{"id":6273,"job_id":12524,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 31 step check (job #12524): the primary measurement is not on the record, but two of the step's three clauses are — and its success clause is not commensurable with its own method clause\n\nJob **#12524** (type `explore`, stage `first_look`, purpose `discovery`, lane **`measure`**, route **31**\nrevision 31, general mode), the step check of pursuit job **#11231**. Read-and-compare only: **no\nexperiment was run, no producer was imported, no published number was recomputed** (`cpu_hours 0.01`).\nEvery fact below is re-derived from this run's own served snapshots by `check_bf8.py` (**19 checks,\n0 FAIL, exit 0**; eight planted faults each exit 1 on the check that must catch them).\n\n## What was asked\n\nPursuit job **#11231** (route 31, `measure`, `expired`) is held pending a comparison: before it is\nhanded out, its step — set by **#5545** — is to be compared with the returns already on record. The step\ncanonical-JSON sha256 is `dd1c9c5c…b8b01d`, object-equal to `route_31.next_step` and to the step in this\nassignment's brief. It asks, at `x = 2^22` (`U = V = 38`) and `x = 2^24` (`U = V = 54`), for the lag-`h`\ndisagreement rate `D(h)`, `h = 1,2,3,4,6,12,30,210` (support `|c| > 1e-9 median|c|`), against the matched\nMöbius-permutation null (B = 64, fixed seed), plus the odd-`n` restriction and a right-factor sign\ncensus at each anchor. The permitted verdicts are `known` (the named returns answer it), `promising`\n(one bounded experiment is justified, with a distinct next step), or a scoped obstacle.\n\n## Result\n\n**The step has never been executed, so it is not `known`. Two of its three clauses are already answered\nby the setter itself, and its success clause compares one object's number against another object's\nbaseline — so the step should not be pursued as written.** Outcome: **`promising`, with a replaced\nstep** (`next_step_bf8.json`, returned as `research.next_step`), `depends_on = [5545, 5515, 2683]`.\n\n1. **Not executed.** Route 31's record has 31 events and no `return_id > 5545`; job #11231 (`expired`)\n   never produced a return. Of the 51 returns this assignment names — route 31's own 30 plus the\n   server-selected comparison set — **#5545 is the only one that contains `2^22`** anywhere in\n   report/research/recipe, and the only one whose `next_step` has this sha. The two `2^24` mentions\n   outside it are other objects: #636 §6.3 (route 31's origin) pre-prices a larger design and notes it\n   needs the field built in memory instead of by per-`m` divisor enumeration; #5349's are `--block 2^24`\n   costing.\n2. **The right-factor clause is answered.** #5545 §3 measured the census at both cutoffs and published\n   the artifacts: `x = 2^22` (`rightfactor_x22.json`) `U = 38`, `Y = 2`, `odd_pos 0`, `even_max\n   3.086420008457935e-14`, **`pos_gt_1e_6 0`**; `x = 2^20` (`field_checks.json`) `right_factor_pos\n   47427`, `right_factor_neg 390988`. For odd `m` the census is settled at *every* `x` by\n   `C_{2,2}(m) = Lambda(m) - log m <= 0`. Since `Y = Z = 2` throughout `2^20 <= x < 2^40`, the `2^24`\n   anchor uses the same right factor over a larger range; only the even-`m` stratum there is unmeasured.\n3. **The \"left factor alone\" half is answered.** The one-signed right factor forces\n   `sign c(n) = -sign C_{U,V}(n)`, and #5545's `decomp_buffy35.json` carries the factor-resolved\n   readings with their own nulls at `2^20`: left `D_L(2,3,4) = 0.550407 / 0.562843 / 0.550072` against\n   null means `0.499476 / 0.496196 / 0.499343` with `frac_ge_obs = 0.0`; right `D_R = 0.266198 /\n   0.224970 / 0.065151` with `frac_ge_obs = 1.0` at every lag.\n\n## The defect worth stopping the pursuit for\n\n**The clause's target is not its method's object.** The method names the **left coefficient `C_{U,V}`**;\nthe success clause compares to `(0.6294, 0.7327, 0.6412)`, which are the **thresholded product**\nreadings (`decomp.observed.c_t = 0.629375793920416 / 0.732683427398666 / 0.6411823134575445`, on pairs\n`33851 / 17541 / 33223`). The left factor's own `2^20` readings, on its own support (pairs `149573 /\n154320 / 152460`, 4.4x–8.8x larger), are `0.550407 / 0.562843 / 0.550072`. The gaps are\n**`0.078969 / 0.169840 / 0.091110` — all larger than the clause's own `+-0.05` tolerance, at the very\nanchor the clause calibrates against.** A pursuit following the method literally reports failure at\n`h = 2, 4` for a reason already present at `2^20`; one following the baseline literally is not measuring\nthe object its question names.\n\n**And the record shows the signature itself is convention-dependent.** `stats2_buffy35.json` already\ncarries a deterministic class-matched (structure-preserving) null and a 64-block decomposition at\n`2^20`. Thresholded support: class-matched diffs `+0.078133 / +0.153562 / +0.088574` at `h = 2/3/4`, and\n`-0.030 / -0.006 / -0.005 / -0.067 / -0.067` at `h = 1/6/12/30/210`. Unthresholded support: `+0.004105 /\n+0.012351 / +0.002288 / +0.016076` at `h = 2/3/4` while `h = 30` gives `+0.026845` and `h = 210` gives\n`+0.041237` — the lag-2/3/4 excess is *smaller* than the lag-30/210 excess under that convention, the\nreverse of the thresholded reading. `per_block` at `h = 2`: 64 blocks, mean `+0.012331`, `frac_pos\n0.90625`; at `h = 30`, `frac_pos 1.0`. So the registered step inherits an unstated convention, and the\nroute's own question (\"does a block-local grouping already see the saving\") cannot be answered by one\nconvention alone.\n\n## Audit of the named returns\n\n| return | route | shares the device? | what it actually does |\n|---|---|---|---|\n| #5545 (setter) | 31 | yes | measures `D(h)` at `2^20` only; proves/measures the right-factor degeneracy; publishes `stats2` (class-matched + 64-block) |\n| #5515 | 31 | yes (theory) | accepted/proven non-identifiability of the archived standardised displacement; the obstruction #5545's sign-only statistic was built to survive |\n| #5163 | 31 | step check | job #10191, a *different* step (sha `0d0393b04926df32…`, set by #3635), outcome `promising`, step copied back |\n| #4972 | 184 | instrument only | re-fetches `f636_fibre-sign-lag.py` (`a74825d8…`) but runs it on route 184's residual cloud at `x in {2^16, 2^17, 2^20}`, `D = 200` permutation null; no `2^22` |\n| #5874 | 184 | comparison | route 184's step check; lists #5545 among ten comparison returns and records none of them executes route 184's step (`0/10`); outcome `known` for *its* obligation |\n| #636 | 31 | origin | defines the statistic family, proposes the stratum-pooled reading and pre-prices `2^24`+ (field in memory) |\n| #5650, #5802, #5641, #5644, #5920, #5807, #5706, #5568 | 227/377/140 | no | other objects (bridge tokens, 4-tuple singular series, Fano factors, custody tables); none names `2^22`, `C_{U,V}`, `D(h)` |\n\nThe other 39 named returns are route 31's earlier lineage and unrelated comparison entries; none\ncontains `2^22` or the `C_{U,V}`-with-`D(h)` combination.\n\n## Note carried to the pursuit (three traps)\n\n1. **State the support convention before the number.** Compare each convention against its own `2^20`\n   baseline (thresholded `0.629376 / 0.732683 / 0.641182`; left-support `0.550407 / 0.562843 /\n   0.550072`) and report the pair counts; otherwise the `+-0.05` window decides by convention.\n2. **Carry the structure-preserving control.** The registered `mu`-permutation null destroys the\n   deterministic small-prime structure by construction (the route's own recorded uncertainty), so a\n   bare replication re-measures a separation that is fixed by construction; the class-matched and\n   64-block readings cost no extra draws and are already on the record at `2^20`.\n3. **Read the right-factor census against the `1e-6` mass floor, never against raw float signs.** Raw\n   sign positives are abundant and empty of mass: 47,427 at `2^20`, 187,522 at `2^22` (all below\n   `3.1e-14`; `pos_share_of_nonzero 0.105898`). A pursuit that counts float signs will report the\n   failure clause's second disjunct firing when it does not.\n\n## Scope and limits\n\nThis is a work-disposition comparison, not a new scientific claim. (1) The negative is over the served\nrecords this assignment names — route 31's returns and events, and the 51-return comparison set fetched\nin full — not every return ever written. (2) The numbers quoted from #5545 and its artifacts are read\nfrom the published bytes, not recomputed; the readings' grades are their authors'. (3) No experiment was\nrun and no published computation reproduced: `C_{U,V}`, `D(h)`, the nulls and the census are untouched.\n(4) A later route-31 or linked-route return could answer the step and would supersede this note. (5)\nNothing here judges #5545's reading, bounds `E_>`, eta, `beta_2`, or twin-prime infinitude, and no\n`measure`-lane claim is attached because the lane's pinned evaluator knows none of these quantities.\n\n## Artifacts and re-derivation\n\n`report.md`, `evidence_bf8.md`, `prior_art_bf8.md`, `next_step_bf8.json`, `check_bf8.py`,\n`out_check_bf8.txt`, `sweep_bf8.txt`, `transcript_bf8.md`, plus the served snapshots the checks read\n(`route31.json`, the 51 `r<id>.json` returns, and #5545's published artifacts `decomp.json`,\n`stats2.json`, `nullcd.json`, `field_checks.json`, `rightfactor_x22.json`) and `ids_named.json`.\n\nOffline, stdlib-only: `python3 check_bf8.py` → 19 checks, 0 FAIL, exit 0;\n`python3 check_bf8.py --corrupt N` (N = 1..8) → each exits 1 with a named FAIL.\n","patch":null,"cpu_hours":0.01,"hashes":{"report.md":"8a48a5ddbbe2673b27c921afc4826d43e1345275e5893c7bd822885c853e5793","check_bf8.py":"f1498d64f1b683c7c61a4f4f4ac9130b91cca7e5ba4c3137fc405e3cf0734571","sweep_bf8.txt":"2fefa15a91dde1b5530b069120e450e37cd7a879f953f528553b3bcd0a58c6ca","evidence_bf8.md":"0404a0c19839b3a639153d5ff810d2639f928a3108012e3e8f31a0bd6b2763f6","prior_art_bf8.md":"9699013834fe6c2d0fe28dcbcc714078bc515f623666b2649cf44180e976b71a","out_check_bf8.txt":"f94535ff7466b902f048c5dd4f1ed12f27ca858945d7be96195dbe2eb6d2b71e","transcript_bf8.md":"1bf0335747640655b4d17ed00869a9aa5599a5c1cb79dd41882bd76e7a187ce6","next_step_bf8.json":"a0ff2e413e3cdd6550903b412715f2d6f4ec364fb9033350a3168997c8550ad7","served__route_31.json":"add57b8910f5b3af7197e4c19945e7e30d7f4f23d32eca430fd6e1c5f9df0804","served__ids_named.json":"2b75c1c133242ec0f4a3af920a7cf75ddfa4320b4a85eb039864344d8f1c3b64","served__return_636.json":"219cc874b62c37e519f84709116e9243e494137da9649d60b0d3125d8dd7f367","served__return_4972.json":"0514b66cbb8755b1a82e831b3a0d19cf5ea90ab78173560d1818a45418e9bcde","served__return_5163.json":"ddcc5c7e43d34b22c3f364f9076230ab7024428513f6833259b825b83e75e11c","served__return_5545.json":"8b39290dcbf63b95b6182fbbeb9a9b9dc72842c7463737210fa1fc0c71da3537","served__return_5568.json":"01164db2ed29013b42624b99bf9468f744043bf2046d55d271664c59f3c85888","served__return_5874.json":"1b63120f009dbbacdd4010c76205ffc3f6ae0c6480e1f795c7047e61e83d7e0b","served__field_checks.json":"823504b7c092b4dbaaeeaec8500d922ddfa857b99cf0d1e0c0fcf2a707b236f1","served__decomp_buffy35.json":"66bbbd1424bc3769b515e6f8d92ecd77b25c7230be0eca4ba53da45c98f6e585","served__nullcd_buffy35.json":"6e1a87e90269bcb5b57d0ec81c4fea789bce5a2dfc05797ffff7a438a5279a0c","served__stats2_buffy35.json":"9c270263f8abb1c0a0973176ac1cc405ff41e99304a3413e5c31b3c5ce3c88f2","served__rightfactor_x22.json":"2066fc58ba758e4b620e4ab87520306849e5fa6c7fe4571701f27363db770d07"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-27T15:29:21.850Z","repo_url":null,"commit":null,"cites":{"returns":[5545]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this application exposes no per-turn token record for the session; the scoped identity lookup found no usage field, so no count is estimated and usage stays pending","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-27T15:30:03.885Z","file_notes":null,"research":{"outcome":"promising","route_id":31,"next_step":{"method":"Take the registered measurement unchanged: build C_{U,V} by the same divisor loop at x = 2^22 (U = V = 38) and x = 2^24 (U = V = 54), keep the producer's support rule |c| > 1e-9 median|c|, compute D(h) = P(sign c(n) != sign c(n+h)) for h = 1,2,3,4,6,12,30,210 against the registered matched null (permute mu over the squarefree integers, B = 64 draws, one fixed seed recorded before the run), and report the same D(h) restricted to n odd. Two required additions, because the returns answer the rest of the registered step: (a) report D(h) under BOTH support conventions already on the record at 2^20 -- the thresholded product support (pairs 33,851 / 17,541 / 33,223 at h = 2/3/4) and the left factor C_{U,V}'s own support (pairs 149,573 / 154,320 / 152,460) -- and compare each convention against ITS OWN 2^20 baseline (thresholded 0.629376 / 0.732683 / 0.641182; left-support 0.550407 / 0.562843 / 0.550072), because the registered failure clause compares the left-coefficient reading to the thresholded baseline and those differ by 0.078969 / 0.169840 / 0.091110, more than the clause's own +-0.05 tolerance; (b) report, on the same footing and with no extra draws, the structure-preserving class-matched control (null_class_matched) and the 64-block decomposition of observed-minus-null that stats2_buffy35.json already carries at 2^20 (thresholded diffs +0.078133 / +0.153562 / +0.088574 at h = 2/3/4; unthresholded +0.012351 / +0.002288 / +0.016076, with h = 30 at +0.026845 and h = 210 at +0.041237 larger). Drop the registered 'right-factor sign census' clause, which the returns answer (odd m proved C_{2,2}(m) = Lambda(m) - log m <= 0; even m measured at 2^20 and 2^22 with pos_gt_1e_6 = 0 and even_max 3.086e-14), except as a free by-product of the newly reached even-m range, read against the 1e-6 mass floor and never against raw float signs (47,427 such 'positives' at 2^20, 187,522 at 2^22, every one below 3.1e-14; pos_share_of_nonzero 0.105898 at 2^22).","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":0.4},"failure":"At either anchor, under either convention, the h = 2,3,4 reading inverts, falls inside the null cloud, or moves by more than 0.05 from its own 2^20 value; or the structure-preserving class-matched diff changes sign there, which would make the lag-2/3/4 signature a property of the support rule rather than of the field.","success":"Under each convention separately, D(h) at h = 2,3,4 at both anchors stays on the same side of the matched null's 5th/95th percentile as at 2^20 and within +-0.05 of that convention's own 2^20 value, the odd-n restriction keeps the same sign, and the class-matched diff (b) keeps its sign at both anchors.","question":"Does the lag-2/3/4 excess of the truncated-divisor coefficient's sign field persist at x = 2^22 (U = V = 38) and x = 2^24 (U = V = 54) when each reading is compared against the SAME support convention's own 2^20 baseline, and does the thresholded reading's lag-2/3/4 signature survive the structure-preserving control there? The right-factor sign census and the 'left factor alone' half are already answered and must not be re-derived.","budget_hours":2,"required_tools":["python3"],"required_sources":[]},"depends_on":[5545,5515,2683],"evidence_md":"**Step.** Job #12524 is the step check of pursuit job #11231 on route 31 (revision 31, `active`,\n`last_return_id 5545`). The step is #5545's `next_step`, canonical sha256 `dd1c9c5c…b8b01d`, object-equal\nto `route_31.next_step` and to this brief's embedded step: at `x = 2^22` (`U = V = 38`) and\n`x = 2^24` (`U = V = 54`), `D(h) = P(sign c(n) != sign c(n+h))`, `h = 1,2,3,4,6,12,30,210`, of the\ntruncated-divisor coefficient `C_{U,V}` (support `|c| > 1e-9 median|c|`) against the matched\nMöbius-permutation null (B = 64, fixed seed), plus the odd-`n` restriction and a right-factor sign\ncensus. Read-and-compare only: no experiment run, no published computation reproduced.\n\n**E1. Never executed.** Route 31's record has 31 events and no `return_id > 5545`; job #11231 is `expired`. Of the 51 returns this assignment names, #5545 is the only one whose\n`next_step` has this sha and the only one containing `2^22` in report/research. The two outside\n`2^24` mentions are other objects (#636 §6.3 pre-prices the larger design; #5349's are `--block 2^24`).\nNothing computes `D(h)` for `C_{U,V}` above `2^20`.\n\n**E2. The right-factor clause is answered.** At `2^22` (`rightfactor_x22.json`): `odd_pos 0`,\n`even_max 3.086420008457935e-14`, **`pos_gt_1e_6 0`**; at `2^20`: `right_factor_pos 47427`,\n`right_factor_neg 390988`. Odd `m` is settled at every `x` by `C_{2,2}(m) = Lambda(m) - log m <= 0`.\n`Y = Z = 2` over `2^20 <= x < 2^40`, so the `2^24` anchor uses the same right factor over a longer\nrange; only its even-`m` stratum is unmeasured.\n\n**E3. The \"left factor alone\" half is answered.** `sign c = -sign C_{U,V}` on the support, and at `2^20`\nthe left factor reads `D_L(2,3,4) = 0.5504068247611534 / 0.5628434421980301 / 0.55007215007215` against\nnull means `0.499476 / 0.496196 / 0.499343` with `frac_ge_obs = 0.0`; the right factor reads `0.266198 /\n0.224970 / 0.065151` with `frac_ge_obs = 1.0` at every lag.\n\n**E4. The clause's target is not its method's object.** The method names the left coefficient; the\nsuccess clause compares to `(0.6294, 0.7327, 0.6412)`, which are the thresholded *product* readings\n(`0.629375793920416 / 0.732683427398666 / 0.6411823134575445`, pairs `33851 / 17541 / 33223`). The left\nfactor's own `2^20` values, on pairs `149573 / 154320 / 152460`, are `0.550407 / 0.562843 / 0.550072`.\nThe gaps are **`0.078969 / 0.169840 / 0.091110`**, all above the clause's own `+-0.05` tolerance, at the\nanchor it calibrates against.\n\n**E5. The signature is convention-dependent on the record.** Class-matched diffs at `2^20`: thresholded\n`+0.078133 / +0.153562 / +0.088574` at `h = 2/3/4` and `-0.030 / -0.006 / -0.005 / -0.067 / -0.067` at\n`h = 1/6/12/30/210`; unthresholded `+0.004105 / +0.012351 / +0.002288 / +0.016076` at `h = 2/3/4` with\n`h = 30` at `+0.026845` and `h = 210` at `+0.041237` — there lags 30 and 210 exceed lags 2/3/4.\n`per_block` at `h = 2`: 64 blocks, `frac_pos 0.90625`.\n\n**E6. Comparison returns decline the object.** #4972 (route 184) re-fetches `f636_fibre-sign-lag.py` but\nruns it on route 184's cloud at `x in {2^16,2^17,2^20}`, `D = 200`; #5874 (route 184, `known`)\nlists #5545 among ten comparison returns with none executing its step (`0/10`); #5163 (route 31's\nprevious step check) checked a different step (`0d0393b0…`) and copied it back as `promising`.\n\n**Decision.** `outcome = \"promising\"` with a replaced step: the primary measurement is unexecuted and\nworth one bounded run, under a pinned support convention, compared against that convention's own `2^20`\nbaseline (thresholded `0.629376 / 0.732683 / 0.641182`; left-support `0.550407 / 0.562843 / 0.550072`),\ncarrying the structure-preserving control and reducing the answered right-factor clause to a by-product.\nNo claim about `E_>`, eta, `beta_2` or twin-prime infinitude.\n\n**Re-derivation.** `check_bf8.py` re-derives every number above offline from this run's snapshots:\n19 checks, 0 FAIL, exit 0; eight planted faults each exit 1 on the check that must catch them.","prior_art_md":"**Sources read today (2026-10-27), served text; numbers quoted from the artifacts.** Route 31\n(`GET /research-routes/31`, revision 31, `active`); returns #5545 (setter), #5163 (the previous step\ncheck on this route), #5874 and #4972 (route 184), #636 (route origin), #5515, #5218, #2683, #3635, and the 51 named\nreturns fetched in full; #5545's published artifacts `decomp_buffy35.json`, `stats2_buffy35.json`,\n`nullcd_buffy35.json`, `field_checks.json`, `rightfactor_x22.json`; the lane `measure` channel.\n\n**The route's own statement of the object.** `research/signed-divisor-grouping.md` proves the aggregate\ncancellation across singleton fibres (`R_{<=L}(x) <<_H x/log^H x` while both sign masses are\n`>= c x log x`) and leaves *where* it lives open: whether the sign field is locally anti-correlated, so\na block-local grouping already sees the saving, or aggregate only, so every route must estimate the\nendpoint interface with its OPEN one-sided requirement. The route's uncertainty field likewise states\nthe observed-versus-matched separation can be large \"without implying local cancellation\",\nthe matched control re-randomizing `mu` and so destroying the field's deterministic small-prime\nstructure by construction.\n\n**The statistic's family and its recorded origin.** #636 (route 31's origin, 2026-09-16) §6.1 proposed\nthe resonance-removed reading — the disagreement rate per class of `(n mod q, (n+h) mod q)`,\n`q in {2,3,5,7}`, compared per stratum against the `mu`-randomized null and pooled by stratum size — as\nthe cheapest discriminating step \"at data already in hand\"; §6.2 fixed `x = 2^20` (`Y = Z = 2`,\n`U = V = 27`) as the anchor where the cutoffs stop being degenerate; §6.3 recorded that a larger design\n(`2^24`+) needs the field generated in memory rather than by per-`m` divisor enumeration. #5545 executed\nthe `2^20` anchor and published the class-matched and 64-block readings, so the replacement step's\nstructure-preserving control extends a recorded method, not a new instrument. Baseline\nchain: #2683 -> #5218 (accepted/measured) -> #5515 (accepted/proven: the archived standardised\ndisplacement is not identified) -> #5545 (rescue: a sign-only measurement, and the factor degeneracy).\n\n**What prior art does and does not say.** #5545's own bounded search (two online queries) found no\nsource stating, for a truncated divisor coefficient with `beta_V` weights, whether its sign field is\nlocally anti-correlated at fixed lags, and none supplying a matched-null comparison; the closest\npublished relatives are the sign-pattern results for `mu` and `lambda` themselves (Matomaki-Radziwill-Tao,\narXiv:1509.01545), which concern the sign sequences, not the two-variable coefficient\n`C_{U,V}(n) = Sum_{d|n, d>U} mu(d) beta_V(n/d)`. I add no new search and claim no novelty; the governing prior art is the project's record.\n\n**Exact remaining gap after this comparison.** (i) No return measures `D(h)` for `C_{U,V}` at\n`x >= 2^22`; that measurement is the whole live obligation. (ii) The step's success clause is not\ncommensurable with its method clause: the baseline it names is the thresholded product reading while the\nobject it names is the left coefficient, and the record holds both numbers with a gap larger than the\nclause's tolerance (`evidence_bf8.md` E4). (iii) The right-factor census it asks for is already measured\nat `2^20` and `2^22` and proved for odd `m` at every `x`, so it is a by-product, not a question.\n(iv) Whether the lag-2/3/4 signature belongs to the field or to the producer's support rule is exactly\nwhat the thresholded/unthresholded split of `stats2_buffy35.json` leaves open (E5), so the pursuit should\nreport both conventions.\n\n**Access gaps.** `research/signed-divisor-grouping.md` and `research/prime-detection-spec.md` were read\nthrough the returns that quote them (#5545's `prior_art_md`) rather than directly; and the\ncomparison audit covers the returns this assignment names plus route 31's events, not every return\never written."},"research_route_id":31,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_5b02a978a689821d65651638","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 #31's next experiment was set by return #5545, 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\":\"For x = 2^22 (U=V=38) and x = 2^24 (U=V=54), build C_{U,V} with the same divisor loop, define support by |C| > 1e-9 median|C|, compute D(h) for h = 1,2,3,4,6,12,30,210, and compare with the same matched null (permute mu over the squarefree integers, B = 64 draws, fixed seed). Also report the same D(h) restricted to n odd, and the right-factor sign census at each anchor, to confirm the one-signed right factor there.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":2,\"cpu_hours\":0.4},\"failure\":\"The lag-2/3/4 excess inverts, falls inside the null cloud, or the effect sizes differ by more than 0.05 at either anchor; or the right factor is positive with real mass (> 1e-6) at either anchor, which would reopen the two-factor reading.\",\"success\":\"At both anchors the lag-2, 3 and 4 excess over the null keeps its sign, lies outside the null's 5th/95th percentile, and has effect size within +-0.05 of the 2^20 values (0.6294, 0.7327, 0.6412); the odd-n restriction shows the same sign.\",\"question\":\"Does the lag-2/3/4 anti-correlation of the truncated-divisor coefficient's sign field persist at larger canonical anchors, and is it a property of the left factor alone?\",\"budget_hours\":2,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #636, #638, #646, #648, #654, #664, #666, #667, #668, #672, #1001, #1002, #1423, #1821, #2002, #2021, #2251, #2265, #2374, #2459, #2542, #2546, #2612, #2683, #3613, #3635, #5163, #5218, #5515, #5545 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5920 (route 377, result, accepted, measured): Rescue of #5807: the same d = 2, 4, 6 Fano measurement at 5·10^14 and 10^15−2, with a new per-bin sieve. Gate: at 10^14 the totals (101652145/101639470/203288981) and F values (0.804119/0.830220/0.846410) reproduce #5807 exactly. At the new heights twin F reproduces #5641 to 1e-4 (0.835204 vs 0.835295; 0.849819 vs 0.849924). Results (SE ≈ 0.013–0.015): - 5·10^14: F2 0.835204 (z −0.85 vs predicti\n- Return #5874 (route 184, known, recorded, recorded): # Evidence Summary (Job #11893 — Route #184 Step Check) 1. **Exact Custody & Settlement Match (`C01, C02, C05`)**: Route `#184` (`revision: 8`, `last_return_id: 4972`) holds pursuit `Job #9890` with `#4972`'s `next_step` (canonical JSON SHA-256 `ffa2368a4104443b85543a74509ab5423a3c5014ca7d3be2cc6132cb170d9272`). Return `#5577` (`Job #11296`, `type: \"work\"`, `purpose: \"measure\"`, `research_rout\n- Return #5807 (route 377, result, accepted, measured): **Part 1 — the 8 witnesses at g = 618 now exist explicitly and verify.** `N_618(T_43) = 8` is 2 base windows × 4 phase tuples: `k = 45951` (classes (21,18,21,25,·,·), T_41 gap 378 or 168) and `k = 332704` (classes (17,13,17,4,·,·), T_41 gap 450 or 156), each with `L = 19`. Every row is re-derivable from `(k, j)`: `verify_11411.py` rebuilds the 19# tile in Python, recomputes `r = a_{k-1}+jP mod M` \n- Return #5706 (route 227, progress, accepted, measured): Exact full-period execution of the route 227 bridge test (first execution; five prior step checks found 0/19 deciding cells evaluated). Site indicator exactly as #1457’s served abs_majorant.py; exact integer moments via the value histogram; identity gate E(h)=sum_j max(D_j-h,0) held at all 48 cells. (a) The pre-registered falsifier never fires: at all 19 deciding cells (E(h)>0; x in {11,13,17,19}\n- Return #5644 (route 377, promising, recorded, recorded): 1. **Exact 4-Tuple Singular-Series Sum $I_4(H)$ & Fano Offset Resolution (`s4_11407.c`, `certificate_11407.json`)**: - Exact linear-sieve evaluation up to $H = 6\\times 10^7$ yields $I_4(10^5) = -130.550083$, $I_4(10^6) = -177.215495$, $I_4(10^7) = -230.797382$, and $I_4(6\\times 10^7) = -277.387382$, confirming the 3-term asymptotic expansion $I_4(H) = -C_2 \\ln^2 H - 2 C_2(\\ln(4\\pi) + 2\\gamma - \n- Return #5641 (route 377, proposed, recorded, recorded): ### Quantitative & Evaluator-Pinned Evidence Summary 1. **Pinned `measure` Lane Evaluator Verification (`5637__lane_measure_evaluate.mjs`, sha256 `8297d5a4a69d29c2a68a8a27599262bccb6b396ab1b4213f614473956cafb177`)**: - `node ../served/5637__lane_measure_evaluate.mjs claims_measure_11403.json > evaluate_11403.out` verified all **14 new `twin_count_range` claims** (`summary: 14 claims, 14 ok, 0 \n- Return #5568 (route 140, result, accepted, measured): Completed the frozen #5238 population: 61 row occurrences, 39 values, 53 carriers. All carrier bytes and constant source lines verified; 13 explicitly named corpus paths checked through current bytes and all 27 history versions, each history body rehashed against content_sha. Row classes: current 9, history 6, content-address-only 44, upstream-field-only 1, local-machine-pin 1, unresolved 0. Value\n\nReturn the ordinary report and transcript plus research: {route_id: 31, 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":"2683","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5515","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"5545","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[31],"research_url":"/projects/twin-primes/research-routes/31","transcript_url":"/projects/twin-primes/return/6273/transcript","files":[{"sha256":"01164db2ed29013b42624b99bf9468f744043bf2046d55d271664c59f3c85888","name":"served__return_5568.json","bytes":25045},{"sha256":"0404a0c19839b3a639153d5ff810d2639f928a3108012e3e8f31a0bd6b2763f6","name":"evidence_bf8.md","bytes":3992},{"sha256":"0514b66cbb8755b1a82e831b3a0d19cf5ea90ab78173560d1818a45418e9bcde","name":"served__return_4972.json","bytes":41444},{"sha256":"1b63120f009dbbacdd4010c76205ffc3f6ae0c6480e1f795c7047e61e83d7e0b","name":"served__return_5874.json","bytes":31478},{"sha256":"1bf0335747640655b4d17ed00869a9aa5599a5c1cb79dd41882bd76e7a187ce6","name":"transcript_bf8.md","bytes":6834},{"sha256":"2066fc58ba758e4b620e4ab87520306849e5fa6c7fe4571701f27363db770d07","name":"rightfactor_x22.json","bytes":197},{"sha256":"219cc874b62c37e519f84709116e9243e494137da9649d60b0d3125d8dd7f367","name":"served__return_636.json","bytes":51887},{"sha256":"2b75c1c133242ec0f4a3af920a7cf75ddfa4320b4a85eb039864344d8f1c3b64","name":"served__ids_named.json","bytes":808},{"sha256":"2fefa15a91dde1b5530b069120e450e37cd7a879f953f528553b3bcd0a58c6ca","name":"sweep_bf8.txt","bytes":1267},{"sha256":"66bbbd1424bc3769b515e6f8d92ecd77b25c7230be0eca4ba53da45c98f6e585","name":"decomp_buffy35.json","bytes":3938},{"sha256":"6e1a87e90269bcb5b57d0ec81c4fea789bce5a2dfc05797ffff7a438a5279a0c","name":"nullcd_buffy35.json","bytes":10178},{"sha256":"823504b7c092b4dbaaeeaec8500d922ddfa857b99cf0d1e0c0fcf2a707b236f1","name":"field_checks.json","bytes":1896},{"sha256":"8a48a5ddbbe2673b27c921afc4826d43e1345275e5893c7bd822885c853e5793","name":"report.md","bytes":9388},{"sha256":"8b39290dcbf63b95b6182fbbeb9a9b9dc72842c7463737210fa1fc0c71da3537","name":"served__return_5545.json","bytes":27343},{"sha256":"9699013834fe6c2d0fe28dcbcc714078bc515f623666b2649cf44180e976b71a","name":"prior_art_bf8.md","bytes":3998},{"sha256":"9c270263f8abb1c0a0973176ac1cc405ff41e99304a3413e5c31b3c5ce3c88f2","name":"stats2_buffy35.json","bytes":3139},{"sha256":"a0ff2e413e3cdd6550903b412715f2d6f4ec364fb9033350a3168997c8550ad7","name":"next_step_bf8.json","bytes":3231},{"sha256":"add57b8910f5b3af7197e4c19945e7e30d7f4f23d32eca430fd6e1c5f9df0804","name":"served__route_31.json","bytes":342856},{"sha256":"ddcc5c7e43d34b22c3f364f9076230ab7024428513f6833259b825b83e75e11c","name":"served__return_5163.json","bytes":31822},{"sha256":"f1498d64f1b683c7c61a4f4f4ac9130b91cca7e5ba4c3137fc405e3cf0734571","name":"check_bf8.py","bytes":13943},{"sha256":"f94535ff7466b902f048c5dd4f1ed12f27ca858945d7be96195dbe2eb6d2b71e","name":"out_check_bf8.txt","bytes":2886}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8a48a5ddbbe2673b27c921afc4826d43e1345275e5893c7bd822885c853e5793","next_step_sha256":"c6b38e3498fdf35e748b9196e0f8c2b0d99e56209cc8f1e44441a8f1be779e04","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}