{"id":5079,"job_id":10036,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #10036 — route 111 step check: the step is open, but its prescribed edit is inert and its failure threshold is wrong (4/3 vs 3 at n=0, 1.92 at the band's own N)\n\nType `explore`, stage **`first_look`**, lane `measure`, purpose discovery, `research_route_id` **111**,\nstep check before pursuit, general mode, session 1/1. `cpu_hours 0`: nothing is computed beyond exact\n`Fraction` arithmetic and one 51-check rerun of an existing offline checker (~3 s of one core).\nNo twin margin, no `o(x)`, no `P_band` and no `G_2` statement is claimed or refuted, and **no page-image\nreading is claimed** — that is the step, and it is what stays open.\n\n## 0. The step and the decision\n\nRoute 111's next experiment was set by **#3570** (job #4967): read ONE display of Fouvry 1987 at the page\nimage — the `(C.2)` line on p.619, the `(C.2)`-certifying display on p.632, and `S = lambda N^?` on p.637 —\nand then \"edit only `inputs_br.json`'s `recorded_C2_second_monomial` to the page-image reading\" and re-read\nthe frozen decision function's branch table. This return is the check before that pursuit is paid for.\n\n**Decision: the step is open on the record (outcome `promising`, step re-queued with a corrected decision\nrule), and the step as written cannot deliver its own verdict.** Two defects are measured, not argued:\n**(F1)** the prescribed edit is **inert** — the frozen checker never reads that field, so the table is the\nsame before and after any page reading; **(F2)** the step's own **failure threshold is wrong** — `(C.2)`\nstarts failing at `b >= 3` when `n -> 0` and at `b >= 1.9238` at the band's own `N`, not at the\n`R`-exponent `4/3` the clause names, so a correct intermediate reading (`R^{3/2}`, `R^{9/5}`, ...) would be\nrecorded under the failure branch while the frozen test says `(C.2)` still holds.\n\n## 1. What the record already says (bounded scan, 31 returns)\n\nRoute 111 is `active`, revision 20, `last_return_id 3570`, `next_job_id` **absent**; all 20 route events\ncarry `return_id <= 3570`, so **nothing on the route answers the step**. I fetched and read the route's 20\nreturns (#1340, #1351, #1414, #1418, #1818, #1982, #2046, #2084, #2156, #2161, #2166, #2168, #2290, #2294,\n#2521, #2565, #3511, #3523, #3546, #3570) plus the 16 comparison returns the brief lists (#5013, #2290,\n#2287, #2192, #2183, #2178, #2172, #2164, #2161, #2157, #2156, #2084, #2077, #2053, #1982, #1940), 31 files\nafter overlap. Measured token counts over that corpus:\n\n| question | answer |\n|---|---|\n| returns pairing \"page image\" with **both** `7/4` and `15/4` | **only #3570** (the setter) |\n| returns naming `recorded_C2_second_monomial` | **only #3570** |\n| returns citing p.619 | 10 (#1818, #2046, #2084, #2156, #2161, #2166, #2168, #2290, #2294, #3570) |\n| returns carrying the `(C.2)` question at all | 9 including #5013 (route 52) |\n\nThe p.619 citations are **literature** citations (the `(C.1)-(C.5)` condition list as the route's input);\nnone reports an exponent read off the scan. #5013 (route 52, 2026-10-20) records #3570's finding as progress\nand replaces its own decision rule with #3570's step, so it inherits the question, it does not answer it.\nSo the step is **not** `known`, and a pursuit is justified **once the step is executable**.\n\n## 2. The step's premise does hold: the layer cannot supply these exponents (independently reproduced)\n\n`src/fouvry1987.pdf` is the record's file: sha256 `13dec04a3f215c0b5809dcefe77cd11fcad8a8982ddb9c471f1b6b08fad61c7f`,\n1,874,562 bytes. The positioned-text dumps the step relies on **regenerate byte-identically** here\n(`layout_38/90/110.txt`, sha256 `56a8567b…`, `aadc121f…`, `9c3d3d49…`, equal to #3570's copies), and the\ntokens that matter are:\n\n* p.619 `(C.2)` line: superscript runs `[\"2\",\"2\",\"1\",\"6\"]` (i.e. `R^2`, `S^2`, `x^{1-e}`) and **5 literal\n  caret slots** — the second monomial's `R` and `S` exponents are among the carets.\n* p.632 display above *\"Ainsi le theoreme est prouve sous la condition (C. 2)\"*: superscript runs\n  `[\"15\",\"4\",\"1\",\"26\"]`, i.e. it carries `R^{15/4}` and `x^{-1}`; the string `7/4` occurs **nowhere** on p.632.\n* p.637 §VI.3: `R=x` (exponent `9` = `theta1`), `S= lambda N ^` — the `S` exponent is a caret.\n\nSo one page-image read is genuinely needed for one exponent, and the step's custodial premise is confirmed\nrather than merely repeated.\n\n## 3. F1 (measured): the prescribed edit cannot change any verdict\n\n`check_br.py` in `runs/run-2026-10-13-br/work` reproduces **51/51, exit 0** here. It contains **0**\noccurrences of `recorded_C2_second_monomial`: the field exists only in `inputs_br.json`, and the branch\ntable hard-codes `\"7/4\"` and `\"15/4\"`. Three scratch copies of the checker, each with the field set to a\ndifferent page-image reading, produce **byte-identical output** (51/51, same verdict block):\n\n| `recorded_C2_second_monomial` | exit | checks | printed verdicts |\n|---|---|---|---|\n| `N^(5/4) R^(7/4) S^2` (record) | 0 | 51/0 | `R^7/4: pass`, `R^15/4: fail` |\n| `N^(5/4) R^(15/4) S^2` | 0 | 51/0 | identical |\n| `N^(5/4) R^(4/3) S^2` | 0 | 51/0 | identical |\n\nA successor following the step verbatim will see 51/51 both before and after the edit and can mistake that\nfor confirmation. The instrument is a **fixed two-case table**, not a function of the reading; the carried\nexponent must be evaluated on its own.\n\n## 4. F2 (measured): the failure clause's threshold is not the branch boundary\n\nThe frozen model (stated in `check_br.py` itself) is\n`(C.2) = max(R^2 S, N^{5/4} R^b S^2) < x^{1-eps}` with `R = x^{theta1} = x^{1/3}` and `S = lambda N^nu`,\n`nu <= rho1 = 1/30`. The second monomial's condition is `(5/4 + 2nu) n + b/3 < 1`, `n = log N/log x`, so\n\n* `b = 7/4`: budget `5/12` (pass) — the record's branch;\n* `b = 15/4`: budget `-1/4` (fail for every `n >= 0`) — #3570's branch;\n* `b = 4/3`: budget **`+5/9`** (pass) — so *\"any R-exponent `>= 4/3` fails\"* is false;\n* the unconditional boundary is `b = 3` (`n -> 0`), and with the band's own `N = (log x)^L` (route 111's\n  `contribution_md`) it is `b*(x,L,nu) = 3 (1 - (5/4+2nu) L log log x / log x)`: at `x = 1e10`, `L = 2`,\n  `nu = 1/30` this is `n = 0.27244` and **`b* = 1.9238`**.\n\nSo at the band's own `N`, `R^{3/2}` **passes** the frozen test while the step's failure clause says any\n`R`-exponent `>= 4/3` fails; `R^2` fails, so the boundary is real, not a formality. The clause's numeric\nclaim is also only true at `b = 15/4`: the gap `(monomial / x)` is `x^{1/4}` there, but `x^{-5/9}` at\n`b = 4/3`. A page reading between `4/3` and `b*` would close the route on a case that the route's own model\ndoes not close.\n\n## 5. What the step gets right, and the one input it omits\n\nRight: the caret census on `(C.2)` (5 slots, `[\"2\",\"2\",\"1\",\"6\"]` recovered); p.632's `15/4` with no `7/4` on\nthe page; p.637's `S`-exponent caret; the first monomial `R^2 S` being automatic for every admissible `nu`\n(`2/3 + 1/30 = 7/10 < 1`); the case-3 window still needing `k >= 6` (`11/360 <= 1/30 < 11/300`); and the\nsuccess clause's bound `(5/4 + 2nu) n < 5/12 - eps`, which is exactly the `b = 7/4` budget.\n\nOmitted: the success clause asks for the band's own `N`, and the frozen instrument carries **no** `N`\n(`inputs_br.json`'s band block is exactly `{mu_cofactor_exponent, mu_max, subdivision, factor_d}`). The\nroute's own contribution supplies it — `N = (log x)^L`, so `n = L log log x / log x` — and the corrected\nstep should name that instead of leaving the successor to search for it.\n\n## 6. Rungs, falsifiers, scope\n\n* **Measured:** route/record state and the 20 route events; the 31-return scan and its token counts; PDF\n  custody; dumps regenerating byte-identically; the caret/exponent tokens on the three pages; the\n  inertness experiment (3 readings, identical output); all rational arithmetic above (`Fraction`, exact).\n* **Derived:** the boundary `b*(x,L,nu)` from the record's own `(C.2)` model; `n` at the band's own `N`.\n* **Labelled inference:** none is made about the page. The `(C.2)` exponents remain **unknown** and the\n  case-3 verdict remains **open**; this return does not reopen or close route 111.\n* **Falsifiers.** F1: a check that the named checker copy reads the field (it does not — 0 occurrences, and\n  the three scratch runs are byte-identical). F2: a reading of the step's failure clause that is meant as\n  \"the *record*'s `7/4` against p.632's `15/4` only\" — then the clause is a two-case shorthand and the\n  general threshold is not what it says; both readings disagree with the frozen test for `4/3 <= b < 1.92`.\n  The step is `known` if some return outside the 31 fetched already records the p.619 `(C.2)` exponents.\n* **Scope:** documentary and accounting only. Nothing here concerns the band's BFI II lemma, `P_band`,\n  `(4.9)`, `G_2`, `beta_2`, the `13/7980` deficit's value, or twin primes. `check_eg.py` is a step-check\n  instrument, not a new mathematical result.\n\n## 7. Reproduction\n\n```\ncd .solveathome/runs/run-2026-10-20-eg/work\npython3 check_eg.py                  # 34/34 PASS, exit 0\nfor n in 1 2 3 4 5 6 7 8; do python3 check_eg.py --corrupt $n; echo exit=$?; done   # each 1\npython3 fetch_eg.py route 111        # the route record and its events\ncd /work/.solveathome/runs/run-2026-10-13-br/work && python3 check_br.py            # 51/51, exit 0\n```\n\nArtifacts: `check_eg.py`, `check_eg.out`, `check_eg.control.out`, `check_eg.control1..8.out`,\n`fetch_eg.py`, `served/` (route + 31 returns + the three positioned dumps), `inputs_br.json` (a copy;\n#3570's file was not edited), `evidence_eg.md`, `recipe_eg.md`.\n\n6 of @Benjaminsen's returns still wait for a verdict; nothing is asked of the person here.\n","patch":null,"cpu_hours":0,"hashes":{"check_eg.py":"e7420f29f2fcc50979550ca925dd110a18eee27b3e706207e82c7c59206f0dd0","check_eg.out":"fc2d7eb48cbce0803fffa3a152c32c9a1fb88dca394ea76d9531e0ae8af45464","recipe_eg.md":"b04f640067b8bc4646ccb37602fb78c93ae3ebc93698c41c6ce7976da55000f7","report_eg.md":"cc8943a1e666353cb5476bffb127e6ef2d8e535a45e3283bc37cb13e483bf97e","evidence_eg.md":"b56535b9721387714162c07147f7cb188a249a7c834c6d27d73acd0908053fff","check_eg.control.out":"2dbb5a47b85d9709abce1060d46767c51e86035ddfe72e85c1d4bb9f07109990"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T18:19:37.538Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3570,5013,2294],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the freebuff/manicode harness exposes no per-turn input/output token counts to this agent, so usage is reported as unmeasured rather than estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — run-2026-10-20-eg (route 111 step check, job #10036)\n\n## What this return did (repeat exactly)\n\n```\ncd .solveathome/runs/run-2026-10-20-eg/work\npython3 fetch_eg.py route 111                      # route record (rev 20, last_return_id 3570, events, jobs)\npython3 fetch_eg.py return 1340 1351 1414 1418 1818 2046 2166 2168 2294 2521 2565 3511 3523 3546\npython3 fetch_eg.py return 5013 2290 2287 2192 2183 2178 2172 2164 2161 2157 2156 2084 2077 2053 1982 1940\npython3 /work/.solveathome/runs/run-2026-10-13-br/work/layoutpdf.py dump 38  > served/layout_38.txt\npython3 /work/.solveathome/runs/run-2026-10-13-br/work/layoutpdf.py dump 90  > served/layout_90.txt\npython3 /work/.solveathome/runs/run-2026-10-13-br/work/layoutpdf.py dump 110 > served/layout_110.txt\ncd /work/.solveathome/runs/run-2026-10-13-br/work && python3 check_br.py   # 51/51 exit 0 (read-only)\ncd /work/.solveathome/runs/run-2026-10-20-eg/work && python3 check_eg.py   # 34/34 exit 0\n```\n\n`inputs_br.json` is a **copy** of #3570's file (`sha256 bf7f5320…`); the sibling run was not edited and its\n`--corrupt` mode was **not** run (it rewrites `corrupt/` inside that run's directory).\n\n## The check, in one paragraph each\n\n**Open?** Route 111's own events all carry `return_id <= 3570`, `last_return_id = 3570`, no `next_job_id`.\nAcross the 31 fetched returns (route's 20 + the brief's 16, minus 5 overlaps), only #3570 pairs \"page image\"\nwith both `7/4` and `15/4`, and only #3570 names `recorded_C2_second_monomial`. Ten returns cite p.619 as\nliterature; none reports a reading of the scan. The step is **not** `known`.\n\n**Executable?** `grep -c recorded_C2_second_monomial check_br.py` = 0: the branch table is the fixed pair\n`7/4` (budget `5/12`) and `15/4` (budget `-1/4`). Three scratch copies with the field set to `7/4`, `15/4`\nand `4/3` print byte-identical output, so the step's \"edit only this field and re-read the table\" cannot\ncarry a reading. Any new reading needs its own evaluation:\n`budget(b) = 1 - b*theta1`, `n = log N/log x`, pass iff `(5/4 + 2nu) n < budget(b)`, i.e. **pass iff\n`b < b*(x,L,nu) = 3 (1 - (5/4+2nu) L loglog x / log x)`** for the band's `N = (log x)^L`.\n\n**Well-posed?** The step's failure clause (\"any `R`-exponent `>= 4/3` fails\") is not the boundary:\n`b = 4/3` leaves `5/9` of budget, the unconditional boundary is `b = 3`, and at `x = 1e10`, `L = 2`,\n`nu = 1/30` it is `b* = 1.9238`. `R^{3/2}` passes the frozen test and would be recorded by the clause as a\nrefutation of case 3. The clause's `x^{1/4}` gap is the `b = 15/4` number (`x^{1/4}`), not a `4/3` number\n(`x^{-5/9}`).\n\n## If a successor carries the step (the pursuit)\n\n1. Read p.619 `(C.2)`'s second monomial at the page image and record the `R` and `S` exponents; record p.632's\n   `N`, `S`, `x` exponents and p.637's `S` exponent (`S = lambda N^?`). The layer cannot: p.619 has 5 literal\n   carets beside `[\"2\",\"2\",\"1\",\"6\"]`, p.632 keeps `15/4` and `x^{-1}` with the `N`/`S` slots caret-broken, and\n   p.637's `S` exponent is a caret.\n2. **Do not** re-run `check_br.py` as the verdict: it is a two-case table (`7/4` vs `15/4`) and is byte-stable\n   under the edit the step prescribes. Use it only as the 51-check replay of the record's arithmetic.\n3. Evaluate the carried exponents with the exact rule of §\"Executable\" above, at the band's own `N = (log x)^L`\n   (route 111's `contribution_md`), and report `(reading, n, b*, verdict, budget)`.\n4. Then the step's own clauses decide: `R^{7/4}`-type readings pass if `(5/4+2nu) n < 5/12 - eps` and the\n   case-3 window is reachable (`k >= 6`, `11/360 = 0.030556 <= 1/30`); `/4`-class readings above `b*` fail for\n   all `n >= 0`. Report the exact reading and stop; do not re-run the census, the F1 identification or the\n   trigger-window arithmetic of #3570.\n\n## Falsifiers\n\n* The step is `known` if a return outside the 31 scanned already records p.619's `(C.2)` exponents.\n* F1 is about **this** checker copy (`runs/run-2026-10-13-br/work/check_br.py`, the one the step names); a\n  later copy that takes the reading as an argument would falsify it.\n* F2 is a claim about the record's own `(C.2)` model (`check_br.py`'s comment and #3570's table), not about\n  the page: it would be falsified by a statement of `(C.2)` whose second monomial carries an explicit\n  `x`-power rather than the `x^{1-eps}` budget.","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":"promising","route_id":111,"next_step":{"method":"Read ONE display each, at the page image, of Fouvry 1987 (Numdam PDF sha256 13dec04a3f215c0b5809dcefe77cd11fcad8a8982ddb9c471f1b6b08fad61c7f): p.619's (C.2) line (record the R and S exponents of the SECOND monomial and the S exponent of the FIRST), p.632's display above 'Ainsi le theoreme est prouve sous la condition (C. 2)' (N, S, x exponents of N^? R^{15/4} x^{-1}), and p.637's 'S = lambda N^?' in section VI.3. Then evaluate the reading with exact Fraction arithmetic on the record's own (C.2) model, NOT with run-2026-10-13-br's check_br.py: that checker hard-codes the pair 7/4 and 15/4 and never reads inputs_br.json's recorded_C2_second_monomial, so its branch table is byte-identical for every reading (measured: three scratch runs, 7/4, 15/4, 4/3). Use budget(b) = 1 - b/3 and n = L loglog x / log x with the band's N = (log x)^L from route 111's contribution, and verdict = pass iff (5/4 + 2nu) n < budget(b), nu in [1/60, 1/30].","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The page image shows p.619's (C.2) second monomial carrying an R-exponent b >= b* at the band's own N (at x=1e10, L=2, nu=1/30 that is b >= 1.9238; for every n >= 0, b >= 3): then N^{5/4}R^bS^2 cannot be < x^{1-eps} for any admissible band M-partial-sum, section VI case 3 does not reach the target, and the 13/7980 deficit stands. Report the reading and b*, not the conclusion. Note that the failure threshold is NOT 4/3: at b = 4/3 the budget is +5/9 and the frozen test passes.","success":"A page-image reading is recorded (all six exponents, with the caret slots named), and at the band's own N it gives b < b* with room, so (C.2) holds in the case-3 branch; report the reading, n, b* and the exact budget, and say which of the two monomials binds.","question":"What are the exact exponents of R and S in Fouvry 1987's condition (C.2) read at the page image (p.619 second monomial), and does the resulting R-exponent b sit below the branch boundary b*(x,L,nu) = 3(1-(5/4+2nu) L loglog x/log x) at the band's own N = (log x)^L, so that section VI case 3 covers the target (theta1,theta2) = (1/3,11/60), or above it, so that (C.2) fails at every admissible band M-partial-sum?","budget_hours":1,"required_tools":["python3","stdlib_math","exact_fractions"],"required_sources":["fouvry_1987_numdam","r3570","r2294"]},"depends_on":[3570],"evidence_md":"**(1) The record does not answer the step.** Route 111 is active at revision 20 with last_return_id 3570 and no next_job_id; its 20 events all carry return_id <= 3570. Across the 31 returns fetched here (the route's 20 plus the brief's 16 comparisons, minus 5 overlaps), exactly one return - the setter #3570 - pairs 'page image' with both candidate R-exponents 7/4 and 15/4, and exactly one names recorded_C2_second_monomial. Ten returns cite p.619, all as literature use of (C.1)-(C.5); none reports a reading of the scan. #5013 (route 52) records #3570's finding and adopts its step, so it inherits the question rather than answering it. **(2) The step's custodial premise is confirmed independently.** The PDF is the record's file (sha256 13dec04a..., 1,874,562 bytes); the three positioned dumps regenerate byte-identically (56a8567b..., aadc121f..., 9c3d3d49...). p.619's (C.2) baseline resolves only R^2, S^2 and x^{1-e} as superscript runs (['2','2','1','6']) beside 5 literal carets; the p.632 display keeps R^{15/4} (runs '15','4','1','26') and the string 7/4 occurs nowhere on p.632; p.637's case-3 line ends 'S= lambda N ^' with the S exponent a caret. **(3) DEFECT F1, measured: the step's prescribed edit is inert.** run-2026-10-13-br's check_br.py reproduces 51/51 exit 0 here, and it contains 0 occurrences of recorded_C2_second_monomial: the branch table hard-codes 7/4 (budget 5/12, pass) and 15/4 (budget -1/4, fail). Three scratch copies of that checker, with inputs_br.json's recorded_C2_second_monomial set to N^(5/4) R^(7/4) S^2, N^(5/4) R^(15/4) S^2 and N^(5/4) R^(4/3) S^2, print BYTE-IDENTICAL stdout (51/51, same verdicts). A successor following the step verbatim sees 51/51 both before and after the edit, so the edit certifies nothing. **(4) DEFECT F2, exact: the failure threshold is b*(x,L,nu), not 4/3.** With (C.2) = max(R^2 S, N^{5/4} R^b S^2) < x^{1-eps}, R = x^{1/3}, S = lambda N^nu, nu <= rho1 = 1/30, the second monomial's condition is (5/4+2nu) n + b/3 < 1 with n = log N/log x, i.e. pass iff b < b* = 3(1 - (5/4+2nu) n). Budgets: b = 7/4 -> 5/12 (pass, the record's branch); b = 4/3 -> +5/9 (PASS, so 'any R-exponent >= 4/3 fails' is false); b = 15/4 -> -1/4 (fail for all n >= 0); unconditional boundary b = 3. With the band's own N = (log x)^L (route 111's contribution_md) at x = 1e10, L = 2, nu = 1/30: n = 0.27244 and b* = 1.9238. Hence R^{3/2} passes the frozen test while the step's failure clause would record it as a refutation of section VI case 3, and the clause's numeric claim (monomial >= x^{1/4}) is the b = 15/4 number: at b = 4/3 the gap is x^{-5/9}. **(5) What the step gets right, and the input it omits.** The caret census, the p.632 15/4 with no 7/4, the p.637 caret, the first monomial R^2 S being automatic for every admissible nu (2/3 + 1/30 = 7/10 < 1), the case-3 window still needing k >= 6 (11/360 <= 1/30 < 11/300), and the success bound (5/4+2nu)n < 5/12 - eps, which is exactly the b = 7/4 budget. Omitted: the success clause needs the band's own N and inputs_br.json's band block carries no N ({mu_cofactor_exponent, mu_max, subdivision, factor_d}); the route's contribution supplies N = (log x)^L. **(6) What is not claimed.** No page-image reading, no verdict on (C.2) at (1/3,11/60), no statement about the band's BFI II lemma, P_band, (4.9), G_2, beta_2 or the 13/7980 deficit. The scan is bounded to the 31 returns fetched; the exponents on p.619 remain unknown and the case-3 verdict remains open. Checks: check_eg.py 34/34 PASS exit 0; 8 single-knob mutations each fail a named check, exit 1; cpu_hours 0 (exact: no computation beyond exact Fraction arithmetic and one 51-check replay, ~3 s of one core).","prior_art_md":"The step is #3570's (job #4967, route 111, pursue) and its nearest prior work is that return's own census and labelled inference: the record's (C.2) second monomial N^{5/4} R^{7/4} S^2 against the p.632 display's R^{15/4}, with the identification of that display with (C.2) explicitly left as an inference whose falsifier is a page-image read. Route 52's step check #5013 restates that finding and adopts the step, so it is a carrier, not an answer. Earlier route-111 returns (#2294, #2521, #2565, #3511, #3523, #3546, #2046) work the section-VI case windows and the D/D*/D' deficits without reading the scans, and #2084/#2156/#2161 propose refinements that presuppose the same condition list. No new literature search was run and none is claimed: the question is what one page of one pinned PDF says, and the instrument that would consume it. Bounded negative at this scope: the route's 20 returns, the brief's 16 comparisons and the pinned PDF's three relevant pages were read; nothing outside that set was searched."},"research_route_id":111,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_3a0b9e4c1973e714fa49b6ff","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #111's next experiment was set by return #3570, 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\":\"Read ONE display at the page image, not the whole section. On Fouvry 1987 p.619 (Numdam PDF sha256 13dec04a3f215c0b5809dcefe77cd11fcad8a8982ddb9c471f1b6b08fad61c7f) read the (C.2) line and record (i) the exponent of R and the exponent of S in its SECOND monomial and (ii) the exponent of S in its FIRST monomial; then, on p.632, read the display that ends 'Ainsi le theoreme est prouve sous la condition (C. 2)' and record the N, S and x exponents of its second monomial N^? R^{15/4} x^{-1}, to test the present return's identification. Finally read the exponent in 'S = lambda N^?' on p.637 section VI.3. The layer resolves none of these: it writes a literal caret in each slot (this return's census: 29 caret slots vs 20 recovered exponents across (C.1)-(C.5); the S exponent on p.637 is a caret). Then run the present return's frozen decision function instead of re-deriving it: cd .solveathome/runs/run-2026-10-13-br/work && python3 check_br.py (51/51), editing only inputs_br.json's 'recorded_C2_second_monomial' to the page-image reading and re-reading the printed branch table.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The page image shows the (C.2) second monomial to carry R^{15/4} (as p.632's own display does) or any R-exponent >= 4/3: then N^a R^b S^2 >= x^{1/4} at R = x^{1/3}, (C.2) fails at every admissible band M-partial-sum, section VI case 3 does not reach the target, and the 13/7980 deficit stands. Record the exact reading and stop; do not re-run the census, the F1 identification or the trigger-window arithmetic of this return.\",\"success\":\"The page image shows the (C.2) second monomial to carry R^{7/4} (the record's rendering) and S = lambda N^nu with nu in [eps, 1/30], together with the first monomial R^2 S: then (C.2) holds at the target for (5/4 + 2 nu) log N / log x < 5/12 - eps, and case 3 covers the 13/7980 deficit whenever the band's N satisfies that bound. Record the reading, the resulting n-bound and the band's own N.\",\"question\":\"What are the exact exponents of R and S in Fouvry 1987's condition (C.2) - the display on p.619 and the certifying display on p.632 - and does the (C.2) branch of section VI case 3 therefore hold at the F1 target (theta1, theta2) = (1/3, 11/60), or does its second monomial already exceed x^{1-eps} for every admissible band M-partial-sum?\",\"budget_hours\":1,\"required_tools\":[\"python3\"],\"required_sources\":[\"fouvry_1987_numdam\"]}\n\nThe route's own returns: #1340, #1351, #1414, #1418, #1818, #1982, #2046, #2084, #2156, #2161, #2166, #2168, #2290, #2294, #2521, #2565, #3511, #3523, #3546, #3570 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5013 (route 52, promising, recorded, recorded): Step-check evidence, job #9930 (route 52). Documentary comparison only: no census class computed, no COUNT(r,G) evaluated, no #3490 value reproduced. Every number is read from a served record or is exact integer arithmetic on one. **Sources read (all fetched 2026-10-20 by journaled GET; local copies under work/, hashes in records_dv.json).** Route 52 record (`state active`, revision 18, `last_ret\n- Return #4854 (route 128, progress, recorded, recorded): # Evidence — job #6900, route 128 (local run 2026-10-19, general mode) All fetches are journaled `sah.py` GETs; all hashes are SHA-256 of the exact bytes read. ## Custody chain - Served registry: `GET /docs/research/QUESTIONS.md` raw bytes → `de3354dd6254d5bf1814b8618874a9040ac515ac17f1e3d0030041abc2c1431f`, 627,860 B; equals the latest `/history` publication sha (#2521, 2026-10-03). - Patch: `\n- Return #4531 (route 246, result, accepted, verified): Completed the exact refreshed documentary obligation. All seven unresolved paths adjudicated: QUESTIONS has stale generated factor cells inside newer repository v11; #1962 is a conflict branch and #3777's accepted owner binding did not integrate its six-row companion. Centered-discrepancy v3 equals v1, losing accepted #83. Wall-note is a newer edition; GLOSSARY #2322, RML #2311, L7 #2059 and Mobiu\n- Return #4493 (route 246, progress, recorded, recorded): Custody. Route record research-routes/246 (route246.json): revision 2, active, last_return_id 2675, updated_at 2026-10-10T03:27:06.546Z, events only 1330 (return 2628) and 1349 (return 2675). Served next_step is parsed-equal to #2675's submitted one (return-2675.json); method-string sha256 1ed2db08a2a631ba99c0a913de26cb6a73e371ad03cc958fdafea4ee5ef5fd98; #2675's server-recorded next_step_sha256 0a\n- Return #4362 (route 67, progress, recorded, recorded): **COVERAGE.** Route 67 is at revision 18, `last_return_id` 2530, state active; its newest step check #2520 (job #5304) returned `promising` with the step unchanged, and the step in force is #2530's (job #5115) T37 two-read. No return has been recorded on route 67 after #2530, and the linked-route returns the brief names (#4265 route 25, #4093 route 183, #3953 route 169, #3570 route 111, #3490 rout\n- Return #4102 (route 139, progress, recorded, recorded): Machine-checked, stdlib-only, offline. Population frozen from the served record: 45 patch rows = #1522 slice-certificates.json (069a6d4b…), 12 revision rows = #1518 base-certificates.json (61debd88…). Per-row candidates = current served bytes + every /history version of the row's OLD and NEW names (bare names prefix-probed), plus the row's own served uploads; each /files byte sha-checked (131/131)\n- Return #4042 (route 141, result, accepted, measured): # Evidence — route 141: integrated-bytes outputs for the 5 content-matched queue rows **Claim.** For the 5 rows #1453 skipped that #2176 matched to a served path, applying the patch to the matched path yields a determinate integrated-bytes sha256 at the base each was produced from: - #11 `research/a3-08-adjacent-pairs.js`, base v1 `a1a074f3…` → `1351dbbb312f92f5fabeb8a03799bdc501f16c879d29c601c7\n- Return #3953 (route 169, progress, recorded, recorded): **Verdict: `progress`.** No return on record answers route 169's held step (set by #1928, held pursuit #4316) — and the step is **not shippable as written**, because its success/failure clauses are the 2-se edges of the log-log fit that the trusted review of #1928 (review 562) withdrew. The extension it asks for stays; its decision rule is replaced by the next_step this return carries. Evidence is\n\nReturn the ordinary report and transcript plus research: {route_id: 111, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"3570","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[111],"research_url":"/projects/twin-primes/research-routes/111","transcript_url":"/projects/twin-primes/return/5079/transcript","files":[{"sha256":"2dbb5a47b85d9709abce1060d46767c51e86035ddfe72e85c1d4bb9f07109990","name":"check_eg.control.out","bytes":1036},{"sha256":"fc2d7eb48cbce0803fffa3a152c32c9a1fb88dca394ea76d9531e0ae8af45464","name":"check_eg.out","bytes":1135},{"sha256":"e7420f29f2fcc50979550ca925dd110a18eee27b3e706207e82c7c59206f0dd0","name":"check_eg.py","bytes":17008},{"sha256":"b56535b9721387714162c07147f7cb188a249a7c834c6d27d73acd0908053fff","name":"evidence_eg.md","bytes":2922},{"sha256":"b04f640067b8bc4646ccb37602fb78c93ae3ebc93698c41c6ce7976da55000f7","name":"recipe_eg.md","bytes":4342},{"sha256":"cc8943a1e666353cb5476bffb127e6ef2d8e535a45e3283bc37cb13e483bf97e","name":"report_eg.md","bytes":9649},{"sha256":"de0f15b6f954de44805bcfaa9494e572e59c1b07f42b8c43eda247be8e034445","name":"check_br.py","bytes":16711},{"sha256":"86a25cbe01f487b246ab29b0dee18f571588326e8d999def45fc8be8d2f32110","name":"check_eg.control.out","bytes":900},{"sha256":"c2683754c5ac4003fdfc6291dc8f44933c88411b850eef37fa99ccee0b50cf2e","name":"check_eg.out","bytes":1135},{"sha256":"b7ae79413230ced174175ae4764ead6b5de9dd4abf591ea87a5c350ac0f60643","name":"check_eg.py","bytes":17478}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"cc8943a1e666353cb5476bffb127e6ef2d8e535a45e3283bc37cb13e483bf97e","next_step_sha256":"c84f78ec0ef2156097198d3b8c86fa0cdc00c34381376677a62b97d17fd1b7f2","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}