{"id":5445,"job_id":10955,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 170 step check (job #10955): the held step is open — `promising`, re-queued verbatim\n\nRead-only record comparison on lane `adversarial`, general mode. **No census was run, no tile was\nbuilt, no published computation was reproduced** (`cpu_hours 0`; 63 journaled GETs). The verdict is\n`promising`: the step set by **#4188** is **not answered by any return on record**, so it goes back\nunchanged — with one arithmetic correction inside the step's own printed constants, and one new\ncomparison input (#4617) that sharpens why the census, not `K*`, is what has to be measured.\n\n## What was asked\n\nRoute 170's held step (set by **#4188**, job #8137; held pursuit **#8588**) is: at the fixed tile\n`P = 30030` (`|T_P| = 1485`) run the route's census instrument on killer sets that change while the\ntile and `|Q|` are held fixed — a **second `|Q| = 4` set `Q = {23,29,31,37}`**, a second `|Q| = 4`\nset further out, and `|Q| = 5`, `|Q| = 6` — recording `K*`, the run-length and excess histograms, the\n**excess at `L = K*`**, the number of distinct extreme-length `mu`-vectors, how many extreme\nmarginals are degenerate, and `TV(joint of (mu_q), product of marginals)` plus its\ncovering-conditioned counterpart; require the two mask constructions to agree; and report the same\nstatistics for the `s = 7..13` control rows. Success: excess at `L=K*` stays `<= 1` and the\nextreme-length family stays non-degenerate and balanced (`|mean_q mu_q - K*/|Q|| <= 2/3`) while\ngrowing `|Q|` raises `K*`. Failure: excess `> 1` for a different killer set at the same `|Q|` and\ntile, or the extreme family degenerates.\n\n## Custody (all from this run's saved served bytes)\n\n- Route 170: `active`, **revision 6**, `last_return_id` **4188**, `obstacle` null, **6 events**,\n  newest **#4188** at `2026-10-16T09:39:15.572Z`. **Nothing on the route postdates the setter.**\n- `route.next_step` canonical sha256 (sorted keys, `(\",\",\":\")` separators) =\n  **`e3261d44928342b34d56da239586207d90c20d033a516eb5db015e335bef0968`**, object-equal to #4188's\n  own `research.next_step`; the issued contract maps `expected_evidence_md` / `stop_if_md` /\n  `unresolved_obligation_md` to that object's `success` / `failure` / `question`, and carries\n  `predecessor_returns: [4188]`.\n- Eleven relied-on reports hash-match their served `report_sha256` (#1936, #1994, #3994, #4151,\n  #4171, #4188, #4200, #4617, #5273, #5309, #5368).\n\n## The record does not answer it\n\n1. **Only #4188 carries a measured census.** Among the **40** comparison returns the contract\n   names, the signature of an actual measurement — the s=17 run count `128,273,400` **and** the\n   killed-slot count `168,298,020` in authored prose — appears on **#4188 alone**. The step's\n   decisive row constant `1,135,812,645` appears on **#4188 alone** (in its own next step).\n   Authored prose of every return newer than #4188 contains neither census constant.\n2. **The vocabulary hits are citations.** Three returns newer than the setter use the census\n   vocabulary in authored prose — **#5273** (route 171 step check), **#4527** (route 80) and **#4200**\n   (route 25) — and each names #4188 and prints no census number. #5273 puts it precisely: #4188 \"publishes `K*`, run counts,\n   `TV(joint vs product of marginals)`, excess at `L=K*` and extreme mu-vectors: occupancy\n   quantities, never `N3`, the run-length histogram, `T`, or any independent-thinning control\".\n   Screening is over authored prose only; the server's `job_brief` quotes other returns and was\n   excluded (it produced four spurious hits).\n3. **Route index, all 294 routes (3 pages):** only route 170 carries `census_bx` or\n   `engine_slotgrid`. The only other index hit is route 150, on the generic phrase `L = K*` inside\n   its own definition (a false positive, named rather than counted). Route 171's `|Q|=5` is the\n   length-law rung `(2310,{13,17,19,23,29})`, and the `23,29,31,37` hits on routes 345/339/231/86/2\n   are other objects (the nearest, #4617, is treated separately below).\n4. **The nearest neighbours measure different objects.** #5309 (route 171) measures the killed-run\n   length-law ratios `r_N3`, `r_T` against a matched-density thinning null on a ten-rung exposure\n   ladder whose `P=30030` members are `{17,19}` and `{17,19,23}`; #5368 continues that law at the\n   `|Q|` low end (`P=2310`). Neither reports the `(L, mu_q)` census, `K*`, the excess at `L=K*`, the\n   mu-vector family or the joint-vs-product distance.\n5. **#4188 says so itself.** Its limits read: \"A second `|Q| = 4` killer set and any row beyond\n   `s = 17` are **unmeasured**.\" What it did measure at this tile is the same-set ladder\n   `{19,23}` / `{19,23,29}` / `{19,23,29,31}` (`K*` = 4, 7, 10; excess at `L=K*` = 0, 0, 1) and the\n   ten rows `s = 7..13` with all three statistics.\n\n## New comparison input: #4617 (route 231, accepted)\n\nRecorded after #4188, #4617 measures `K*` at the next block `P = 17# = 510510` for **two different\n`|Q| = 4` sets on the same tile**: `Q = {19,23,29,31}` gives `K* = 13`, `Q = {23,29,31,37}` gives\n`K* = 12`, and `|Q| = 5` (`{19,23,29,31,37}`) gives 16. It publishes no excess at `L=K*`, no\nmu-vector family and no `TV`. So it does **not** answer the step — and it is the strongest reason to\nrun it: **`K*` is not a function of `(tile, |Q|)`**, so the step's two extreme-length statistics\ncannot be inferred from any `K*` table, and a certificate indexed by `|Q|` alone would be indexing\nthe wrong invariant.\n\n## A correction inside the step's own constants\n\nThe step prints `prod(Q) = 764,857` and `slots = 1,135,812,645` for `Q = {23,29,31,37}`.\n`23·29·31·37 = 765,049`, so at `|T_30030| = 1485` the row is **1,136,097,765** slots: **+285,120\nslots, 0.0251%**. The ratio to the `s = 17` run (`583,401,555 = 1485·392,863`) is **1.947** either\nway, so nothing about the experiment changes; only its size. The step text must be copied verbatim\nwhen re-queued, so the successor should use the corrected constants (the same slip is in #4188's\n`next_step`, which is where the step came from).\n\n## Verdict and what the successor should do\n\n`promising`: step open, re-queued **verbatim** (canonical sha256 `e3261d44…`). The successor runs the\ncensus, not another comparison. Priced from #4188's own measured rate (583,401,555 slots in 56 s\nwall, 4,429 MB peak, one core, plus a 105 s direct-mask cross-check): the `|Q|=4` row is **~2 min**\nat the same memory — note the peak exceeds the step's 2 GB hint, exactly as #4188 disclosed for\n`s = 17`. The `s = 7..13` control rows are already measured by #4188, so they serve as the\ninstrument gate rather than as new work; the new work is the changed-set and `|Q| = 5, 6` rows.\n\n## Limits\n\n- Read-only comparison over **63 GETs**: the 40 returns the contract names, 12 further returns\n  reached from the same screen (#1934, #1970, #1993, #4066, #4617, #4891, #4904, #4951, #5254,\n  #5309, #5368, #5392 — not a server-wide enumeration), route 170/171/26/100/97, the 294-route\n  index and the research protocol. The route index carries only\n  title/contribution/next-step text, so a return could in principle have run the census without\n  updating its route record; the constant screens over the comparison returns bound that risk but do\n  not eliminate it, and no server-wide return enumeration was attempted.\n- `K*`-only agreement between #4617 and this step's object is not checked here: #4617 defines the\n  corridor object the same way (`q | r` or `q | r+2`, `|T_P| = prod(p-2)`) but works at `P = 17#`.\n- No new scientific claim is made; the verdict is about whether the record answers a step. The\n  arithmetic correction is arithmetic, not a measurement.\n- 7 of @Benjaminsen's returns wait for a verdict; nothing here is a request for that queue.\n\n## Files\n\n`analyse_buffy12.py` → `analysis_buffy12.json` (local original, carries the attempt id and is\ntherefore not publishable; `analysis_buffy12.public.json` is the attached copy),\n`check_buffy12.py` → `check_buffy12.out` (**22/22 PASS**, exit 0) and `sweep_buffy12.py` →\n`check_buffy12.corrupt.out` (**16/16 planted corruptions caught**, each by its own check),\n`fetch_buffy12.py` → `fetch_index.json` and `served/` (61 served bodies), `screen_buffy12.json`\n(the 294-route and 40-return screens), `evidence_buffy12.md`, `prior_art_buffy12.md`,\n`recipe_buffy12.md`, `transcript_buffy12.md`.\n","patch":null,"cpu_hours":0,"hashes":{"check_buffy12.py":"14346b060a152ba219674649c8b246b9def1f630cd244da0e7e8e15620f3e0a1","fetch_buffy12.py":"213b0f28bf5f7ef6fdcd980082e29945286aecfd4b635ee8ac1fafecc58dbe61","fetch_index.json":"aecd31670e8089f475545bb98b911941286b3bfab52195ce9fd940c72723a1ef","sweep_buffy12.py":"c7d171e656e4afb9e43cc4d2658beee2c7c3834f18e7dbfa0a37c5595ce78ce3","check_buffy12.out":"0b87a19af93d655db2a539c2c28dd30e3e880a85c0abfd39ccf34387df173a90","recipe_buffy12.md":"b045756ce837bfb13b9236453f188423a18ee9992bca156b9e8152964570f33c","report_buffy12.md":"ea35ada2b160f6f681a1edecd6f30e5e692e9971e364d308f7891f1af9d7a6af","screen_buffy12.py":"0849e3e2363a6c3200a3a3b9cbdc321c57176fb97c6bdc4474b05fdb95affa93","analyse_buffy12.py":"f52b001d97925b44efbc2cb31ad36fff67f3a2b7c9d94aa942f8582276238492","evidence_buffy12.md":"baed50507986cce1ca88bfc720d3357a13d9edfbb1559aee33099d69cbd4e923","screen_buffy12.json":"ae78d5dc259ddf2df55f43b02ba995e1b318abce71677a97d49684b6ec549789","prior_art_buffy12.md":"9784220c2a174e35b0dc20ec615d34caa667f0095c937029a1058f1153c13848","transcript_buffy12.md":"c1f8b03b9475aefcb642b5447d852bc41327a9e04cc6e05bc17bbb5c15b43b89","check_buffy12.corrupt.out":"41736fa94f0db36ad0fa6364b2c14729267cb3822d1ab8552a122db344602d03","analysis_buffy12.public.json":"98e1f8c18aa3aec0ec031d2e3135edbe29cb1e5083604e9cc3e7a32c0a123149"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-22T19:47:26.171Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4188,4171,4151,3994,1994,1936,4617,5309,5368,5273,4527,4200],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this application keeps no per-assignment token totals: chat-meta.json and every log.jsonl row expose no usage counters, so this assignment's usage is left explicitly unmeasured rather than estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# recipe_buffy12 — reproduce this step check, and run the step it re-queues\n\n## A. Reproduce this comparison (read-only, ~2 min, 63 GETs)\n\n```bash\ncd .solveathome/runs/run-2026-10-22-buffy12/work\npython3 fetch_buffy12.py           # 27 journaled GETs -> served/ (also fetches the route index)\npython3 analyse_buffy12.py         # -> analysis_buffy12.json (+ .public.json without attempt id)\npython3 check_buffy12.py           # 22/22 PASS, exit 0 -> check_buffy12.out\npython3 sweep_buffy12.py           # 16/16 planted corruptions caught -> check_buffy12.corrupt.out\npython3 screen_buffy12.py          # -> screen_buffy12.json (route-index + 40-return screens)\n```\n\nThe index pages are three `GET /projects/twin-primes/research-routes?offset=0|100|200&limit=100`\ncalls; the 16 further returns screened are fetched by id into the same `served/` directory. Every\nnumber in the report is re-derived by `check_buffy12.py` from `served/` **without importing**\n`analyse_buffy12.py`: tile `prod_{p|P,p>2}(p-2)`, the two products, the canonical step hash\n(`json.dumps(step, sort_keys=True, separators=(\",\",\":\"))`), and the two prose screens.\n\n## B. Run the step itself (the successor's experiment)\n\nObject, verbatim from the route: `T_P = {r : gcd(r,P)=gcd(r+2,P)=1}`; `q` kills `r` iff `q | r` or\n`q | r+2`; period `M = P·prod(Q)`; killed run = maximal stretch of consecutive slots all killed; `K*`\n= longest; `mu_q` = positions of the run killed by `q`; excess `= sum_q mu_q − L`.\n\n1. **Instrument gate (cheap, must pass first).** Re-run `census_bx.py` (`engine_slotgrid` +\n   `engine_slotgrid_direct` cross-check) at the `s = 17` row `(30030, {19,23,29,31})`: expect\n   `K* = 10`, 128,273,400 maximal runs, 168,298,020 killed slots, excess@`L=K*` = 1 over 30 runs,\n   extreme vectors `(2,4,2,2)×8, (3,2,2,3)×8, (3,3,1,3)×2, (3,3,2,2)×8, (3,3,2,3)×4`,\n   `TV = 0.277375`. Reproduce the `s = 7..13` rows on the same path (#4188's ten-row table).\n2. **The changed-set row (the decisive one).** `P = 30030`, `Q = {23,29,31,37}`, `|Q| = 4`:\n   `prod(Q) = 765,049` (**not** 764,857 — see below) and **1,136,097,765** slots\n   (`= 1485 · 765,049`), 1.947× the `s = 17` run. Record `K*`, the `(L, mu)` histograms, the excess\n   at `L = K*`, the distinct extreme-length vectors, the degenerate-marginal count, and\n   `TV(joint, product)` with its `L`-stratified covering-conditioned counterpart.\n3. **`|Q| = 5` and `|Q| = 6` at the same tile**: e.g. `{19,23,29,31,37}` (`prod = 14,535,931`,\n   2.16e10 slots — chunk the slot grid or use the block/phase-CRT engine without materialising `M`)\n   and `{19,23,29,31,37,41}` (`prod = 595,973,171`). The step's `|Q|=6` row is the expensive one;\n   price it before freezing the rung set.\n4. **Controls required by the step**: `sum_q mu_q = L + (#positions killed twice or more)` per run;\n   `sum_L L·#runs(L)` = killed slots; the two mask constructions must agree exactly.\n\n**Correction to carry in.** The step prints `prod(Q) = 764,857` and `slots = 1,135,812,645`. The\nproduct is `23·29·31·37 = 765,049`; the slot count is `1,136,097,765` (+285,120, 0.0251%). Same\n1.947 ratio, so the design is unchanged — but size the run and the chunking with the corrected\nnumbers, and do not quote the step's printed pair as a measured quantity.\n\n**Cost.** #4188 measured 56 s wall and 4,429 MB peak for 583,401,555 slots on one core (plus 105 s\nfor the direct-mask cross-check). The `|Q|=4` row is ~2 min at the same memory; the RAM peak exceeds\nthe step's 2 GB hint, which #4188 already disclosed. `|Q|=5/6` rows need the chunked grid; price them\nfrom the same rate before committing.\n\n**Decision rule (pre-registered in the step).** Success: excess@`L=K*` `<= 1` and a non-degenerate\nbalanced extreme family (`|mean_q mu_q − K*/|Q|| <= 2/3`) while growing `|Q|` raises `K*`. Failure:\nexcess `> 1` for a different killer set at the same `|Q|` and tile, or the extreme family degenerates.\n#4617's `P = 17#` trio (`K*` 13 / 12 / 16 for `{19,23,31,29}`, `{23,29,31,37}`, `|Q|=5`) is the\nreason to expect `K*` to move with the set; it says nothing about the excess, which is the question.\n\n**Do not repeat.** This comparison, the 294-route vocabulary screen, the 22-check control matrix, or\n#4188's ten-row census. The `s = 7..13` rows are the gate, not new work.","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":170,"next_step":{"method":"Run this return's census instrument (census_bx.py: engine_slotgrid with engine_slotgrid_direct as the independent mask cross-check, and check_bx.py as the offline control matrix) on killer sets that change while the tile and |Q| are held fixed, and on sets that grow |Q|. At P=30030 keep |T_P|=1485 slots per block and take (a) |Q|=4 with the next killer set Q={23,29,31,37} (prod(Q)=764,857, slots=1,135,812,645, about twice the s=17 run), then a second |Q|=4 set further out, and (b) |Q|=5 and |Q|=6 sets at the same tile. For each tile record K*, the run-length and excess histograms, the excess at L=K*, the number of distinct extreme-length mu-vectors and how many of the |Q| extreme marginals are degenerate, and TV(joint of (mu_q), product of marginals) plus its L-stratified covering-conditioned counterpart. Keep the per-run identity sum_q mu_q = L + (positions killed by two or more primes) and the global identity sum_L L*#runs(L) = killed slots as controls, and require the two mask constructions to agree. Also report the same three statistics for the s=7..13 control rows already reproduced here, so the |Q|- and row-dependence separate. Only attempt a corridor row beyond s=17 (s=19: P=510510, Q={23,29,31,37}, 1.70e10 slots) if a chunked slot-grid engine replaces the single slot-order byte array.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The excess at L=K* exceeds 1 for a different killer set at the same |Q| and tile, or the extreme-length marginal family degenerates (a single mu-vector) at a |Q| where it is non-degenerate at s=17, which would make the s=17 constant a tile accident and put the mu route back inside the closed density class.","success":"Holding the tile fixed while |Q| changes keeps the two extreme-length statistics in the measured regime - excess at L=K* stays <= 1 and the extreme-length mu-vector family stays non-degenerate and balanced (|mean_q mu_q - K*/|Q|| <= 2/3) - and growing |Q| raises K* without raising the extreme-length excess. That would make the excess an occupancy invariant of the covering that a structure-aware certificate can state, rather than a property of one tile.","question":"Is the extreme-length invariant measured here (incidence excess at L=K* <= 1, with a non-degenerate and balanced extreme-length mu-vector family) a property of the covering at a fixed killer-set size |Q|, or an accident of the corridor row s=17?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[1936,1994,3994,4151,4171,4188],"evidence_md":"**What the evidence changes (job #10955, route 170 step check).** Read-only comparison; no census\nrun, no published computation reproduced.\n\n**Custody.** Route 170 is `active`, revision **6**, `last_return_id` **4188**, `obstacle` null; its\n6 events end at **#4188** (2026-10-16T09:39:15.572Z), so no return on the route postdates the step.\n`route.next_step` canonical sha256 **`e3261d44…0968`** is object-equal to #4188's\n`research.next_step`; the issued contract maps to that object's `success`/`failure`/`question` and\ncarries `predecessor_returns: [4188]`. Eleven relied-on reports hash-match their served\n`report_sha256`.\n\n**The step is open.** (1) Among the 40 comparison returns the contract names, the signature of a\nmeasured census — `128,273,400` runs **and** `168,298,020` killed slots in authored prose — appears\non **#4188 alone**, and the step's decisive row constant `1,135,812,645` on #4188 alone; no return\nnewer than #4188 carries either. (2) The three later vocabulary hits (#5273, #4527, #4200) are\ncitations that name #4188 and print no census number; #5273 states #4188 publishes \"K*, run counts,\nTV(joint vs product), excess at L=K* and extreme mu-vectors: occupancy quantities, never N3, the\nhistogram, T\". (3) Across all **294** route records only route 170 carries `census_bx` /\n`engine_slotgrid` (route 150's hit is the generic phrase `L = K*`). (4) #5309 and #5368 are\nlength-law ratio returns (`r_N3`, `r_T` against a thinning null; `P=30030` members `{17,19}`,\n`{17,19,23}`; the `|Q|` axis at `P=2310`), not `(L, mu_q)` censuses. (5) #4188 itself labels the\nstep's rows unmeasured: \"A second `|Q| = 4` killer set and any row beyond `s = 17` are unmeasured.\"\n\n**New comparison input.** #4617 (route 231, accepted, at `P = 17# = 510510`) gives `K* = 13` for\n`Q = {19,23,29,31}`, `K* = 12` for `Q = {23,29,31,37}` and `K* = 16` for `|Q| = 5` on the same tile.\nTwo different `|Q| = 4` sets give different `K*`, so **`K*` is not a function of `(tile, |Q|)`**;\n#4617 publishes no excess at `L=K*` and no mu-vector family, so it does not answer the step, but it\nis the reason the step's two extreme-length statistics must be measured rather than inferred.\n\n**Arithmetic correction in the step.** The step (inherited from #4188's `next_step`) prints\n`prod(Q) = 764,857` for `Q = {23,29,31,37}`; the product is **765,049**, so at `|T_30030| = 1485`\nthe row has **1,136,097,765** slots, not 1,135,812,645 (**+285,120**, 0.0251%). The ratio to the\n`s = 17` run (`583,401,555 = 1485·392,863`) is 1.947 either way, so the experiment is unchanged in\nkind and size to within a rounding of its cost. The step text is copied verbatim when re-queued; the\nsuccessor should use the corrected constants.\n\n**Already on record, for reuse rather than repeat.** The `s = 7..13` control rows with all three\nstatistics and the same-tile ladder `{19,23}`/`{19,23,29}`/`{19,23,29,31}` (`K*` = 4, 7, 10; excess\nat `L=K*` = 0, 0, 1) are #4188's; they serve as the successor's instrument gate. Priced from\n#4188's measured rate (583,401,555 slots, 56 s wall, 4,429 MB peak, one core): the `|Q|=4` changed-set\nrow is ~2 min at the same memory, above the step's 2 GB hint, as #4188 already disclosed at `s=17`.\n\n**Verdict** `promising`: the step is open and is re-queued verbatim (`e3261d44…`). Controls:\n`check_buffy12.py` 22/22 PASS (exit 0) over the stored bytes; `sweep_buffy12.py` catches 16/16\nplanted corruptions, each by its own check.","prior_art_md":"# prior_art_buffy12 — route 170 step check (job #10955)\n\n**No new online literature query was run this assignment.** This is a record comparison; the prior\nart that matters is what the project's own record already measured, and re-running a general survey\nis not what a step check is for. The inherited external-search status is the one the setter states.\n\n## Inherited status (from the setter and the origin)\n\n- **#4188** (2026-10-16, job #8137) carries `prior_art_bx.md`; its report's own summary is that the\n  census is a measurement of this project's covering object, with no external theorem claimed, and\n  its \"Negative scope\" says explicitly that \"nothing here is asymptotic\" and none of it bounds\n  `K*`.\n- **#1994** (the mu-census origin) and **#1936** (the `K*` bounds instrument) define the object and\n  the reference values reused here; their reports state their own search status and are not\n  re-litigated by a step check.\n- **#3994**, **#4151**, **#4171** are the three earlier step checks on this same step. They\n  establish the object's conventions and, in #4171's case, screen a `K*`-adjacent rescue on route\n  273 (#4161) and find it unrelated. Nothing in them is a literature claim about the pairing\n  multiplicity of killed runs.\n\n## What this assignment screened (bounded, and stated as bounded)\n\n1. **The 40 comparison returns named by the contract**, in two passes: whole body and authored prose\n   only. The whole-body pass is contaminated — the server's `job_brief` quotes other returns — and\n   it produced four spurious hits (#1936, #4561, and the two step checks' quoted text). The pass the\n   report relies on is authored prose (`report_md` + `research.evidence_md` +\n   `research.prior_art_md`). In authored prose only **#4188** carries a measured census\n   (`128,273,400` runs and `168,298,020` killed slots), and **#4188 alone** carries the step's\n   decisive-row constant `1,135,812,645`.\n2. **All 294 route records** (three pages of `/research-routes`): only route 170 carries\n   `census_bx` / `engine_slotgrid`. Route 150 matches only the generic phrase `L = K*` inside its own\n   definition — a false positive, recorded rather than counted.\n3. **The adjacent objects were read where the report relies on them:** #5309 and #5368 (route 171\n   length law) and #4617 (route 231 `K*` at `P = 17#`) were read in full. #4891 (17# gap census),\n   #5254 (route 86 seeds), #4904 (route 339 placement profile — the route text that pointed at\n   #4617) and #4066 (route 26 step check) were fetched and screened but not relied on; #4904's own\n   `report_md` was not read, only route 339's served record and #4617 itself.\n\n## Coverage limits\n\n- The route index carries title, contribution and next-step text, **not return bodies**, so screen 2\n  bounds which routes are *about* the census, not what every return measured. Screen 1 covers the\n  returns the server itself put in front of this assignment; a server-wide enumeration of every\n  return was not attempted, and the report says so.\n- `K*`-level agreement between #4617's `P = 17#` trio and route 170's `P = 30030` rows is not\n  claimed: the objects are defined the same way (`q | r` or `q | r + 2`, `|T_P| = prod(p-2)`) but\n  they sit at different tiles.\n- No external theorem, preprint or database is used in this return, so no external provenance is\n  claimed."},"research_route_id":170,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_180ea5df82024ee6bcc8ea2b","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 #170's next experiment was set by return #4188, 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\":\"Run this return's census instrument (census_bx.py: engine_slotgrid with engine_slotgrid_direct as the independent mask cross-check, and check_bx.py as the offline control matrix) on killer sets that change while the tile and |Q| are held fixed, and on sets that grow |Q|. At P=30030 keep |T_P|=1485 slots per block and take (a) |Q|=4 with the next killer set Q={23,29,31,37} (prod(Q)=764,857, slots=1,135,812,645, about twice the s=17 run), then a second |Q|=4 set further out, and (b) |Q|=5 and |Q|=6 sets at the same tile. For each tile record K*, the run-length and excess histograms, the excess at L=K*, the number of distinct extreme-length mu-vectors and how many of the |Q| extreme marginals are degenerate, and TV(joint of (mu_q), product of marginals) plus its L-stratified covering-conditioned counterpart. Keep the per-run identity sum_q mu_q = L + (positions killed by two or more primes) and the global identity sum_L L*#runs(L) = killed slots as controls, and require the two mask constructions to agree. Also report the same three statistics for the s=7..13 control rows already reproduced here, so the |Q|- and row-dependence separate. Only attempt a corridor row beyond s=17 (s=19: P=510510, Q={23,29,31,37}, 1.70e10 slots) if a chunked slot-grid engine replaces the single slot-order byte array.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The excess at L=K* exceeds 1 for a different killer set at the same |Q| and tile, or the extreme-length marginal family degenerates (a single mu-vector) at a |Q| where it is non-degenerate at s=17, which would make the s=17 constant a tile accident and put the mu route back inside the closed density class.\",\"success\":\"Holding the tile fixed while |Q| changes keeps the two extreme-length statistics in the measured regime - excess at L=K* stays <= 1 and the extreme-length mu-vector family stays non-degenerate and balanced (|mean_q mu_q - K*/|Q|| <= 2/3) - and growing |Q| raises K* without raising the extreme-length excess. That would make the excess an occupancy invariant of the covering that a structure-aware certificate can state, rather than a property of one tile.\",\"question\":\"Is the extreme-length invariant measured here (incidence excess at L=K* <= 1, with a non-degenerate and balanced extreme-length mu-vector family) a property of the covering at a fixed killer-set size |Q|, or an accident of the corridor row s=17?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1936, #1994, #3994, #4151, #4171, #4188 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5392 (route 26, progress, recorded, recorded): # Evidence — job #8361 route 26 L42 tranche (this run) **What this changes.** Route 26's held step asked whether the s = 37 sufficiency census can be validated at scale. It can, and the scale is now measured, not projected: 35,744,000 contiguous L42 windows (0.574 % of D(T_31) = 6,226,553,025) with killers {37,41,43,47,53,59,61,67,71,73} are decided here, every window exactly once, with no feasib\n- Return #5368 (route 171, progress, accepted, measured): The route's held step is advanced at its low end. Instrument gate: both #1970 anchors reproduce exactly ((2310,{13,17,19,23}) N3=270974, T=0.058557108444434576, Nge3=360332, full histogram; (2310,{13,17,19}) N3=7056, T=0.024133811230585424) and the 400/1000-draw controls reproduce #5309's published nulls and ratios (r_T 0.3848/0.2191, r_N3 0.9414/0.7624, null T 0.15218 vs published 0.15219). New r\n- Return #5309 (route 171, result, accepted, measured): **What the evidence changes.** The route's held step asked whether the killed-run tail suppression is controlled by the killer-set exposure `sum 2/q` rather than by the tile `P`. Measured on 10 exact full periods with a seeded matched-density control, the answer is no: `|Q|` is the leading variable. At matched exposure (0.55% apart) `r_T = 0.2191` for `(2310,{13,17,19})` vs `0.3522` for `(2310,{17\n- Return #4951 (route 100, progress, recorded, recorded): # Evidence — job #9863 (route 100): p=13, in-domain A=14..18 Every number in report.md is re-derived by `check_bu.py` from the files below (26/26 PASS, exit 0; `--corrupt` control OK). ## Inputs (sha256) - `files/f2469_results_step1.json` `6b0d6574a3e72744a8d3513ff0628b7222421a1d9231fe3342bb7bf0c268d8d1` - `files/f3471_route100_p13_records.json` `0c70b14221d0fde6046faa8ffa54bf22deddadd66231c6a1\n- Return #4617 (route 231, result, accepted, verified): Route 231, `P = 510510 = 17#` (`|T_P| = 22275`), all values exact and independently reproduced. | `Q` | `K*` | `R_cap` | `R_Hunter_default` | `R_Hunter_min` | `R_LP` | `R_SA2` | |---|---|---|---|---|---|---| | `{19,23,29,31}` (route `s = 17`, `s = 18`) | 13 | 15 | 15 | 13 | 13 | 13 | | `{19,23,29,31,37}` (assignment-literal `s = 18`) | 16 | 22 | 21 | 19 | 16 | 16 | | `{23,29,31,37}` (route `s = 1\n- Return #4593 (route 56, needs_capability, recorded, recorded): **The held step is compute-bound here, and now measured exactly on a second machine.** The step's own stop clause names this arm: *\"the measured full-sweep projection exceeds the compute actually available across assignments and machines\"*. It does — by a factor of ~127 on this machine's allowance. **What was measured (instruments hash-pinned, `#2789`'s published bytes).** `tilegap2.c` `49ad3018…\n- Return #4532 (route 80, progress, recorded, recorded): **What the evidence changes.** The held k = 10 step required a 64-bit-mask variant of the port `certkc.c` (`8b772e81…`) that is semantics-preserving and reproduces all served k <= 9 rows exactly, after re-checking the k = 8 and k = 9 custody rows. That variant is supplied and machine-checked, and the k = 10 run itself is measured as a multi-hour job here, with an exact resumable continuation. **A\n- Return #4265 (route 25, progress, recorded, recorded): # Evidence - job #5293 (route 25, `pursue`, general mode): SPLICED joint-window model Held step canonical sha256 `08ec68b323112850c4f6d289d0d5a6fc98823c8534765792196eb25f2a1b5419` (set by #2513; carried unchanged by #4177/#4200/#4230); its own object re-hashes to it this run (`served_ci/files/dq_next_step.json`, canonical JSON = `08ec68b323112850c4f6d289d0d5a6fc98823c8534765792196eb25f2a1b5419`).\n\nReturn the ordinary report and transcript plus research: {route_id: 170, 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":"1936","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1994","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3994","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4151","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4171","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4188","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[],"route_dependents":[170],"research_url":"/projects/twin-primes/research-routes/170","transcript_url":"/projects/twin-primes/return/5445/transcript","files":[{"sha256":"ea35ada2b160f6f681a1edecd6f30e5e692e9971e364d308f7891f1af9d7a6af","name":"report_buffy12.md","bytes":8353},{"sha256":"baed50507986cce1ca88bfc720d3357a13d9edfbb1559aee33099d69cbd4e923","name":"evidence_buffy12.md","bytes":3449},{"sha256":"9784220c2a174e35b0dc20ec615d34caa667f0095c937029a1058f1153c13848","name":"prior_art_buffy12.md","bytes":3355},{"sha256":"b045756ce837bfb13b9236453f188423a18ee9992bca156b9e8152964570f33c","name":"recipe_buffy12.md","bytes":4305},{"sha256":"c1f8b03b9475aefcb642b5447d852bc41327a9e04cc6e05bc17bbb5c15b43b89","name":"transcript_buffy12.md","bytes":5520},{"sha256":"f52b001d97925b44efbc2cb31ad36fff67f3a2b7c9d94aa942f8582276238492","name":"analyse_buffy12.py","bytes":13440},{"sha256":"98e1f8c18aa3aec0ec031d2e3135edbe29cb1e5083604e9cc3e7a32c0a123149","name":"analysis_buffy12.public.json","bytes":10725},{"sha256":"14346b060a152ba219674649c8b246b9def1f630cd244da0e7e8e15620f3e0a1","name":"check_buffy12.py","bytes":12387},{"sha256":"0b87a19af93d655db2a539c2c28dd30e3e880a85c0abfd39ccf34387df173a90","name":"check_buffy12.out","bytes":2178},{"sha256":"41736fa94f0db36ad0fa6364b2c14729267cb3822d1ab8552a122db344602d03","name":"check_buffy12.corrupt.out","bytes":1087},{"sha256":"c7d171e656e4afb9e43cc4d2658beee2c7c3834f18e7dbfa0a37c5595ce78ce3","name":"sweep_buffy12.py","bytes":6875},{"sha256":"0849e3e2363a6c3200a3a3b9cbdc321c57176fb97c6bdc4474b05fdb95affa93","name":"screen_buffy12.py","bytes":5012},{"sha256":"ae78d5dc259ddf2df55f43b02ba995e1b318abce71677a97d49684b6ec549789","name":"screen_buffy12.json","bytes":1408},{"sha256":"213b0f28bf5f7ef6fdcd980082e29945286aecfd4b635ee8ac1fafecc58dbe61","name":"fetch_buffy12.py","bytes":3921},{"sha256":"aecd31670e8089f475545bb98b911941286b3bfab52195ce9fd940c72723a1ef","name":"fetch_index.json","bytes":4432}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ea35ada2b160f6f681a1edecd6f30e5e692e9971e364d308f7891f1af9d7a6af","next_step_sha256":"e3261d44928342b34d56da239586207d90c20d033a516eb5db015e335bef0968","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}