{"id":4030,"job_id":8215,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #8215 — route 179 (first look): the held streaming-kernel step is not answered on record; copied exactly\n\n**Outcome: `promising`.** The step held for pursuit **#4781** (canonical sha256\n`eaced2362a8ab60f661618717115fabc38b9658c84d72827409bc5bcd2c44af4`, set by **#2180**) asks to rebuild\nthe served `O(x log Q)` centered-discrepancy kernel as a **streaming** evaluator so `2^28` fits under\nthe observed 6 GiB cgroup cap, to pre-register a signed ladder-wide `min_{j=18..28} z(2^j)` criterion\nand a fitted-slope test with ≥8 independent random-sign seeds plus the census's `mu(n)->±1` control at\nthe common `j`, and to reconcile the low-scale `z` with the census control's large negative high-scale\nratios. **No return on record performs this**, so the step is copied **exactly** and the pursuit goes\nout with it. This is a step check: no kernel was rebuilt, no census re-run, no published number\nrecomputed — a bounded comparison of the step against the returns already on the record.\n\n## Step custody\n\n`canon(route 179 next_step)` = `eaced2362a8ab60f661618717115fabc38b9658c84d72827409bc5bcd2c44af4`\n= #2180's served `next_step_sha256` = `canon(#2180.research.next_step)` = `canon(issued step)`.\nThe issued `research_task.{unresolved_obligation,expected_evidence,stop_if}` repeats the step's\n`{question, success, failure}` verbatim (`intent:\"extend\"`, `predecessor_returns:[2180]`).\n\n*Custody trap.* The server's canonicalization is `json.dumps(..., sort_keys=True,\nseparators=(\",\",\":\"), ensure_ascii=False)` — UTF-8, so the step's `mu(n)->±1` stays a literal `±`.\nHashing the ASCII-escaped canonical form gives `b3d75022…`, which does **not** match the declared\n`eaced236…`; only `ensure_ascii=False` reproduces it. Recorded for successors.\n\n## Why the step is not answered (record comparison)\n\nRoute 179 (`rev 2`, `active`, origin **#2174**, `last_return_id` **2180**) has exactly two events:\n`986 proposed` (#2174) and `991 promising` (#2180). **#2180 is the last; nothing postdates it** — no\nevent id exceeds 991 and no route-179 return exists after #2180. #2180 (job #4773, \"route 179 first\nlook\") set this very step in its §6 (\"Next step (corrected)\") and left it undone: it reports that the\nserved kernel materializes four `x+1` double arrays (32 B/n) plus a 4 B/n `spf` sieve, so `2^28` needs\n≈9.25 GiB and `2^30` ≈37 GiB against the container's observed **6.00 GiB** cap; the `2^28` attempt\nfinished its sieve (55.1 s) and was **killed by signal 9** at the decision scale (an OOM, not a\ntimeout). It states plainly that \"**A streaming rewrite** (or capping the ladder at `2^26` …) **is\nrequired**\". So the load-bearing method of the step (memory feasibility) is exactly what remains\nunbuilt.\n\nThe returns the brief lists for comparison — **#3953** (route 169), **#3058**, **#2910**, **#2512**,\n**#2383**, **#2282** (route 45) — are step checks/investigations on **other** routes: #3953 decides\nroute 169's held transfer step (`Delta_a/x` beyond j = 26); the five route-45 returns are the dyadic\ncover / log-size-model work. A scan of all six reports for the step's distinctive phrases\n(\"STREAMING evaluator\", \"2^28 fits under the observed 6 GiB\", \"min_{j=18..28} z(2^j)\",\n\"fitted-slope test of z vs log x\", \"independent random-sign seeds\", \"memory-feasible past 2^24\")\nreturns **zero hits**, and none of their `research.next_step` objects equals the step. They neither\nbuild the streaming kernel nor run the signed ladder-wide criterion.\n\nThe route's own basis returns are the setter #2180 (promising) and its predecessor #2174 (proposed /\norigin), plus the named-but-undeclared evidence #2151 (the statistic's design) and #165 (the census\nwith its own random-sign control). #2151/#2174 ran only the low ladder `2^12..2^24`/`2^26`; #165's\ncontrol is unsigned `|real|/rms` with four seeds, not the exact-`sigma` standardized `z` with a\npre-registered ladder-wide criterion. So the route's **central uncertainties stand**: (1) family-wise\npower (a single `z<=-2` in nine scales is ~19% likely under the null), (2) the cross-check against the\nserved census artifact — **retired by #2180** at every common scale (`j=16,18,20,22,24,26` match to\nsix decimals), and (3) the control choice (only the random-sign control is used). The step is sound\nand runnable here (`required_tools:[\"python3\"]`, `compute.ram_gb 6`, `cpu_hours 3`; the binding\nconstraint is memory, which the streaming rewrite addresses), so it is copied exactly.\n\n## Named prerequisite and named file\n\nThe brief names a prerequisite, job **#3880** (handoff #1): a generated-index correction that needs a\nspecifically chosen source expert. It is a source/provenance blocker explicitly delegated away from\nordinary general-mode agents; it does not bear on this step and is carried, not acted on. The brief\nalso names `research/centered-discrepancy-ladder-4772.md` as **not in the served snapshot**: fetching\nit once at `/docs/research/centered-discrepancy-ladder-4772.md` and at\n`/docs/centered-discrepancy-ladder-4772.md` both return **404**. Worked from the served record and the\nreturn's own statements, as the brief directs.\n\n## Machine-checked\n\n`check_dm.py` -> `check_dm.out`, **12/12 PASS**, exit 0 (stdlib-only, offline, imports no producer\ncode, runs no kernel, recomputes no published quantity). `--corrupt 1..12` each exit 1 with exactly\nits named check FAIL (`check_dm.corrupt_exit.txt`). C01 step custody (`ensure_ascii=False`);\nC02 `sha256(#2180 report_md) == declared report_sha256`; C03 the issued contract repeats the step\nverbatim; C04 job #8215 is `explore`/`first_look`, route 179, source #2180, `step_check_of` #4781,\nrev 2; C05 route metadata; C06 events exactly {986 proposed, 991 promising} with nothing after;\nC07 route jobs #8215 `assigned` / #4781 `expired` (held for step check) / #4773 `returned`;\nC08 #2180 leaves the streaming rewrite undone (OOM/clause); C09 the six compared returns are on\nroutes 169/45 and carry no step; C10 fifteen served artifacts hash to their requested sha256;\nC11 the memory-boundary numbers; C12 the ladder `z` readings.\n\n## Not claimed\n\nThat the streaming kernel can or cannot reach `2^28` under 6 GiB; that the signed ladder-wide\ncriterion will reject or fail to reject; or anything about `D_y >= -4x/25 + o(x)`, any exponent, or\ntwin-prime infinitude. No census was run and no published number was recomputed. #2180's scope caveats\ncarry unchanged: its census control uses four seeds and a different sd normalization, and the high-scale\nsigned ratios are indicative, not decisive.\n\n## Next step\n\nThe held step, copied **exactly** (canonical `eaced236…`): rebuild the served kernel as a streaming\nevaluator so `2^28` fits under 6 GiB; pre-register the signed ladder-wide running-minimum criterion and\na fitted slope for `z` over `j=18..28` with ≥8 seeds and the census `mu(n)->±1` control at the common\n`j`; and reconcile the kernel's low-scale `z` (inside the null at `2^26`) against the census control's\nlarge high-scale ratios. Success is a signed ladder-wide rejection or a clean signed null bounding the\nadmissible drift; failure is the criterion staying inside the control range at every reachable rung.\n\n## Note for the person\n\n4 of @Benjaminsen's returns wait for a trusted verdict, the oldest since 2026-10-06.\n","patch":null,"cpu_hours":0.05,"hashes":{"check_dm.py":"db02493886e22be8cfe1ec8aef9c4ea6774553e8460e6deca1b5206939b65bb0","fetch_dm.py":"9d8f8f14b338db9965ffc9b529561b0f8d92b745d838e40594cd27dc491327ef","ns2180.json":"21425b77204ddf8f7c1c98ef058cc3e3f389241eb858dc122981c40b20b8b1f0","check2180.py":"3459ba7edf1fa0fff2da51c44d1747b9a03e177b4c31cd9d2b3f6fb62fcb3ca7","check_dm.out":"c5563e80f80af1f4799cbae1432b011469a9dc51616b5ac16e2a47c462cc0e67","job4746.json":"4a1c81ed2b791af0286d099850df1083cb9e04381030b8df89e2d2133e25d470","job4772.json":"fdea852a83c339923e3d093b0ebe36c1a4e3c3e8e9d4498cce9ae7f908b5aa93","job4773.json":"0da6b240d3ee6b35f04ad364e59670160ec673ca1eac838e12bdd905fc12e0a2","job4781.json":"fc21e1b277582ee31b00243709cfdbac3a10ac1f1ef3c7aaa88d128b90d807ff","job8215.json":"ec4b4f88633b483a3cdc8daf6245975e1c897f0d24452bd679e8843f4fd9088b","recipe_dm.md":"5f7e5594a0b7f5ea13c8a90fcb84b14fef64cf9ef84392e8116474132f8a7c55","report_dm.md":"4f22f044326ba823f3ef253c8e9b4bf8034aa6d2b6788669122f1b3621ca943c","check2180.out":"750e8d7f18f665ae4fb71ff55125be072d75302432f44d925f5a0728338ee173","fetch_dm.json":"287059d2e3381276c28b0abb0fe2d85456b58b63fa5db7beb5fa10eea8415d0d","report2180.md":"2b721cc1e62c71d61c97e8419724c99d013d3d05c80a88c8b283a438495377de","route179.json":"1d594fa5cb323fe6af03997e14ccb83c28e0fb5468e8fef0d2804c4dff20ada7","evidence_dm.md":"f0bce76f24ce3a585fb5565cbf5bbbda3237c4a237797190632241d9873212e2","scale_2_26.out":"556e9208cda3684069f941e97bf209ef80184dd38de1055a76a8f792bcedab83","scale_2_28.out":"46f3c9716a7906fabbba027fd717449730317b47a9c5c2876905431102c6e4d5","evidence2180.md":"ee043690ad6a54721e75cd470bcf737d79fe24abbe67e42bbb4bad55e4298c29","prior_art_dm.md":"3ceb060d212ae80e1287d85bd2dc77b6858a60b3d32a99f3dbc7edd394cb0634","return_155.json":"801cec36beee7675bd3dd48814cf384b9e5fe323d132675425f0243f2c26a7d4","return_165.json":"baa4dd8c48a61446d78675fce42062767d6506f71bf18667153244ea24da704e","prior_art2180.md":"6cb4a5f08b3a83fb2dc4154c095b2c8f6a4cbd84a5081b2d12d30e82ef14e92e","return_2151.json":"6c59aa2971aa5dea8fe8f5f822756cecf40d92c3cfd0744b5c8d69b05f886774","return_2174.json":"449b529ca19a8eeb83d6eb7dc2b2ee088e11678bc46d34ddfd78311e1a5e1397","return_2180.json":"cda84627a2ba4ce128f26214e7dfa784e3a8f221be3fb428385c1c3151ee1fb5","return_2282.json":"aa954946b169f0de828e4cdc70da326a1859242a5843f81d82882aca2e8a86e4","return_2383.json":"49391621e8c5d7b69c9e5c0e771b312e302fc9986c46b0ceab6a96abcd5d7f0a","return_2512.json":"003f0c2e69cbc4c39dbdb156e2a529df6cc63c99ab3aa75f166b4729c0966b6d","return_2910.json":"7007c7d15ed0e096cef08b02732e28349ef17c3a07000e6adf8d357296084695","return_3058.json":"458be0a5ba403cd43dedbd44df87b8f38b4da66dfd22299cfeedad527d832f64","return_3953.json":"35be235b94820267f540e5129886458e9d9e4284ce03e942059f2191258729bb","bg_kernel_2174.py":"05d0c83d164c990742328ce71a862e10a1363ebc97c1f4e7870bc99ae25fe65a","next_step_dm.json":"42aae8136277093fbd33709781ea0e427f82aab9b8e77251536d3dc6c3154b95","scrub_local_dm.py":"b8689054d1da7646c664619a9d3cc017ae410322b822cdd07e15f7230fdd3a24","bg_kernel_2174.out":"ea36f435b63e43731868e87beacc435297a21157dc512304b1b8c99d619e2733","census_ctrl_2180.py":"acc1f31aae151018b941e59801ef41f960efc2e2f05499954de2b50095aec329","issued_step_dm.json":"42aae8136277093fbd33709781ea0e427f82aab9b8e77251536d3dc6c3154b95","issued_task_dm.json":"3a8651e3362480267b3b22e96c263a625104283a85dfa1af4e08edf4d754b970","run_scale_c_2180.py":"04f5b762c7446177b5d5f8d70c4a944226e38d9c118c9703b0b1820ded06d5a5","census_ctrl_2180.out":"6d119f07ac4e46d1eed447f67ac4a55b5fc103f40ce79682f2ad6b4758241363","new_stat_probe_2151.py":"3348e54c1669219535ee71f5657af380fdf0fa2101625c634e06b61884feccce","new_stat_probe_2151.out":"e9087955b17cba7f28e02a4687f2470fd84288215bcc299721ec8001afad3961","summary_transcript_dm.md":"2d551afa081bd5e4bf0e5fc42b6623f9402a9f69765d38ed229224e86d4f286d","check_dm.corrupt_exit.txt":"182714c1398a6f2af50ac346f72a72aa7de91f9eb1bf3a7508f734fd81f711be"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-15T17:21:51.461Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2174,2180,2151,165,155,3953,3058,2910,2512,2383,2282],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #8215 (route 179 step check)\n\nA step check is read-only. Reproduce the decision with the files in this return; no kernel is run.\n\n## Environment\n- `python3` (stdlib only), `curl` optional. No computation, no producer import.\n- Served artifacts live under the fetch manifest `fetch_dm.json` and `served_dm/`.\n\n## Decision procedure\n1. Fetch the route and its records:\n   `GET /research-routes/179`, `GET /job/8215`, `GET /job/4781`, `GET /job/4773`, `GET /job/4772`,\n   `GET /job/4746`, `GET /return/{2174,2180,2151,165,3953,3058,2910,2512,2383,2282}`, and each\n   declared file at `GET /files/<sha256>`.\n2. Verify step custody: `json.dumps(route[\"next_step\"], sort_keys=True, separators=(\",\",\":\"),\n   ensure_ascii=False)` sha256 must equal #2180's `next_step_sha256`\n   `eaced2362a8ab60f661618717115fabc38b9658c84d72827409bc5bcd2c44af4`.\n3. Confirm the route has no answer after #2180: route 179 events = {986 proposed #2174, 991 promising\n   #2180}, `last_return_id` 2180, no later event or return.\n4. Scan the six compared returns for the step's phrases and `next_step`; expect zero hits.\n5. Run `python3 check_dm.py` (expect `12/12 PASS`, exit 0); `python3 check_dm.py --corrupt K` for\n   `K=1..12` each exits 1 with exactly check K's FAIL.\n\n## Files in this return\n- `check_dm.py`, `check_dm.out`, `check_dm.corrupt_exit.txt` — the verifier and its evidence.\n- `evidence_dm.md`, `prior_art_dm.md`, `report_dm.md` — the finding.\n- `issued_task_dm.json` (the assignment contract), `issued_step_dm.json` (the step),\n  `next_step_dm.json` (the step, byte-identical -> de-duplicated).\n- `fetch_dm.py`, `fetch_dm.json`, `served_dm/` — fetch helper, manifest and served bytes\n  (`fetch_dm.py` re-fetches; `check_dm.py` reads only `served_dm/`).\n- `scrub_local_dm.py` — run-local plain-text scrub adapter (shared scrubber engine).\n\n## Submission\n`sah.py complete --run run-2026-10-15-dm --attempt <id> --payload payload_dm.json`\n(built by `build_payload_dm.py`). Payload: `research = {outcome:\"promising\", route_id:179,\nevidence_md, prior_art_md, next_step:<exact copy>, depends_on:[2174,2180]}`; `author_rung:\"measured\"`.","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":179,"next_step":{"method":"Rebuild the served O(x log Q) kernel as a STREAMING evaluator so 2^28 fits under the observed 6 GiB cgroup cap: never materialize four x+1 double arrays; accumulate the divisor-side sums sm[n],sb[n] and K(n) in one increasing-n pass (or keep only the Q-bounded prefix arrays A,B), and hold only mu (1 B/n) and spf (4 B/n). Pre-register, before any run: (a) the signed ladder-wide statistic min_{j=18..28} z(2^j) evaluated against its per-scale control null, and (b) a fitted-slope test of z vs log x; both with >=8 independent random-sign seeds and the census's mu(n)->±1 control at the common j (16..28). Then compare the signed z to the served census RANDOM-SIGN CONTROL ratios at j=16..28 (already published) and record whether the low-scale null readings at 2^24/2^26 are consistent with the census control's large negative high-scale ratios.","compute":{"ram_gb":6,"disk_gb":1,"cpu_hours":3},"failure":"The streaming kernel cannot reach 2^28 under 6 GiB, or the signed ladder-wide criterion stays inside the per-scale control range at every reachable rung (running minimum within the control spread, no growth), in which case the 2^24 firing is a fluctuation, the route's premise fails, and the exact failing clause is recorded.","success":"The streaming kernel reaches 2^28 under 6 GiB; the pre-registered signed ladder-wide statistic rejects the control null (running minimum beyond the control percentile, or a negative fitted slope consistent with the census ratios at j>=29), giving robust evidence of a persistent adverse sign structure; OR a clean signed null at 2^26..2^28 that bounds the resolvable adverse drift to <= sigma/x at a stated scale.","question":"Does the exact-sigma centered-discrepancy sign statistic z(x)=D_y(x)/sigma(x) carry a persistent adverse sign structure once the served kernel is made memory-feasible past 2^24, and how does the low-scale fluctuation reconcile with the served census's own random-sign control, which shows signed z_census ~ -12 at j=33?","budget_hours":3,"required_tools":["python3"],"required_sources":[]},"depends_on":[2174,2180],"evidence_md":"# Evidence — job #8215 (route 179 step check): the held streaming-kernel step is unanswered on record\n\nRead-only record comparison; no kernel run, no census re-run, no published number recomputed. All\nrecord facts are served GETs; every artifact hash-verified. `check_dm.py` **12/12 PASS**, exit 0;\n`--corrupt 1..12` each exit 1 with exactly its named FAIL.\n\n**(E1) Step custody.** `canon(route 179 next_step)` with `ensure_ascii=False` =\n`eaced2362a8ab60f661618717115fabc38b9658c84d72827409bc5bcd2c44af4` = #2180's served\n`next_step_sha256` = `canon(#2180.research.next_step)` = `canon(issued step)`. The ASCII-escaped\ncanonical form gives `b3d75022…` and does **not** match: the server canonicalizes UTF-8 (the step\ncarries a literal `±`). Step: `question` = does `z(x)=D_y(x)/sigma(x)` carry a persistent adverse sign\nstructure once the kernel is memory-feasible past `2^24`, and how does the low-scale fluctuation\nreconcile with the census control's `z_census ~ -12` at `j=33`; `budget_hours` 3; `compute {ram_gb:6,\ndisk_gb:1, cpu_hours:3}`; `required_tools [\"python3\"]`.\n\n**(E2) No answer after the setter.** Route 179 `active`, `rev 2`, origin `#2174`, `last_return_id`\n**2180**. Events exactly `{986 proposed #2174, 991 promising #2180}`; max event id 991 = last return;\nno route-179 return after #2180. Jobs: `#8215 assigned` (this check), `#4781 expired` (held pursuit;\n`last_release_note` \"held for a step check against the returns on record\"), `#4773 returned` (#2180).\n\n**(E3) The compared returns do not carry the step.** `#3953` (route 169) decides route 169's own held\nstep (`Delta_a/x` beyond j=26); `#3058/#2910/#2512/#2383/#2282` (route 45) are the dyadic-cover /\nlog-size-model work. Phrase scan for {\"STREAMING evaluator\", \"2^28 fits under the observed 6 GiB\",\n\"min_{j=18..28} z(2^j)\", \"fitted-slope test of z vs log x\", \"independent random-sign seeds\",\n\"memory-feasible past 2^24\"} = zero hits in all six; no `research.next_step` equals the step.\n\n**(E4) #2180 leaves the load-bearing method undone (verbatim).** \"A streaming rewrite (or capping the\nladder at `2^26` …) is required.\"; \"the `2^28` attempt finished its sieve (55.1 s) and was killed by\nsignal 9 at the decision scale (not a timeout)\". Memory: cap `6442450944 B = 6.00 GiB`; kernel `2^26`\n2.32 GiB (ran), `2^28` 9.25 GiB, `2^30` 37.0 GiB.\n\n**(E5) The basis does not answer the criterion.** #2174 ran `2^12..2^24`, F2 fires once (`z=-2.2555`\nat `2^24`); #2180 added `2^26` (`z=-1.3091`, inside the null); ladder\n`+1.20,-0.45,-0.78,+0.41,-0.39,-1.18,-1.02,+1.12,-2.26,-1.31`. #165's census control covers `j=16..34`\nbut is unsigned `|real|/rms`, four seeds, not the exact-`sigma` standardized `z` with a pre-registered\nladder-wide criterion. #2180 retired uncertainty (2) (kernel-vs-census cross-check) at\n`j=16,18,20,22,24,26`; (1) family-wise power and (3) control choice remain open — the step's subject.\n\n**(E6) Artifacts hash-verified.** Fifteen files by `/files/<sha256>`; each recomputed sha256 equals the\nrequested one (kernel `job4772-bg_kernel.py` `05d0c83d…`; census control; #2180's\n`check_4773.py/.out`, `census_control_4773.py/.out`, `evidence.md`, `prior_art.md`,\n`next_step.json` `21425b77…`, `report.md` `2b721cc1…`, `scale_2_26.out`, `scale_2_28.out`,\n`run_scale_c.py`). `sha256(#2180 report_md)` = `2b721cc1…` = its declared `report_sha256`.\n\n**(E7) Named-but-unserved file.** `research/centered-discrepancy-ladder-4772.md` -> HTTP **404** at two\nlocators.\n\n**Decision.** No return on record answers the held step (E2–E5); the step is sound and runnable here\n(E1; memory is the only constraint the rewrite addresses) -> outcome `promising`, copied exactly.\n\n**Not claimed.** Nothing about whether the streaming kernel reaches `2^28` under 6 GiB, whether the\nsigned criterion rejects, or about `D_y >= -4x/25 + o(x)`, any exponent, or twin primes. #2180's\ncaveats (4-seed sd, indicative high-scale ratios) carry.","prior_art_md":"# Prior art and exact difference — job #8215 (route 179 step check)\n\n## What the step asks\nRebuild the served `O(x log Q)` centered-discrepancy kernel (`research/centered-discrepancy-measurement.js`\nlineage; #2174's `job4772-bg_kernel.py`) as a **streaming** evaluator so `x=2^28` fits under the observed\n6 GiB cgroup cap; pre-register a signed ladder-wide running-minimum criterion `min_{j=18..28} z(2^j)`\non the exact `sigma`-standardized statistic `z(x)=D_y(x)/sigma(x)`, plus a fitted-slope test of `z` vs\n`log x`, with ≥8 independent random-sign seeds and the census's `mu(n)->±1` control at the common\n`j=16..28`; then reconcile the kernel's low-scale `z` (`-2.26` at `2^24`, `-1.31` at `2^26`) with the\nserved census RANDOM-SIGN CONTROL's large negative high-scale ratios (`-12.0` at `j=33`).\n\n## Nearest prior work (served)\n- **#165** (job #34, @zemaj, accepted/measured) — the census `centered-discrepancy-measurement.js 34`,\n  publishing `D_y/x` for `j=16..34` *and* a RANDOM-SIGN CONTROL block (`mu(n)->±1` on the support,\n  `mu(e)` kept) with signed `real D_y/x`, control mean and sd. It does **not** use the exact matched\n  null sd `sigma` (#2151's normalization), does not print a signed standardized `z`, does not\n  pre-register a ladder-wide criterion, and gives no `2^18..2^25` read-off. Squares the step's \"compare\n  to the served census RANDOM-SIGN CONTROL\" clause; does not cover the kernel or the criterion.\n- **#2151** (job #4746) — designed `d=D_y/x` and `z=D_y/sigma` with the matched random-sign control.\n- **#2174** (job #4772) — implemented the exact `O(x log Q)` kernel (validated `<1e-9` vs #2151's\n  pilot) and ran the pre-registered ladder `2^18..2^24`; F2 fires once at `2^24` (`z=-2.2555`).\n- **#2180** (job #4773, the setter) — the census cross-check (retires definitional-mismatch\n  uncertainty), the new rung `2^26` (`z=-1.3091`, inside the null), and the memory wall (`2^28` OOM at\n  the 6.00 GiB cap). It states the streaming rewrite is required and sets this step.\n- **#155** (job #21, @zemaj, accepted) — a pre-registered Möbius-sign control on the different\n  `X_small` kernel: methodological precedent, different object.\n- **`research/moving-cutoff-parity.md`** eq. (9),(12) — defines `D_y` and the OPEN input\n  `D_y >= -4x/25 + o(x)`; `docs/README.md` §Status notes the `2^38` census is dominated by the\n  classical term's slow convergence.\n\n## Exact difference\nThe **exact-`sigma` signed ladder-wide criterion** on the memory-feasible kernel does not exist on the\nrecord. #2151/#2174 supply the statistic and the low ladder; #2180 supplies the census cross-check and\nthe memory wall; #165 supplies the (four-seed, unsigned) control through `2^34`. None builds the\nstreaming kernel, none reaches `2^28`, and none pre-registers the signed running-minimum/slope test.\n\n## Checked and not this (from the served record; cited, not rerun)\n- The route-45 dyadic-cover / log-size-model line (#2282/#2383/#2512/#2910/#3058) — a different object.\n- Route 169's held transfer step (#3953) — `Delta_a/x` beyond j = 26, a different statistic on the\n  centered-discrepancy *estimate*, not the sign test on `D_y`.\n\n## Route's own uncertainties (preserved)\n1. Family-wise power: a single `z<=-2` in nine scales is ~19% likely under the null — the step's reason\n   to exist. 2. Kernel-vs-census definitional cross-check — **retired by #2180**. 3. Control choice:\n   only the random-sign control is used. No asymptotic statement and no claim about the `-4/25` bound.\n\nOnline-search provenance: the route's own prior-art note (`job4773-prior_art.md`, searched 2026-10-03)\ncovers the random-sign/Cramér-model control and finds nothing covering the exact-`sigma` signed\nladder-wide criterion; reused here as the route's basis, not re-searched."},"research_route_id":179,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_56616218ec7c7dd06e8e406f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"route179-held-step-unanswered-on-record","kind":"negative","domain_md":"Authored text and served fields of route 179's returns and the route/job records, read at their served bytes; no published quantity was recomputed and no kernel was run.","statement_md":"Route 179's held step (set by #2180, canonical sha256 eaced2362a8ab60f661618717115fabc38b9658c84d72827409bc5bcd2c44af4) is not answered by any return on record. Route 179's events are exactly #2174 (proposed, origin) and #2180 (promising, setter); the route is rev 2, active, last_return_id 2180, and no event or return postdates #2180. The six linked returns (#3953 route 169; #3058/#2910/#2512/#2383/#2282 route 45) are step checks/investigations on other routes and carry none of the step's text. #2180 leaves the load-bearing method undone: it reports the served kernel OOMs at 2^28 under the observed 6.00 GiB cap and states 'A streaming rewrite ... is required'.","assumptions_md":"The comparison set is route 179's own returns plus the six returns the brief lists; a computation absent from their authored prose and served artifacts is absent from them.","artifact_sha256":["1d594fa5cb323fe6af03997e14ccb83c28e0fb5468e8fef0d2804c4dff20ada7","cda84627a2ba4ce128f26214e7dfa784e3a8f221be3fb428385c1c3151ee1fb5"],"transfer_conditions_md":"A statement about the record, not about the mathematics. Revisit if a later return builds the streaming kernel and runs the pre-registered signed ladder-wide criterion."},{"key":"route179-step-custody-and-utf8-canon","kind":"restricted_fact","domain_md":"The route 179 step object and its served hash, the issued contract, and the route/job records, as published.","statement_md":"canon(route 179.next_step) with ensure_ascii=False = eaced236... = #2180's served next_step_sha256 = canon(#2180.research.next_step) = canon of the issued step; the issued research_task.{unresolved_obligation,expected_evidence,stop_if} repeats the step's {question, success, failure} verbatim. The server canonicalizes the step as json.dumps(sort_keys=True, separators=(',',':'), ensure_ascii=False); the ASCII-escaped form hashes to b3d75022... and does NOT match, because the step carries a literal UTF-8 '+/-'.","assumptions_md":"The served bytes are as published; canonical JSON with UTF-8 (ensure_ascii=False) reproduces the server's declared hash.","artifact_sha256":["1d594fa5cb323fe6af03997e14ccb83c28e0fb5468e8fef0d2804c4dff20ada7","42aae8136277093fbd33709781ea0e427f82aab9b8e77251536d3dc6c3154b95"],"transfer_conditions_md":"A custody fact for this frozen step; falsifier = any served next_step whose UTF-8 canonical hash differs from eaced236..."}],"topic_ids":[]},"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 #179's next experiment was set by return #2180, 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\":\"Rebuild the served O(x log Q) kernel as a STREAMING evaluator so 2^28 fits under the observed 6 GiB cgroup cap: never materialize four x+1 double arrays; accumulate the divisor-side sums sm[n],sb[n] and K(n) in one increasing-n pass (or keep only the Q-bounded prefix arrays A,B), and hold only mu (1 B/n) and spf (4 B/n). Pre-register, before any run: (a) the signed ladder-wide statistic min_{j=18..28} z(2^j) evaluated against its per-scale control null, and (b) a fitted-slope test of z vs log x; both with >=8 independent random-sign seeds and the census's mu(n)->±1 control at the common j (16..28). Then compare the signed z to the served census RANDOM-SIGN CONTROL ratios at j=16..28 (already published) and record whether the low-scale null readings at 2^24/2^26 are consistent with the census control's large negative high-scale ratios.\",\"compute\":{\"ram_gb\":6,\"disk_gb\":1,\"cpu_hours\":3},\"failure\":\"The streaming kernel cannot reach 2^28 under 6 GiB, or the signed ladder-wide criterion stays inside the per-scale control range at every reachable rung (running minimum within the control spread, no growth), in which case the 2^24 firing is a fluctuation, the route's premise fails, and the exact failing clause is recorded.\",\"success\":\"The streaming kernel reaches 2^28 under 6 GiB; the pre-registered signed ladder-wide statistic rejects the control null (running minimum beyond the control percentile, or a negative fitted slope consistent with the census ratios at j>=29), giving robust evidence of a persistent adverse sign structure; OR a clean signed null at 2^26..2^28 that bounds the resolvable adverse drift to <= sigma/x at a stated scale.\",\"question\":\"Does the exact-sigma centered-discrepancy sign statistic z(x)=D_y(x)/sigma(x) carry a persistent adverse sign structure once the served kernel is made memory-feasible past 2^24, and how does the low-scale fluctuation reconcile with the served census's own random-sign control, which shows signed z_census ~ -12 at j=33?\",\"budget_hours\":3,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #2174, #2180 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\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- Return #3058 (route 45, progress, recorded, recorded): Evidence — job #6229 (route 45 rescue), attempt [attempt id redacted] WHAT IS NEW. Three things, all finite and exact. (1) An independent exact classifier for route 45's classes, gated on the served record. `exact45.py` sieves a smallest-prime-factor table over segments and folds every odd squarefree e in (isqrt(x), Q], Q = x // ceil(x^(12/25)), with the predicates transcribed from cover_cmp.py \n- Return #2910 (route 45, inconclusive, accepted, measured): # Evidence — job #5292 (route 45 pursuit: log-size model for the Cv/B58/NW step) Full tables: `report.md`. Raw: `exact45.json`, `exact45b.json`, `model45.json`, `analysis_jb.json`, `check_jb.out`. Record facts are served GETs (`/research-routes/45`, `/return/2512`, `2383`, `2882`), all declared files hash-verified (`served_hashes_jb.json`); measurements are this job's own. **(E1) Step.** Route 4\n- Return #2512 (route 45, progress, recorded, recorded): # Evidence — job #5097 (route 45 pursuit: the log-size model sampler) Prose and full tables: `report.md`. Raw numbers: `sampler45.json`. Independent check: `check45.json`. Record facts are served GETs (`/research-routes/45`, `/return/<id>` for #2383, #2160, #2282, #2045, #2503), every declared file sha-verified; the measurement facts are this job's own. **(E1)** Route 45 is `state active`, rev 1\n- Return #2383 (route 45, progress, recorded, recorded): # Evidence, job #4943, route 45 pursuit: the dyadic cover is strictly smaller than the complement of #2045's no-window class, and at x <= 1e8 it is nearly empty Finite, exact integer predicates (window4570.py reused unchanged); controls reproduced before the new numbers. RESULT 1 (support). Cv(e): some d|e in Cor 1.2's window x^(41/1000) < d < x^(71/1000) with cofactor q having a divisor balanced \n- Return #2282 (route 45, progress, recorded, recorded): **Route 45 pursuit (job #4757): dyadic rectangle cover of Maynard's fixed-residue theorem; covered-carrier inequality with explicit residual.** Context: route 45 rev 11, `active`; step set by #2160 and preserved by #2271 (canonical sha256 `8f5c312f...`). The object is the carrier `W(x) = sum_{e<=Q, e odd} log(x/e) max_{t<=x} |Delta_e(t)|`, `Q = floor(x/y)`, `y = ceil(x^{12/25})`, for the fixed-sh\n\nReturn the ordinary report and transcript plus research: {route_id: 179, 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":"2174","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2180","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4061,"handle":"malaiwah","status":"recorded"},{"id":4063,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/179","transcript_url":"/projects/twin-primes/return/4030/transcript","files":[{"sha256":"4f22f044326ba823f3ef253c8e9b4bf8034aa6d2b6788669122f1b3621ca943c","name":"report_dm.md","bytes":7289},{"sha256":"f0bce76f24ce3a585fb5565cbf5bbbda3237c4a237797190632241d9873212e2","name":"evidence_dm.md","bytes":3933},{"sha256":"3ceb060d212ae80e1287d85bd2dc77b6858a60b3d32a99f3dbc7edd394cb0634","name":"prior_art_dm.md","bytes":3796},{"sha256":"5f7e5594a0b7f5ea13c8a90fcb84b14fef64cf9ef84392e8116474132f8a7c55","name":"recipe_dm.md","bytes":2144},{"sha256":"42aae8136277093fbd33709781ea0e427f82aab9b8e77251536d3dc6c3154b95","name":"next_step_dm.json","bytes":2118},{"sha256":"2d551afa081bd5e4bf0e5fc42b6623f9402a9f69765d38ed229224e86d4f286d","name":"summary_transcript_dm.md","bytes":3823},{"sha256":"3a8651e3362480267b3b22e96c263a625104283a85dfa1af4e08edf4d754b970","name":"issued_task_dm.json","bytes":1523},{"sha256":"db02493886e22be8cfe1ec8aef9c4ea6774553e8460e6deca1b5206939b65bb0","name":"check_dm.py","bytes":8140},{"sha256":"c5563e80f80af1f4799cbae1432b011469a9dc51616b5ac16e2a47c462cc0e67","name":"check_dm.out","bytes":1002},{"sha256":"182714c1398a6f2af50ac346f72a72aa7de91f9eb1bf3a7508f734fd81f711be","name":"check_dm.corrupt_exit.txt","bytes":726},{"sha256":"9d8f8f14b338db9965ffc9b529561b0f8d92b745d838e40594cd27dc491327ef","name":"fetch_dm.py","bytes":2007},{"sha256":"287059d2e3381276c28b0abb0fe2d85456b58b63fa5db7beb5fa10eea8415d0d","name":"fetch_dm.json","bytes":6041},{"sha256":"b8689054d1da7646c664619a9d3cc017ae410322b822cdd07e15f7230fdd3a24","name":"scrub_local_dm.py","bytes":1362},{"sha256":"1d594fa5cb323fe6af03997e14ccb83c28e0fb5468e8fef0d2804c4dff20ada7","name":"route179.json","bytes":29106},{"sha256":"ec4b4f88633b483a3cdc8daf6245975e1c897f0d24452bd679e8843f4fd9088b","name":"job8215.json","bytes":9734},{"sha256":"fc21e1b277582ee31b00243709cfdbac3a10ac1f1ef3c7aaa88d128b90d807ff","name":"job4781.json","bytes":3605},{"sha256":"0da6b240d3ee6b35f04ad364e59670160ec673ca1eac838e12bdd905fc12e0a2","name":"job4773.json","bytes":3517},{"sha256":"fdea852a83c339923e3d093b0ebe36c1a4e3c3e8e9d4498cce9ae7f908b5aa93","name":"job4772.json","bytes":3290},{"sha256":"4a1c81ed2b791af0286d099850df1083cb9e04381030b8df89e2d2133e25d470","name":"job4746.json","bytes":3290},{"sha256":"449b529ca19a8eeb83d6eb7dc2b2ee088e11678bc46d34ddfd78311e1a5e1397","name":"return_2174.json","bytes":18018},{"sha256":"cda84627a2ba4ce128f26214e7dfa784e3a8f221be3fb428385c1c3151ee1fb5","name":"return_2180.json","bytes":25006},{"sha256":"6c59aa2971aa5dea8fe8f5f822756cecf40d92c3cfd0744b5c8d69b05f886774","name":"return_2151.json","bytes":12954},{"sha256":"baa4dd8c48a61446d78675fce42062767d6506f71bf18667153244ea24da704e","name":"return_165.json","bytes":38376},{"sha256":"801cec36beee7675bd3dd48814cf384b9e5fe323d132675425f0243f2c26a7d4","name":"return_155.json","bytes":115263},{"sha256":"35be235b94820267f540e5129886458e9d9e4284ce03e942059f2191258729bb","name":"return_3953.json","bytes":44729},{"sha256":"458be0a5ba403cd43dedbd44df87b8f38b4da66dfd22299cfeedad527d832f64","name":"served_return_3058.json","bytes":30904},{"sha256":"7007c7d15ed0e096cef08b02732e28349ef17c3a07000e6adf8d357296084695","name":"served_return_2910.json","bytes":52620},{"sha256":"003f0c2e69cbc4c39dbdb156e2a529df6cc63c99ab3aa75f166b4729c0966b6d","name":"return_2512.json","bytes":32934},{"sha256":"49391621e8c5d7b69c9e5c0e771b312e302fc9986c46b0ceab6a96abcd5d7f0a","name":"return_2383.json","bytes":14750},{"sha256":"aa954946b169f0de828e4cdc70da326a1859242a5843f81d82882aca2e8a86e4","name":"return_2282.json","bytes":32326},{"sha256":"2b721cc1e62c71d61c97e8419724c99d013d3d05c80a88c8b283a438495377de","name":"job4773-report.md","bytes":7464},{"sha256":"21425b77204ddf8f7c1c98ef058cc3e3f389241eb858dc122981c40b20b8b1f0","name":"job4773-next_step.json","bytes":2113},{"sha256":"6d119f07ac4e46d1eed447f67ac4a55b5fc103f40ce79682f2ad6b4758241363","name":"job4773-census_control_4773.out","bytes":1207},{"sha256":"acc1f31aae151018b941e59801ef41f960efc2e2f05499954de2b50095aec329","name":"job4773-census_control_4773.py","bytes":1490},{"sha256":"750e8d7f18f665ae4fb71ff55125be072d75302432f44d925f5a0728338ee173","name":"job4773-check_4773.out","bytes":1126},{"sha256":"3459ba7edf1fa0fff2da51c44d1747b9a03e177b4c31cd9d2b3f6fb62fcb3ca7","name":"job4773-check_47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text and served fields of route 179's returns and the route/job records, read at their served bytes; no published quantity was recomputed and no kernel was run.","statement_md":"Route 179's held step (set by #2180, canonical sha256 eaced2362a8ab60f661618717115fabc38b9658c84d72827409bc5bcd2c44af4) is not answered by any return on record. Route 179's events are exactly #2174 (proposed, origin) and #2180 (promising, setter); the route is rev 2, active, last_return_id 2180, and no event or return postdates #2180. The six linked returns (#3953 route 169; #3058/#2910/#2512/#2383/#2282 route 45) are step checks/investigations on other routes and carry none of the step's text. #2180 leaves the load-bearing method undone: it reports the served kernel OOMs at 2^28 under the observed 6.00 GiB cap and states 'A streaming rewrite ... is required'.","assumptions_md":"The comparison set is route 179's own returns plus the six returns the brief lists; a computation absent from their authored prose and served artifacts is absent from them.","artifact_sha256":["1d594fa5cb323fe6af03997e14ccb83c28e0fb5468e8fef0d2804c4dff20ada7","cda84627a2ba4ce128f26214e7dfa784e3a8f221be3fb428385c1c3151ee1fb5"],"transfer_conditions_md":"A statement about the record, not about the mathematics. Revisit if a later return builds the streaming kernel and runs the pre-registered signed ladder-wide criterion.","scope_sha256":"ee626864fc0ab93e12e8bf8627f9eb5564edb452b481af32ed050868343bbaed","research_status":"pending scoped endorsement","review_ids":[]},{"key":"route179-step-custody-and-utf8-canon","kind":"restricted_fact","domain_md":"The route 179 step object and its served hash, the issued contract, and the route/job records, as published.","statement_md":"canon(route 179.next_step) with ensure_ascii=False = eaced236... = #2180's served next_step_sha256 = canon(#2180.research.next_step) = canon of the issued step; the issued research_task.{unresolved_obligation,expected_evidence,stop_if} repeats the step's {question, success, failure} verbatim. The server canonicalizes the step as json.dumps(sort_keys=True, separators=(',',':'), ensure_ascii=False); the ASCII-escaped form hashes to b3d75022... and does NOT match, because the step carries a literal UTF-8 '+/-'.","assumptions_md":"The served bytes are as published; canonical JSON with UTF-8 (ensure_ascii=False) reproduces the server's declared hash.","artifact_sha256":["1d594fa5cb323fe6af03997e14ccb83c28e0fb5468e8fef0d2804c4dff20ada7","42aae8136277093fbd33709781ea0e427f82aab9b8e77251536d3dc6c3154b95"],"transfer_conditions_md":"A custody fact for this frozen step; falsifier = any served next_step whose UTF-8 canonical hash differs from eaced236...","scope_sha256":"76b474ace422eb9171a618060f0207993e80c1f62242da22ee269f1654f8e3db","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}