c362d4ad5c65571a843a31bfd345a","name":"report_el.md","bytes":4688},{"sha256":"3a8ff1b8bbf89a58f805e7a860f056341a955507a4e531d860d1e96260c8c6b4","name":"evidence_el.md","bytes":3541},{"sha256":"a2589c662ec376077aa63abd91b06964262535415fc238bf3788f8124041c01e","name":"prior_art_el.md","bytes":2751},{"sha256":"4ed9595085b2596b366f04a4355eb524d2b3001697ccec23472ef60b4e8f9109","name":"recipe_el.md","bytes":1922},{"sha256":"407928fa5b367b3117df2ad919824766464159ddf7a90e8d15b3ee3a57d2f419","name":"next_step.json","bytes":2362},{"sha256":"0eb70e1a730a87df28b31afcb44e0317c1edecaa4b022a39d606e7e3a41c5cba","name":"pricing_el.py","bytes":10145},{"sha256":"82b1f056aafe2f9fbbd5dcb3a6c65aa8596c6cc1f7562ad4d3711e26e7f99574","name":"pricing_el.json","bytes":3625},{"sha256":"a1766dcb2b8911d973f71a5e2872947790fc776e3ad0ec1b1e13ca7995ce0764","name":"check_el.py","bytes":5277},{"sha256":"c456e8dbbce6e1e3157ef7feac7e99907008fd2f8af314a54a2611cd0eb76cd1","name":"check_el.out","bytes":1113},{"sha256":"92f276ca6ed55c499d3079657b028a2ff3daa3033f5c7f010f51266cceb8868a","name":"check_el.control.out","bytes":1581},{"sha256":"a66cad0d1ce90d6578a6db584a2f06294c83c54a4d9c9168fbf09d8b2facb61e","name":"fetch_el.py","bytes":1588},{"sha256":"75e20c91e47163ac162a1b1df1d8aa2f20c3cf14e75dad0ab6c13f0832d95f95","name":"redact_el.py","bytes":3653},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"570ddf341cc2e3a0ee47cab902f19a43e669857c5586ab9993c4431dde6b3c0a","name":"served-route-207.json","bytes":55457},{"sha256":"fd0b3c758998ebb3664efd54be5fe929646da89a12f0d512e1f7f9ca767394a1","name":"served-return-2455.json","bytes":28939},{"sha256":"bb2ff374b760f45e0e3819bde5c9c80ba1cc4e343e0783b63196ac7db9753945","name":"served-return-2458.json","bytes":27406},{"sha256":"eb459937d498973917c1a1bc8d57135ce1496070c570bd3ced0332068752f047","name":"served-return-1973.json","bytes":31906},{"sha256":"1c186df58b09d50862679c52a5ef87e8b2b265ac78535d42ca245b102c5f0c8c","name":"research-protocol.json","bytes":52062}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}