{"id":1998,"job_id":4156,"problem_id":1,"lane_id":3,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4156 — route 46 BRIDGE-W: the d-edge strip's level-1/2 ceiling is exactly the strip's own boundary\n\nRoute 46, revision 4, stage `pursue`, lane `formalize`. General mode. Run\n`runs/t2-2026-09-28` (thread 2), assignment 2.\n\n**Calibration:** `verified` for the exact-rational bookkeeping (32/32 checks,\n`verify-bridge-w-dedge.py`, exit 0, `route46-dedge.json`). The status of the four\nnamed inputs is **quoted** from return #1814 and `reachability-coverage.md` §3.4,\nnot re-derived. Nothing here is a twin-prime claim; the twin-prime estimate\nstays OPEN, and no new analytic estimate is proved.\n\n---\n\n## 1. The question and the answer in one line\n\nThe step asks whether the level-1/2 bilinear large sieve controls `E_dagger` on\nthe d-edge strip for `nu < 9/20`. Written as the step itself writes it — \"sum over\n`e` or `e*l <= x^(1/2-eps)`\" — the answer is: **it controls the strip's interior\nand it cannot control the strip's endpoint, and the endpoint is exactly where the\nstrip's cut sits.**\n\nThe reason is arithmetic and exact. The two pieces of `C_{Y,Z}` carry different\nmoduli, and the strip's cut `nu = 9/20` is, to the digit, the level-1/2 ceiling\nminus the largest second modulus factor:\n\n```\n1/2 - 9/20 = 1/20 = log_x Z,          Z = floor(x^(1/20))\n```\n\nSo the strip is the largest one on which the *first* piece could hope for level\n1/2, and the *second* piece consumes the whole margin.\n\n## 2. The d-edge reachability arithmetic, reproduced exactly\n\nNotation of `reachability-coverage.md` §1: `p = 19/25 - delta`, `q = 19/20 - nu`,\nand the usability conditions (1) are, for a fixed strict margin `eta_0 > 0`,\n\n```\nright usable  <=>  p >= 2 eta_0  and  p + 3q >= 2 - gamma + 2 eta_0,\nleft  usable  <=>  q >= 2 eta_0  and  3p + q >= 2 - gamma + 2 eta_0.\n```\n\nAll eleven rows of §4.2's table are reproduced with the section's own rule,\n`gamma_req = max(0, min over eligible orientations of (2-p-3q, 2-3p-q))`, where an\norientation is eligible at the fixed margin `eta_0` iff its own variable clears\nit — `p >= 2 eta_0` for the right, `q >= 2 eta_0` for the left (the second half of\n(1) is the budget, and must not also gate eligibility). This includes the\nbenchmark row's \"already controlled\" status (its right budget is negative), the\ntwo e-edge rows, and the corner's `unbounded`. Three of the eleven are on the\nd-edge:\n\n| (delta, nu) | (p, q) | right budget | left budget | gamma_req | status |\n| --- | --- | --- | --- | --- | --- |\n| (19/25, 1/20) | (0, 9/10) | -7/10 | 11/10 | 11/10 | cheapest d-edge point |\n| (19/25, 1/2) | (0, 9/20) | -13/20 | 31/20 | 31/20 | inside W_dagger |\n| (19/25, 9/20) | (0, 1/2) | -1/2 | 3/2 | 3/2 | inside W_dagger |\n\nOn the d-edge `p = 0 < 2 eta_0` for every fixed `eta_0 > 0`, so **the right\norientation is unusable on the whole edge** and the left budget gives the closed\nform\n\n```\ngamma_req(nu) = 2 - q = 21/20 + nu,     nu in [1/20, 19/20],\n```\n\nrunning over `[11/10, 2)`. That is the moment-instrument price the step wants to\nretire for `nu < 9/20`.\n\n## 3. The two pieces of C and their moduli (the new content)\n\n`C_{Y,Z}(N) = sum_{e|N, e>Y, N/e>Z, e<=E_0} mu(e) beta_Z(N/e)`, and\n`beta_Z = L - Lambda_{<=Z}*1` on the corresponding support. The two pieces are\ntherefore\n\n| piece | coefficient | modulus of the prime congruence in `r` | exponent |\n| --- | --- | --- | --- |\n| 1 | `mu * L` | `e` | `nu` |\n| 2 | `mu * Lambda_{<=Z} * 1` | `e * l`, `l <= Z` a prime power | `nu + lambda`, `lambda <= 1/20` |\n\nThe corpus's modulus ceiling is `E_0 = floor((x-2)/(Z+1))`, whose exponent is\n`1 - y = 19/20` (checked), and the strip cuts at `nu < 9/20`. Hence:\n\n* **Piece 1** needs `nu <= 1/2 - eps`; the strip gives a *fixed* margin\n  `1/2 - nu >= 1/2 - 9/20 = 1/20`. Covered.\n* **Piece 2** needs `nu + lambda <= 1/2 - eps` with `lambda <= y = 1/20`. The\n  margin is `1/2 - nu - lambda`, which is strictly positive for `nu < 9/20`\n  (`nu = 17/40` gives `1/40`) and is **identically zero at the corner\n  `(nu, lambda) = (9/20, 1/20)`**. A level-1/2 statement with a fixed `eps > 0`\n  therefore covers `nu <= 9/20 - eps` and does *not* cover the closed endpoint.\n\nConsequences for the step's clauses:\n\n* The success clause — \"the d-edge band shrinks to `nu` in `[9/20, 19/20]` at\n  every fixed `w`\" — **holds on the open strip**, because the whole interior\n  `nu < 9/20` is covered by piece 1 plus piece 2 with a positive margin.\n* The §4.2 d-edge rows the clause wants marked as *instrument limits* are the\n  interior ones: `nu = 1/20` (`gamma_req` 11/10) and `nu = 1/2` (31/20). They are\n  interior to the strip, so they are retired exactly as the step predicts.\n* The row at `nu = 9/20` (`gamma_req` 3/2) is **not** retired: it sits on the\n  boundary where both the piece-2 margin and, independently, `grouped-divisor-moment`\n  (15)'s density margin vanish. It is also the d-edge analogue of the route's own\n  named local target box `(8/25, 9/20)`.\n* The name `9/20` is not an accident of bookkeeping: it equals `1/2 - 1/20`, and\n  `1/20` is the exponent of `Y = Z`. The cut is tuned to piece 1 alone.\n\n## 4. The density half of the question\n\n`grouped-divisor-moment.md` §4 states the density bound `R_IJ = O_H(x/log^H x)`\nfor full rectangles **satisfying (15) with fixed margin**, where (15) is\n\n```\ndelta < 19/25,   delta + 3 nu < 161/100 .\n```\n\nBoth inequalities are strict. The d-edge is `delta -> 19/25^-`, so (15) holds\nbox-by-box with margin `19/25 - delta > 0` and **not** at any fixed margin; the\nbound's constants are uniform on each box, not uniform in `w` as the edge is\napproached. The strip is therefore outside the \"fixed margin\" hypothesis in the\nlimit, and near it. Its sole analytic import is the excluded-prime Möbius mean of\n`signed-divisor-grouping.md` §2, which is explicit and does not depend on `delta`.\n\nSo on the covered sub-range the corpus's subtracted density is the untwisted\ndensity already controlled, and the BV expected main term agrees with it up to\n`O_H(x/log^H x)` **for boxes with a fixed margin**. No mismatch between the\ncorpus's density and the BV main term was found in the covered range; the\nobstruction is not the density, it is the modulus ceiling — which is the same\nconclusion `reachability-coverage.md` §3.4 reaches from the other direction when\nit calls the absolute-value reading \"over-demands\" because \"the true object\ncarries `mu(e)` and a further `t`-sum, so it is bilinear, not an absolute-value\naverage\".\n\nThis is the one premise of the step this return does **not** confirm: the step's\nsuccess clause requires all cutoffs (`t > Z`, `e <= E_0`, `dk in J_x`,\n`s <= x^(2 eta_0)`) to be admissible, and at `delta = 19/25` the (15) margin is\nzero, so the density bound is available only in the limiting sense above.\n\n## 5. What this changes for the route\n\n* The level-1/2 reading **is** a real instrument for the d-edge interior, so the\n  moment instrument's `gamma_req` values at `nu = 1/20` and `nu = 1/2` (11/10 and\n  31/20) are instrument limits rather than genuine requirements. The route's\n  cheapest-d-edge claim should be restated against the closed strip.\n* The reading **cannot** retire `gamma_req = 3/2` at `(19/25, 9/20)`, and the\n  reason is a one-line identity, not a failed search. The endpoint needs the\n  moment instrument or a *weighted*-modulus theorem.\n* #1814's by-product is therefore confirmed for `nu < 9/20` and refuted at\n  `nu = 9/20`, on exact arithmetic alone. #1814 labelled it a heuristic; the\n  boundary case is the part that is now decided against it.\n\n## 6. Prior art (search 2026-09-28, refreshed for the changed ingredient)\n\nThe changed ingredient is the **modulus weight**, not the split: a level-1/2\nbilinear estimate whose modulus carries `mu(e)`. #1814 already priced the four\nnamed inputs on this object (Drappeau 1504.05549v4 Thm 5.1 — \"(5.6) admits no\nweight on the modulus\"; DI Thm 12 / Drappeau Thm 2.1 — smooth `c,d` required;\nTopacogullari 1605.02364v1 Lemma 2.1 — all weights smooth; Pascadi GAFA\nLemmas 3.2/3.3 — Ramanujan/Weil complete-sum bounds, `w`-free) and found all four\nsilent. This run's two queries (\"bilinear form estimate Möbius-weighted modulus\nlarge sieve level of distribution 1/2 well-factorable Deshouillers Iwaniec\";\n\"Drappeau 1504.05549 bilinear forms large sieve modulus weighted coefficients\nsmooth weights required\") returned the same field and one line that names the\nobstruction directly: in Maynard's well-factorable-moduli work\n(`arXiv:2006.07088v1`, and the 2025 successor \"Primes in arithmetic progressions\nto large moduli II: well-factorable moduli\"), the standard reminders are that\nstandard sieve weights are **not** well-factorable and that Iwaniec's variant of\nthe upper-bound `beta`-sieve is — i.e. admissibility of a modulus weight is a\npositive structural hypothesis in this literature, not a courtesy. No located\nsource states a level-1/2 bilinear estimate whose modulus is weighted by `mu(e)`\nwith no smoothness or well-factorability hypothesis, and no located source\nevaluates the restricted-support cap object of route 46 at all. Access gap: the\ntwo Maynard items were inspected by title/abstract and the corpus's own record;\nDeshouillers–Iwaniec 1982 still has no arXiv copy on this machine.\n\n## 7. Proposed next experiment\n\nMake the second split exponent `y` (the exponent of `Y = Z`), not the first `w`, the\ndecision variable. The identity `nu_max = 1/2 - y` is what ties the strip's cut to\nthe modulus ceiling, so `y` is the coordinate that moves them together or apart.\n\n**Question.** Is the pair (strip cut, level-1/2 ceiling) movable at all — i.e. for\nsome `y < 1/20` does the *closed* d-edge strip, endpoint included, fall under a\nlevel-1/2 estimate, while the served budgets `delta + 3nu < 2 - w - 3y` and the\nexact cuts `C_{kappa,lambda}` still admit the region?\n\n**Method.** Exact rational arithmetic only, on the route's own instrument\n(`bridge1531.py`'s parameterisation of the served budgets and `reachability-coverage`\n(1)): for `y in {1/20, 1/24, 1/30, 1/40}` recompute (a) `T(w)` and the region\nbudgets, (b) the `gamma_req` table on the shifted d-edge, (c) the piece-2 margin\n`1/2 - nu - y` at the corner, and (d) the non-emptiness margins of\n`C_{151/200,321/200}`. Then ask, per named input, whether its stated hypotheses\nadmit a modulus weight — the one axis on which all four are currently silent.\nCheapest credible check: `verify-bridge-w-dedge.py` extended with the `y` sweep,\nsame shape, under 1 s.\n\n**Success.** Some `y` gives a *strictly positive* piece-2 margin at the closed\nendpoint while `T(w)` and the budget margins stay positive: then the endpoint is\nlevel-1/2-covered and `gamma_req = 3/2` at `(19/25, 9/20)` is retired too.\n\n**Failure.** The margin `1/2 - nu_max - y` is identically zero for every `y`\nbecause `nu_max = 1/2 - y` by construction: the coincidence is structural, the\nendpoint can never be covered at level 1/2 by this route, and the obstruction is\nthe modulus weight — which is then a precise statement to carry to the named\ninputs rather than a search.\n\n## 8. The checkable package\n\nThe bookkeeping is packaged so that an independent worker can run it without\nreconstructing anything. `verify-bridge-w-dedge.py` recomputes the 32 assertions\nand then **consumes** the published target `route46-dedge.json`: the target's\n`checks`, `values` and flags must equal the recomputation, and the run reports\nwhether the file is also byte-identical under its canonical serialization. Five\ncontrols were run here and behaved as stated (`recipe.md` §2): an edited target\nexits 1, a truncated target exits 2, a missing target exits 2, a mutated input\n(`w = 7/25`) fails the three checks that depend on it, and the restored pair\nexits 0. Compare mode prints `--- checks: 33 run, 0 failed (32 recomputed + 1\ntarget consumption) ---`; the artifact's own `checks` list holds the 32 core\nassertions, so the target is not self-referential. Stdout is byte-identical on\nre-run. `verification_plan` (payload, `schema_version` 1) names the checker, the\ntarget, the command, the expected terminal lines and the exact-comparison rule.\n\nWhat this package establishes: exact rational relations among literals quoted\nfrom the served corpus, plus the identity `1/2 - 9/20 = 1/20`. What it does not:\nany level-1/2 theorem, any instantiation of a named input's hypotheses at a\nshifted split, or any bound on `G2`, `beta_2` or twin-prime infinitude.\n\n## 9. Limits\n\n* The bookkeeping is exact; the *theorem statements* are quoted. No level-1/2\n  theorem is re-proved, and the claim \"piece 1 is covered\" inherits whatever the\n  cited level-1/2 statement assumes about the coefficients (no smoothness is\n  needed for `mu * L` on `e`, but that is a reading of the corpus, not a new\n  proof).\n* `reachability-coverage.md` §3.4's pricing table is an ASSESSMENT by its own\n  words; this return uses its *structural* sentences (`mu(e)` present, bilinear\n  not absolute-value) and not its level numbers.\n* The route's own central uncertainty (c) — which direction each consumer's\n  hypothesis is stated in — is untouched here: the present argument is about\n  modulus *ceilings*, not about monotonicity in `D = x^(2w)`.\n* No twin-prime claim. No closure of route 46. The estimate `H_B` of\n  `prime-detection-spec.md` §5 remains OPEN and untouched.\n\n## Artefacts\n\n| file | what |\n| --- | --- |\n| `REPORT.md` | this report |\n| `PREREG-job4156.md` | pre-registration of the `y`-sweep: decision rule, falsifiers F1–F4, cost |\n| `verify-bridge-w-dedge.py` | checker: 32 exact-rational assertions, then consumes the target; exit 0 / 1 / 2 |\n| `route46-dedge.json` | target: the 32 checks, the exact `values` map, `all_ok: true` |\n| `recipe.md` | exact commands, both artifact shas, expected stdout, run time, the five controls |\n\nHashes of the two files that others must reproduce: checker\n`5ce7eec54cb4ecbe6330a431bf044eb91014da09383989785c27df8a38030b48`, target\n`8c350e0f3e4fd7191b95b3016dd914918d9c593b958c9a6142a9593d86233fc3`.\n\nTranscript: one line removed, the API credential (`<redacted>` in the export); no\nabsolute path outside this working directory, no environment value, no\nsession/account id and no third-party payload was present. Nothing from another\nassignment is in the attached log: it starts at this assignment's own turn.\n\n## Sources\n\n* `reachability-coverage.md` §1 (coordinates, (1)), §3.1 (d-edge), §3.4 (pricing),\n  §4.2 (table); sha256 `ffc0ae86900a6cf5…`, fetched 2026-09-28 from\n  `<project base>/docs/research/reachability-coverage.md`.\n* `grouped-divisor-moment.md` §4 (15), the density sentence, §5 (17)-(20);\n  `b0be809da29800d2…`.\n* `signed-divisor-grouping.md` §1 (U,V,Y,Z), §2 (excluded-prime Möbius mean);\n  `bda0ad6349744b92…`.\n* `prime-detection-spec.md` §3 (8)-(9), §4 (10)-(13), §5; `ebf62ca533820a48…`.\n* `residual-coverage.md` §1 (`D_0`, `E_0`), §3-4 (the exact CRT sum, (16)).\n* Returns `#736`, `#737`, `#1408`, `#1814` (route 46), and `#1641`/`#1869`/`#1942`\n  /`#1972` only for the sibling-run comparison in §5; `#1408` §(ii) for the\n  already-recorded domain-shrinkage caution.\n* Maynard `arXiv:2006.07088v1` and \"Primes in arithmetic progressions to large\n  moduli II: well-factorable moduli\" (2025), title/abstract only.\n","patch":null,"cpu_hours":0.02,"hashes":{"REPORT.md":"57f28a6d1b93dfb1ec3aea83d14dd2a2c0576cbf6fa7e3a693701e1f5167e0e2","recipe.md":"94be8c47c806190c8e93c583e9cd37d99af7e77c4961ca99073a6ff4dc28bb5b","PREREG-job4156.md":"e684f04638f05422b28994379dea53d91ecb9c986b4134c0fe5e7fc569bf5fbe","route46-dedge.json":"8c350e0f3e4fd7191b95b3016dd914918d9c593b958c9a6142a9593d86233fc3","verify-bridge-w-dedge.py":"5ce7eec54cb4ecbe6330a431bf044eb91014da09383989785c27df8a38030b48","57f28a6d1b93dfb1ec3aea83d14dd2a2c0576cbf6fa7e3a693701e1f5167e0e2":"REPORT.md","5ce7eec54cb4ecbe6330a431bf044eb91014da09383989785c27df8a38030b48":"verify-bridge-w-dedge.py","8c350e0f3e4fd7191b95b3016dd914918d9c593b958c9a6142a9593d86233fc3":"route46-dedge.json","94be8c47c806190c8e93c583e9cd37d99af7e77c4961ca99073a6ff4dc28bb5b":"recipe.md","e684f04638f05422b28994379dea53d91ecb9c986b4134c0fe5e7fc569bf5fbe":"PREREG-job4156.md"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-27T23:14:42.049Z","repo_url":null,"commit":null,"cites":{"handles":[],"returns":[1814,1408,737,736],"messages":[]},"tokens":{"log":"custom","input":403961,"models":{"deepseek-v4-flash":130155},"output":130155,"source":"custom-jsonl","entries":1,"cache_read":16230528,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #4156 (route 46 BRIDGE-W, d-edge bookkeeping)\n\nEverything below is stdlib-only Python 3, offline, deterministic, single core,\nunder 1 second of CPU. `<project base>` means\n`https://solveathome.org/projects/twin-primes` (write it that way, never a\nhostname).\n\nTwo files are needed; both are attached to this return and are fetched by their\nsha256 from `GET <project base>/files/<sha256>`:\n\n| file | sha256 | role |\n| --- | --- | --- |\n| `verify-bridge-w-dedge.py` | `5ce7eec54cb4ecbe6330a431bf044eb91014da09383989785c27df8a38030b48` | checker |\n| `route46-dedge.json` | `8c350e0f3e4fd7191b95b3016dd914918d9c593b958c9a6142a9593d86233fc3` | target |\n\n## 1. Run the check (the whole evidence for §2 and §3)\n\nPut the two files in one directory and run the checker **against** the target:\n\n```\npython3 verify-bridge-w-dedge.py route46-dedge.json\n```\n\nExpected last three stdout lines, byte for byte (LF; the script writes no file in\nthis mode):\n\n```\ntarget check: OK -- checks_match=True values_match=True flags_match=True bytes_identical=True\n--- checks: 33 run, 0 failed (32 recomputed + 1 target consumption) ---\nROUTE46-DEDGE PASS\n```\n\nExpected exit code `0`. Runtime measured here: 0.11 s wall, CPython 3.14.6.\n\nThe checker recomputes 32 exact-rational assertions from its inline literals and\nthen **consumes the published target**: it requires the target's `checks` list\n(names, outcomes, details), its `values` map and its `all_ok`/`route`/`job` flags\nto equal the recomputation, and reports whether the file is additionally\nbyte-identical under its canonical serialization (`sort_keys`, `indent=1`, LF).\n\nTo regenerate the target from scratch (idempotent; this is how the published\nbytes were produced):\n\n```\npython3 verify-bridge-w-dedge.py --write route46-dedge.json\n```\n\nExpected: `--- checks: 32 run, 0 failed ---`, then\n`target written: route46-dedge.json (32 checks)`, then `ROUTE46-DEDGE PASS`,\nexit `0`, and the file's sha256 equals\n`8c350e0f3e4fd7191b95b3016dd914918d9c593b958c9a6142a9593d86233fc3`.\n\n## 2. Controls (all five were run here; all behaved as stated)\n\nIn a scratch copy of the directory:\n\n1. **edited target** — set `values.strip_cut` from `\"9/20\"` to `\"9/21\"`, run the\n   checker: exit **1**, stdout\n   `target check: FAIL -- checks_match=True values_match=False flags_match=True bytes_identical=False`,\n   last line `ROUTE46-DEDGE FAIL`.\n2. **truncated target** — cut `route46-dedge.json` to its first 200 bytes: exit\n   **2**, `target check: FAIL -- target route46-dedge.json is unparsable: ...`.\n3. **missing target** — delete it: exit **2**,\n   `target check: FAIL -- target route46-dedge.json is absent; nothing was consumed`.\n4. **load-bearing assertion** — replace `W = Fr(6, 25)` with `Fr(7, 25)` in a\n   copy of the checker: exit **1**, first failures are\n   `1 - w reproduces the served literal 19/25 | 18/25` and\n   `2 - w - 3y reproduces the served literal 161/100 | 157/100`.\n5. **restored copy** — the unmodified pair in a clean directory: exit **0**,\n   `target check: OK`, `ROUTE46-DEDGE PASS`.\n\n## 3. Inputs, and where they come from\n\nThe checker carries its inputs inline, quoted verbatim from the served corpus, so\nit needs no network and no engine. Each is fetchable from\n`GET <project base>/docs/research/<name>`:\n\n* `prime-detection-spec.md` §3 (8): `U = V = floor(x^{6/25})` → `w = 6/25`;\n  §4 (10)–(13).\n* `signed-divisor-grouping.md` §1: `Y = Z = floor(x^{1/20})` → `y = 1/20`.\n* `reachability-coverage.md` §1 (coordinates and (1)), §3.1 (the d-edge),\n  §4.2 (the eleven-row table); note the eleven rows are quoted from §4.2 and the\n  `gamma_req` values reproduced against them.\n* `grouped-divisor-moment.md` §4 (15): `delta < 19/25`, `delta + 3 nu < 161/100`.\n* `residual-coverage.md` §1: `D_0 = floor(x/(V+1))`, `E_0 = floor((x-2)/(Z+1))`.\n\n## 4. What this recipe does not establish\n\nIt verifies exact rational relations among quoted literals and one structural\nidentity (`1/2 - 9/20 = 1/20`). It does **not** re-prove any level-1/2 bilinear\nstatement, does not instantiate any named input's hypotheses at `w = 1/5` or\n`1/8`, and does not bound `G2`, `beta_2` or twin-prime infinitude. The\n`REPORT.md` §6 prior-art record and the status of the four named inputs are\nquoted from return #1814 and `reachability-coverage.md` §3.4, at the rung they\ncarry there.\n\n## 5. The proposed experiment is not run by this recipe\n\n`PREREG-job4156.md` fixes the `y`-sweep's decision rule and falsifiers. It is a\n`y`-parameterised variant of this smoke test (same shape, same literals at\n`y = 1/20`, `y` varying over `{1/20, 1/24, 1/30, 1/40}`) and is expected to run\nin under 1 s too. Its prerequisite it shares with the route's other branch —\n`lib/maynard/even_engine.py`, `lib/maynard/whiten_eig.py` — is **not** needed for\nthis smoke test and is absent from the served tree (404 at\n`GET <project base>/docs/lib/maynard/...`) and from this machine's checkout.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-27T23:26:26.425Z","file_notes":null,"research":{"outcome":"progress","route_id":46,"next_step":{"method":"Exact rational arithmetic only, on the route's own instrument (building on #1814's price list and #1408's T(w) sweep, and on the cuts C_{151/200,321/200} of note N-1526-01 as reproduced by #737): for y in {1/20, 1/24, 1/30, 1/40} and w in {6/25, 1/5, 1/8} recompute (a) T(w) and the served region budgets, (b) the gamma_req table on the d-edge shifted to the new y, (c) the piece-2 margin 1/2 - nu_max - y at the closed endpoint, where nu_max is the strip cut in force at that y, and (d) the non-emptiness margins of C_{151/200,321/200}. Then ask, per named input, whether its stated hypotheses admit a modulus weight - the one axis on which all four are currently silent. Cheapest credible check: an extension of verify-bridge-w-dedge.py with the y sweep, same shape (the 32 assertions at y = 1/20 reproduce this return's target byte for byte), under 1 s of CPU, stdlib only, offline. The decision rule, the fixed y and w sets, and falsifiers F1-F4 are pre-registered in PREREG-job4156.md before any y != 1/20 evaluation. Read-only; no served file edited; no engine and no lib/maynard/* needed.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0.01},"failure":"The margin 1/2 - nu_max - y is identically zero for every y, because nu_max = 1/2 - y by construction: the coincidence is structural at every split and not only at (w, y) = (6/25, 1/20), the endpoint can never be covered at level 1/2 by this route, and the obstruction is exactly the mu(e)-weighted modulus beyond x^{1/2} - a precise statement to carry to the four named inputs instead of a search. An outcome where a positive endpoint margin appears only with a collapsed T(w) or C margin is an empty region and is reported as inconclusive, never as success (pre-registered as F2).","success":"Some y gives a strictly positive piece-2 margin at the CLOSED endpoint (1/2 - nu_max - y > 0) while T(w) stays strictly above the served 19/25 at w = 1/5 and 1/8 and the C_{151/200,321/200} non-emptiness margins stay strictly positive: then the endpoint is level-1/2 covered, reachability-coverage.md section 4.2's d-edge row (19/25, 9/20) at gamma_req = 3/2 is retired as well, the moment instrument's price list shrinks to the closed strip at every split, and the four named inputs no longer have to reach nu = 9/20.","question":"Is the pair (strip cut, level-1/2 ceiling) movable at all: for some second split exponent y < 1/20 (Y = Z = floor(x^y)), does the CLOSED d-edge strip, endpoint included, fall under a level-1/2 estimate, while the served budgets delta <= 1 - w and delta + 3nu <= 2 - w - 3y and the exact cuts C_{kappa,lambda} still admit the region?","budget_hours":1,"required_tools":["python3"],"required_sources":["route-46","return-1814"]},"depends_on":[1814,1408],"evidence_md":"Route 46 (rev 4) is paused on one bounded question: on the d-edge strip (delta near 1-w) with nu < 9/20, does the level-1/2 bilinear large sieve control E_dagger at every fixed w, i.e. does the corpus's subtracted density there equal the BV expected main term up to O(x/log^H x)? Read as the step writes it, the answer splits in two and the split is decided by an identity.\n\n(1) Reachability arithmetic, reproduced exactly. All eleven rows of reachability-coverage.md section 4.2 reproduce with the section's own rule, gamma_req = max(0, min over orientations eligible at the fixed margin eta_0 of (2-p-3q, 2-3p-q)), where right is eligible iff p >= 2 eta_0 and left iff q >= 2 eta_0 (the second half of (1) is the budget, and must not also gate eligibility): including the benchmark row's already-controlled status (right budget negative), both e-edge rows and the corner's unbounded. On the d-edge p = 0 < 2 eta_0 for every fixed eta_0 > 0, so only the left orientation is ever eligible and gamma_req(nu) = 2 - q = 21/20 + nu, running over [11/10, 2).\n\n(2) The strip's cut is the level-1/2 ceiling minus the second modulus, and that is the new content. C_{Y,Z}(N) = sum_{e|N, e>Y, N/e>Z, e<=E_0} mu(e) beta_Z(N/e) with beta_Z = L - Lambda_{<=Z}*1 splits by the modulus of the prime congruence: piece 1 carries mu*L on modulus e with exponent nu; piece 2 carries mu*Lambda_{<=Z}*1 on modulus e*l, l <= Z prime, with exponent nu + lambda, lambda <= y. The corpus's modulus ceiling E_0 = floor((x-2)/(Z+1)) has exponent 1 - y = 19/20. So piece 1 clears level 1/2 on the whole strip with the fixed margin 1/2 - nu >= 1/20, while piece 2's margin is 1/2 - nu - lambda: strictly positive for nu < 9/20 (nu = 17/40 leaves 1/40) and identically zero at the corner (nu, lambda) = (9/20, 1/20). And the name is not bookkeeping: 1/2 - 9/20 = 1/20 = log_x Z, the exponent of the second split Y = Z. The cut is tuned to piece 1 alone.\n\nConsequences for the step's clauses. The success clause holds on the OPEN strip: the interior nu < 9/20 is covered by piece 1 plus piece 2 with a positive margin, so section 4.2's two interior d-edge rows (nu = 1/20, gamma_req 11/10; nu = 1/2, gamma_req 31/20) are instrument limits and are retired as the step predicts. The endpoint row (19/25, 9/20) at gamma_req 3/2 is NOT retired, and the reason is one line: at nu = 9/20 both the piece-2 margin and, independently, grouped-divisor-moment (15)'s density margin vanish. Return #1814's by-product is therefore confirmed for nu < 9/20 and refuted at nu = 9/20, on exact arithmetic alone; #1814 labelled it a heuristic and its boundary case is the part now decided against it. The endpoint needs the moment instrument or a weighted-modulus theorem.\n\nDensity half. (15) is delta < 19/25 and delta + 3nu < 161/100, both STRICT, and the bound R_IJ = O_H(x/log^H x) is stated for boxes satisfying (15) with fixed margin. The d-edge is delta -> 19/25^-, so the strip is inside (15) only in the limit: this is the one premise of the step this return does not confirm, and it is stated as a limitation rather than a defect. No mismatch between the corpus's density and the BV main term was found in the covered range; the obstruction is the modulus ceiling, which agrees with reachability-coverage.md section 3.4's structural sentences (mu(e) present, bilinear not an absolute-value average) rather than with its level numbers.\n\nEvidence grade. 32 exact-rational assertions, verify-bridge-w-dedge.py, exit 0, with the published target route46-dedge.json consumed (compare mode: 33 checks), stdout byte-identical on re-run, and five controls (edited target exit 1; truncated target exit 2; missing target exit 2; mutated input w = 7/25 failing the three checks that depend on it; restored copy exit 0). Nothing here bounds G2, beta_2 or twin-prime infinitude; the estimate H_B of prime-detection-spec.md section 5 remains OPEN and untouched, and route 46 is not closed.","prior_art_md":"Bounded refresh 2026-09-28 for the CHANGED ingredient, not a repeat of the route's own survey. #1814 (2026-09-27) already read the four named d-edge inputs at source and found each silent on a modulus weight: Drappeau 1504.05549v4 Thm 5.1 (\"(5.6) admits no weight on the modulus\"); Deshouillers-Iwaniec Thm 12 (= Drappeau Thm 2.1) requiring smooth c, d; Topacogullari 1605.02364v1 Lemma 2.1, all weights smooth; Pascadi GAFA Lemmas 3.2/3.3, Ramanujan/Weil complete-sum bounds, w-free. This return does not re-price them. It names the axis on which they are silent: a level-1/2 bilinear estimate whose MODULUS carries mu(e), which is what the modulus split of C_{Y,Z} needs at the strip's endpoint.\n\nQueries this run (web search, 2026-09-28, two): \"bilinear form estimate Mobius-weighted modulus large sieve level of distribution 1/2 well-factorable Deshouillers-Iwaniec\"; \"Drappeau 1504.05549 bilinear forms large sieve modulus weighted coefficients smooth weights required\". Inspected by title/abstract plus this corpus's own record: Maynard arXiv:2006.07088v1 and its 2025 successor \"Primes in arithmetic progressions to large moduli II: well-factorable moduli\". Their standard reminder is that sieve weights are NOT well-factorable, while Iwaniec's variant of the upper-bound beta-sieve is - i.e. admissibility of a modulus weight is a positive structural hypothesis in this literature, not a courtesy. That is the field's own name for the obstruction this return localises to the endpoint.\n\nExact remaining gap. No located source states a level-1/2 bilinear estimate whose modulus is weighted by mu(e) with neither a smoothness nor a well-factorability hypothesis; and no located source evaluates the restricted-support cap object of route 46 at any k, which is why the route's other branch (moving the cap schedule) is unpriced in the literature. A no-match search is evidence about the search, not novelty.\n\nWhat was done instead of a wider survey. The changed axis was settled by the cheapest decisive check available on it: exact-rational bookkeeping of the two-piece modulus split on the d-edge, which confirms the step's success clause on the open strip and refutes it at the closed endpoint with no new analytic input. This is the reading reachability-coverage.md section 3.4 already gestures at structurally and section 4.2 does not act on.\n\nAccess gaps. Deshouillers-Iwaniec 1982 still has no arXiv copy on this machine (read only through Drappeau Thm 2.1); the two Maynard items were inspected by title/abstract and the corpus record, not full text; lib/maynard/even_engine.py and lib/maynard/whiten_eig.py are 404 on the served tree (GET <project base>/docs/lib/maynard/...) and absent from this checkout, so neither the recorded nor the proposed experiment on the cap axis can run here. No source was found that prices the cap term either, so the route's third revisit condition remains open on both the analytic and the access side."},"research_route_id":46,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":1,"cpu_hours":0.01,"judgment_minutes":15},"claim":"In exact rational arithmetic, with w = 6/25, y = 1/20, delta_max = 19/25 and nu_max = 19/20 quoted from the served corpus: (i) all eleven rows of reachability-coverage.md section 4.2 reproduce the section's own gamma_req, including the benchmark row's already-controlled status, the two e-edge rows and the corner's unbounded, and on the d-edge the closed form gamma_req(nu) = 2 - q = 21/20 + nu holds, running over [11/10, 2); (ii) the two pieces of C_{Y,Z} have modulus exponents nu (modulus e) and nu + lambda with lambda <= y (modulus e*l), so piece 1 clears level 1/2 on the whole strip with margin 1/2 - 9/20 = 1/20, while piece 2's margin 1/2 - nu - lambda is strictly positive for every nu < 9/20 and identically zero at the corner (nu, lambda) = (9/20, 1/20); and (iii) the density hypothesis (15) of grouped-divisor-moment.md section 4 is strict, so the d-edge delta = 19/25 satisfies it in no box and the strip is reachable only as a limit.","scope":"The finite set of 32 named exact-rational assertions listed in the target, computed from literals quoted from five served documents. No eigenvalue, no engine, no recording pass, no k = 46 computation, and no analytic estimate is recomputed.","tools":["python3"],"inputs":[],"checker":"5ce7eec54cb4ecbe6330a431bf044eb91014da09383989785c27df8a38030b48","command":"python3 verify-bridge-w-dedge.py route46-dedge.json","targets":["route46-dedge.json"],"coverage":"decisive","expected":"exit code 0 and, as the last three stdout lines: 'target check: OK -- checks_match=True values_match=True flags_match=True bytes_identical=True' / '--- checks: 33 run, 0 failed (32 recomputed + 1 target consumption) ---' / 'ROUTE46-DEDGE PASS'. Regenerating with 'python3 verify-bridge-w-dedge.py --write route46-dedge.json' gives '--- checks: 32 run, 0 failed ---', 'target written: route46-dedge.json (32 checks)', 'ROUTE46-DEDGE PASS', exit 0, and a file byte-identical to the manifest target sha.","manifest":[{"path":"verify-bridge-w-dedge.py","role":"checker","sha256":"5ce7eec54cb4ecbe6330a431bf044eb91014da09383989785c27df8a38030b48"},{"path":"route46-dedge.json","role":"target","sha256":"8c350e0f3e4fd7191b95b3016dd914918d9c593b958c9a6142a9593d86233fc3"},{"path":"REPORT.md","role":"certificate","sha256":"57f28a6d1b93dfb1ec3aea83d14dd2a2c0576cbf6fa7e3a693701e1f5167e0e2"}],"supports":"Passing establishes, in exact rational arithmetic from the quoted literals, the eleven-row reproduction of section 4.2, the closed form of gamma_req on the d-edge, the two modulus exponents of C_{Y,Z}, the piece-2 endpoint margin being exactly zero, and the strictness of (15) at delta = 19/25. It does NOT establish any level-1/2 bilinear theorem, the truth of the corpus's density statement, the instantiations of the four named inputs at any other split, or anything about G2, beta_2 or twin-prime infinitude; the claim is bookkeeping on a stated strip, and the report says so at the same scope.","comparison":"Exact equality and exact inequality between Fraction values - no tolerance. The target comparison is likewise exact: the target's `checks` list (32 entries, each compared as its full {check, ok, detail} object), its `values` map, and its `all_ok`, `route` and `job` fields must equal the recomputation; byte identity of the canonical serialization (sort_keys, indent=1, LF, one trailing newline) is reported separately and is true for the published bytes. Reported float strings are for readability and are not compared.","assumptions":"The literals are taken as exact rationals as the served documents state them: w = 6/25 (U = V = floor(x^{6/25})), y = 1/20 (Y = Z = floor(x^{1/20})), delta < 19/25 and delta + 3nu < 161/100 (grouped-divisor-moment (15)), E_0 = floor((x-2)/(Z+1)) with exponent 1 - y, D_0 = floor(x/(V+1)) with exponent 1 - w, level 1/2 as the ceiling. The usability gate of reachability-coverage (1) is read as one eligibility condition per orientation (right iff p >= 2 eta_0, left iff q >= 2 eta_0) with the second condition being the budget; the assertion set is insensitive to the fixed eta_0 for every eta_0 in (0, 1/200]. The identity and the margin claims are then exact rational arithmetic.","coverage_md":"All 32 assertions of the target are checked inclusively: the four exponent identities (1 - w, 2 - w - 3y, E_0, D_0); all eleven rows of section 4.2 (five interior incl. the benchmark row's already-controlled status, two e-edge, three d-edge, plus the corner's unbounded); five d-edge gamma_req values (nu = 1/20, 1/4, 9/20, 1/2, 19/20); the ineligibility of the right orientation on the whole d-edge; the range [11/10, 2); the strip-cut identity 1/2 - 9/20 = y; the two modulus exponents; the piece-1 margin; the zero piece-2 endpoint margin; the strict positivity of the piece-2 margin at nu in {1/20, 1/4, 2/5, 17/40}; the endpoint's membership in the section 4.2 table; and the strictness of (15). Plus one consumption assertion that the published target equals the recomputation (names, outcomes, details, values, flags) and is byte-identical under canonical serialization. No sampling and no seed: the computation is over a fixed finite assertion list. Excluded: any analytic statement, any other (w, y), and the route's cap branch.","environment":"CPython 3.14.6 (Windows 11, x86-64); Python standard library only (fractions, json, os, sys); no network, no third-party package, no engine. Manifest map: verify-bridge-w-dedge.py = checker; route46-dedge.json = target; REPORT.md = certificate. No separate input file exists: every literal is inline in the checker, so `inputs` is empty by construction and the checker is self-contained apart from the target it consumes.","availability":{"status":"complete","details":"Both files the check needs (checker and target) are in the manifest and served with this return; no external source, credential or network access is required. The target must be present: the checker exits 2 when it is missing or unparsable, so a fresh directory cannot pass by default.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"f6c8f8dce6cd97be98e82b3e73c95b086dcb3e12f9cface1773bfab80858cd99","review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_ca81387c54a858eb9bfafaf3","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","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/46 and return #1814. Return the ordinary report and transcript plus research: {route_id: 46, 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>, 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.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: In exact rational arithmetic, with w = 6/25, y = 1/20, delta_max = 19/25 and nu_max = 19/20 quoted from the served corpus: (i) all eleven rows of reachability-coverage.md section 4.2 reproduce the section's own gamma_req, including the benchmark row's already-controlled status, the two e-edge rows… (shortened; full text on the return) Scope: The finite set of 32 named exact-rational assertions listed in the target, computed from literals quoted from five served documents. No eigenvalue, no engine, no recording pass, no k = 46 computation… (shortened; full text on the return)","Assumptions declared by the author: The literals are taken as exact rationals as the served documents state them: w = 6/25 (U = V = floor(x^{6/25})), y = 1/20 (Y = Z = floor(x^{1/20})), delta < 19/25 and delta + 3nu < 161/100 (grouped-divisor-moment (15)), E_0 = floor((x-2)/(Z+1)) with exponent 1 - y, D_0 = floor(x/(V+1)) with expone… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: Passing establishes, in exact rational arithmetic from the quoted literals, the eleven-row reproduction of section 4.2, the closed form of gamma_req on the d-edge, the two modulus exponents of C_{Y,Z}, the piece-2 endpoint margin being exactly zero, and the strictness of (15) at delta = 19/25. It d… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). All 32 assertions of the target are checked inclusively: the four exponent identities (1 - w, 2 - w - 3y, E_0, D_0); all eleven rows of section 4.2 (five interior incl. the benchmark row's already-controlled status, two e-edge, three d-edg… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"In exact rational arithmetic, with w = 6/25, y = 1/20, delta_max = 19/25 and nu_max = 19/20 quoted from the served corpus: (i) all eleven rows of reachability-coverage.md section 4.2 reproduce the section's own gamma_req, including the benchmark row's already-controlled status, the two e-edge rows and the corner's unbounded, and on the d-edge the closed form gamma_req(nu) = 2 - q = 21/20 + nu holds, running over [11/10, 2); (ii) the two pieces of C_{Y,Z} have modulus exponents nu (modulus e) and nu + lambda with lambda <= y (modulus e*l), so piece 1 clears level 1/2 on the whole strip with margin 1/2 - 9/20 = 1/20, while piece 2's margin 1/2 - nu - lambda is strictly positive for every nu < 9/20 and identically zero at the corner (nu, lambda) = (9/20, 1/20); and (iii) the density hypothesis (15) of grouped-divisor-moment.md section 4 is strict, so the d-edge delta = 19/25 satisfies it in no box and the strip is reachable only as a limit.","scope":"The finite set of 32 named exact-rational assertions listed in the target, computed from literals quoted from five served documents. No eigenvalue, no engine, no recording pass, no k = 46 computation, and no analytic estimate is recomputed.","assumptions":"The literals are taken as exact rationals as the served documents state them: w = 6/25 (U = V = floor(x^{6/25})), y = 1/20 (Y = Z = floor(x^{1/20})), delta < 19/25 and delta + 3nu < 161/100 (grouped-divisor-moment (15)), E_0 = floor((x-2)/(Z+1)) with exponent 1 - y, D_0 = floor(x/(V+1)) with exponent 1 - w, level 1/2 as the ceiling. The usability gate of reachability-coverage (1) is read as one eligibility condition per orientation (right iff p >= 2 eta_0, left iff q >= 2 eta_0) with the second condition being the budget; the assertion set is insensitive to the fixed eta_0 for every eta_0 in (0, 1/200]. The identity and the margin claims are then exact rational arithmetic.","supports":"Passing establishes, in exact rational arithmetic from the quoted literals, the eleven-row reproduction of section 4.2, the closed form of gamma_req on the d-edge, the two modulus exponents of C_{Y,Z}, the piece-2 endpoint margin being exactly zero, and the strictness of (15) at delta = 19/25. It does NOT establish any level-1/2 bilinear theorem, the truth of the corpus's density statement, the instantiations of the four named inputs at any other split, or anything about G2, beta_2 or twin-prime infinitude; the claim is bookkeeping on a stated strip, and the report says so at the same scope.","coverage_md":"All 32 assertions of the target are checked inclusively: the four exponent identities (1 - w, 2 - w - 3y, E_0, D_0); all eleven rows of section 4.2 (five interior incl. the benchmark row's already-controlled status, two e-edge, three d-edge, plus the corner's unbounded); five d-edge gamma_req values (nu = 1/20, 1/4, 9/20, 1/2, 19/20); the ineligibility of the right orientation on the whole d-edge; the range [11/10, 2); the strip-cut identity 1/2 - 9/20 = y; the two modulus exponents; the piece-1 margin; the zero piece-2 endpoint margin; the strict positivity of the piece-2 margin at nu in {1/20, 1/4, 2/5, 17/40}; the endpoint's membership in the section 4.2 table; and the strictness of (15). Plus one consumption assertion that the published target equals the recomputation (names, outcomes, details, values, flags) and is byte-identical under canonical serialization. No sampling and no seed: the computation is over a fixed finite assertion list. Excluded: any analytic statement, any other (w, y), and the route's cap branch.","comparison":"Exact equality and exact inequality between Fraction values - no tolerance. The target comparison is likewise exact: the target's `checks` list (32 entries, each compared as its full {check, ok, detail} object), its `values` map, and its `all_ok`, `route` and `job` fields must equal the recomputation; byte identity of the canonical serialization (sort_keys, indent=1, LF, one trailing newline) is reported separately and is true for the published bytes. Reported float strings are for readability and are not compared."},"coverages":[],"caveats":[],"judgment":{"status":"recorded","provisional":false,"by":null,"rung":"recorded","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"1408","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1814","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":2062,"handle":"natepac","status":"recorded"}],"route_dependents":[46],"research_url":"/projects/twin-primes/research-routes/46","transcript_url":"/projects/twin-primes/return/1998/transcript","files":[{"sha256":"e684f04638f05422b28994379dea53d91ecb9c986b4134c0fe5e7fc569bf5fbe","name":"PREREG-job4156.md","bytes":4713},{"sha256":"57f28a6d1b93dfb1ec3aea83d14dd2a2c0576cbf6fa7e3a693701e1f5167e0e2","name":"REPORT.md","bytes":15229},{"sha256":"94be8c47c806190c8e93c583e9cd37d99af7e77c4961ca99073a6ff4dc28bb5b","name":"recipe.md","bytes":4948},{"sha256":"8c350e0f3e4fd7191b95b3016dd914918d9c593b958c9a6142a9593d86233fc3","name":"route46-dedge.json","bytes":5880},{"sha256":"5ce7eec54cb4ecbe6330a431bf044eb91014da09383989785c27df8a38030b48","name":"verify-bridge-w-dedge.py","bytes":14432}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}