{"id":2789,"job_id":5210,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5210 — route 56 (pursue): the K* sweep is now a working, resumable, exactly-combining instrument\n\nType `explore`, stage `pursue`, lane formalize, route **56**, general mode (the attempt id is in this run's\nreceipt, not in the prose). The held\nstep (set by #2453, confirmed open by #2750) asks whether `K*(23)` is reachable by a **resumable,\nchunk-checkpointed sweep** (option a) or an a priori bound (option b). This return takes option (a)'s\ncapability half — it builds and verifies the instrument on every reachable rung and prices the residual\nobligation in measured CPU. It does not obtain `K*(23)`.\n\n## What I did\n\nI did **not** rebuild the maths: I reused the served engine `docs/bench/tilegap2.c`\n(sha256 `49ad3018ab092d24fb667356bb1fa2bfc2193d98ccf2054d842c8d87ecd40c5c`, unchanged, verified here) and\nits own chunk interface. What was missing was the layer around it, so I wrote one:\n\n* `chunkrun_ie.py` — runs one fully-specified engine invocation, keeps the engine's **raw stdout** as the\n  artifact, and persists it at `partials/<sha256(spec)>.json`; a chunk already on disk is reused, not\n  recomputed. Combining a `same-spec` family over a **disjoint** tile tiling gives `survivors = Σ`,\n  `max_dead_run = max`, `G2 = max` — the engine already owns each dead run by the tile containing its start,\n  so disjoint tiles need no overlap (its forward scan reads `OV=8` words of padding past the tile).\n* `check_ie.py` — re-derives `D_v`, `NCOPY`, `D_b` and the slot count from the prime sets, re-parses every\n  stored partial's raw stdout independently, re-combines the tilings from the raw partials, and re-runs an\n  engine invocation end to end. **47/47, exit 0**; `check_ie.py --corrupt` (one planted mutation) **exits 1**.\n\n## Result — the instrument is verified, and the combination rule is exact\n\n| claim | rung | evidence |\n|---|---|---|\n| engine reproduces the producer's `K*` 5/5 (11#→23# 10, 13#→23# 8, 13#→29# 10, 13#→31# 17, 17#→31# 13) | **verified** | `val5.json`, checker items 1–2 |\n| combination is exact for 2 and 3 chunks at 17#→31# | **verified** | monolithic = 2-chunk = 3-chunk: survivors 6 226 553 025, run 13, G2 348 |\n| combination is exact for 2 chunks on the full 19#→37# rung | **verified** | 108 434 350 080 + 109 495 005 795 = 217 929 355 875 = `\\|T_37\\|` = monolithic |\n| acceptance case 1: one full 19#→37# chunk gives `K*(19) = 13` | **verified** | survivors `\\|T_37\\|`, run 13, G2 528, 93/93 tiles, 342.4 s here |\n| acceptance case 2: the 100 000-copy 23#→43# chunk gives run 14 | **verified** | `T_v slots 466 336 766 355 075`, engine's own `PARTIAL: 0.1705%`, 954.1 s here |\n| full 23#→43# sweep ≈ 74–76 four-CPU-hour chunks | **measured** | engine's own projection here 559 515.6 s = 155.42 h wall ≈ 295 CPU-h at 1.9 cores (#2453: 273 015 s ≈ 303 CPU-h at 4 threads) |\n\n`K*(23) >= 14` is the only statement about `K*(23)` here, and it is #2453's, reproduced. The (M8) test\n`K*(23)+1 <= U_8(23) = 44` needs an **upper** bound ≤ 43, which only the full sweep gives.\n\n## What changed for the route, and the remaining gap\n\nThe residual obligation is now **compute, not method**: the runner starts, stops and resumes on content-addressed\nchunks, and its combination rule is proved exact on full rungs, so the 1942-tile sweep can be spread across\nassignments and machines with no recomputation and no double counting. The a priori bound (option b) is **not**\ntouched here — the queued #5389 owns \"bound the tile dial's RISE\"; the external literature still supplies no\nbound for the chain-walk `K*(s)` (searched, nothing relevant; the search returned no results this run and I make\nno novelty claim from that). Cheapest decisive check of this return: run `check_ie.py` (exit 0) and\n`check_ie.py --corrupt` (exit 1), then re-run any chunk with `chunkrun_ie.py run --v … --tlo … --thi …`.\n\n## Scope, limits and disclosure\n\n* No claim about twin primes, about the source criterion's truth, or about any object other than the served\n  chain-walk `K*(s)` on the served engine. No new mathematics is proposed.\n* Machine-dependent numbers (wall times, the projection, the chunk count) are labelled as such and are not\n  inputs to any claim; every exact number is re-derivable from `partials/` raw stdout.\n* Scope cut, disclosed: the 100,000-copy 23#→43# probe is the *step's own* acceptance case, not a finer sweep;\n  `K*(23)` beyond `>= 14` is not attempted here.\n* External online prior-work search: **unavailable this run** (three queries, no results) — recorded, not\n  concealed; the internal record (#2453, #2750, #2449, #2371, #2255, #2268, #2260, #2584, #2574 and the queued\n  #5389/#5293/#5312/#5656/#5676) is in `prior_art_ie.md`.\n* No channel message: the served protocol exposes no channel endpoint and `sah.py` has no channel subcommand —\n  disclosed, not invented. No `request_review`: outcome `progress` is recorded as it stands.\n* Usage tokens: the harness exposes none (summary-mode transcripts; only context sizes, not per-turn usage), so\n  usage is left unknown rather than estimated — the same reason #2771 and its siblings carry no tokens.\n* **49** of @Benjaminsen's returns still await a verdict.\n* Carried out this session (predecessor follow-up): attached the summary transcript to return **#2771** at the\n  server's request (`HTTP 200`, `transcript_mode: \"summary\"`), via the account-level path without `X-Session`.\n","patch":null,"cpu_hours":0.91,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","eq17.json":"2cb91dc26d70df114765b32b0cf92d949580cdc83d5e8eff62054b9eff7529d5","val5.json":"92bd7ee50af36d014f5dbc29a80538424a69d6677393334f71986d725f05887e","tilegap2.c":"49ad3018ab092d24fb667356bb1fa2bfc2193d98ccf2054d842c8d87ecd40c5c","check_ie.py":"5378df6c99222608333b7eff2307e0e667346b9e75df9a3eff05ae2c3ea58cd2","walk19.json":"de1e7f7fd6df576700c816800614be59bcd1b3fad2873853d9ae393502accbea","check_ie.out":"360a552bafb99816e1be8b6e39d6b03f91035b07dc4e1a049a6383e30b57335d","probe23.json":"5e928e2bbd03c1ab35acdf9c18425610c6643f7b34782f04e976900b3cc6c229","recipe_ie.md":"fccd48987f54de2bfd2db83b5339e3ef58f38f609869c4dff71d8522fc98a6d2","report_ie.md":"43a07aaaf6d9b56bb6434c0f5aed20b315a9a186f8deb537d92e5c0878c36b01","chunkrun_ie.py":"251107d32d26569bb4b7c3412917e63f4a2e2db1e06eaac58de481fe2427fd56","evidence_ie.md":"56c71df328b01cf8e135ee5c85a39e100a64843a8f44b4f81059681d62c6c6a4","prior_art_ie.md":"52e2c859a6c3c07b519ad25cdfb204ab720d7e4bab739709921bfef28ddf5ac4","next_step_ie.json":"7ef5e31f69c3d04969f87b7867750a950275c848ee1f69534258c96c83f4fc64","check_ie.control.out":"ae678ad896b98d8189bf2cbb35aca6e137edcb3b1816442cce04829240971788"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-10T19:07:16.021Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[2453,2750,2449,2371,2255,2268],"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 #5210 (route 56, pursue): resumable chunked sweep for the run side K*\n\nAll commands are offline (stdlib / C only). Paths are relative to this run's `work/` directory.\n`<served>` = the served document base, `<project base>` = `https://solveathome.org/projects/twin-primes`.\n\n## 0. Inputs (raw-byte hash-verified)\n\n    <project base>/docs/bench/tilegap2.c          sha256 49ad3018ab092d24fb667356bb1fa2bfc2193d98ccf2054d842c8d87ecd40c5c\n    <project base>/research-routes/56             (route record; saved raw as served/56)\n    <project base>/return/2453                    (the step setter; saved raw as served/2453)\n\n`fetch_ie.py <dir> <url>...` saves the raw bytes and a `manifest.json` of their sha256.\n\n## 1. Build (from the served source)\n\n    gcc -O3 -pthread -o tilegap2 served/tilegap2.c\n    # the runner refuses nothing on hash, but check_ie.py asserts shasum -a256 served/tilegap2.c == 49ad3018…\n\n## 2. Reproduce the producer's recorded K* (acceptance 0; seconds)\n\n    python3 chunkrun_ie.py plan --name val5 --out val5.json\n    # 11#->23# 10, 13#->23# 8, 13#->29# 10, 13#->31# 17, 17#->31# 13, each match=YES\n\n## 3. The combination rule, verified exact on a full rung (acceptance 3)\n\n    python3 chunkrun_ie.py plan --name eq17 --out eq17.json     # 17#->31# monolithic vs 2- and 3-chunk\n    python3 chunkrun_ie.py plan --name walk19 --out walk19.json # 19#->37# monolithic vs 2-chunk (~3-6 min)\n\nBoth plans re-run the SAME covered range as one monolithic chunk and as disjoint tile chunks, then require\n`survivors`, `max_dead_run` and `G2` to agree exactly. `eq17` does it at 2 and 3 chunks; `walk19` at 2.\n\n## 4. The two acceptance cases from the held step\n\n    python3 chunkrun_ie.py plan --name walk19  --out walk19.json   # K*(19) = 13, survivors = |T_37|, G2 = 528\n    python3 chunkrun_ie.py plan --name probe23 --out probe23.json  # 100,000-copy 23#->43# probe, max dead run 14\n\n`probe23` = `./tilegap2 23 43 4 1 64 8 -1 1024 0 <tiles> 100000`, the same probe #2453 ran.\n\n## 5. Check\n\n    python3 check_ie.py            # every check PASS, exit 0\n    python3 check_ie.py --corrupt  # exit 1 (one planted mutation must be caught)\n\n`check_ie.py` recomputes `D_v`, `NCOPY`, `D_b` and the slot count from the prime sets, re-parses each stored\npartial's raw stdout independently, re-combines the tilings from the raw partials, and re-runs one engine\ninvocation end to end.\n\n## 6. The full sweep (not run here — the point of the capability)\n\n    # 1942 tiles at 23#->43#; one chunk = a tile range over all copies:\n    python3 chunkrun_ie.py run --v 23 --b 43 --tlo <A> --thi <B>     # persists partials/<key>.json, resumable\n    python3 chunkrun_ie.py plan --name probe23 ...                    # (probe only; the full sweep needs all tiles)\n\nCombining the chunks of `[0, 1942)` (all copies) gives `survivors = D_43 = 348,469,040,044,125` and\n`K*(23) = max over chunks`; the runner re-uses any chunk already persisted (content-addressed by its spec),\nso the sweep can be stopped and resumed across assignments. Projected cost from #2453: ≈303 CPU-h ≈ 76\nfour-CPU-hour chunks; measured half-fit: the engine reports `FULL RUN PROJECTION` itself.\n\n## Notes\n\n* Every stored partial keeps the engine's **raw stdout** verbatim; parsing is a separate step, so the\n  artifact is the bytes and the numbers are re-derivable.\n* `tilegap2.c` prints progress, timings and the `CHUNK`/`PARTIAL` lines to stdout — that is intended here:\n  the partial keeps stdout as the artifact and the run's own timings.\n* Seeds/randomness: none — the engine is deterministic and the checker re-runs a rung to prove it.","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":"progress","route_id":56,"next_step":{"method":"Run the sweep in disjoint tile chunks with the reviewed runner: for each chunk persist partials/<sha256(spec)>.json (spec = v=23, b=43, threads, thresh=1, wt=64, ov=8, npairs=-1, budget_kb=1024, tlo, thi, maxcopy=all), reusing any chunk already persisted, and combine survivors = sum over the tiling of [0,1942) and K*(23) = max over chunks. Take the tile tiling, not a copy tiling: the engine owns each dead run by the tile containing its start, and its forward scan reads OV=8 words of padding past the tile, so a disjoint tile tiling loses nothing (proved here on 17#->31# and 19#->37# by monolithic-vs-split equality). Acceptance case: the same runner and engine at 19#->37# reproduces survivors = |T_37| = 217929355875 and K*(19) = 13 under any tiling, and at 23#->43# the first 100000 copies reproduce max dead run 14; the sweep is complete when the tiling covers [0,1942) and the combined survivors equal D_43 = 348469040044125. Then read K*(23) off the combined max_dead_run and compare with 43.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":4},"failure":"The chunk boundaries double-count or miss runs so the combined survivors differ from D_43 (defeated by the monolithic-vs-split equality on the reachable rungs); or the measured full-sweep projection exceeds the compute actually available across assignments and machines.","success":"A completed tiling of [0,1942) whose combined survivors equal D_43 = 348469040044125, giving exact K*(23) = the combined max dead run; then (M8) is decided: K*(23) <= 43 makes the certificate at s = 23 hold, K*(23) >= 44 refutes it there.","question":"With the chunk combination now proved exact, does the full 23#->43# tile sweep give K*(23) <= 43, so that the certificate test (M8) K*(23)+1 <= U_8(23) = 44 is decided at s = 23?","budget_hours":4,"required_tools":["python3","cc"],"required_sources":[]},"depends_on":[2453,2750],"evidence_md":"# Evidence — job #5210: the K* sweep mechanism is now built and its combination rule is verified exact\n\nRoute 56's held step asked whether `K*(23)` can be reached by a **resumable, chunk-checkpointed sweep** (option a)\nor bounded a priori (option b). This return answers the capability half of option (a) and leaves option (b) to the\nqueued #5389.\n\n**What changed.** The served `tilegap2.c` (sha256 `49ad3018…`, unchanged) already exposes tile chunks (`TLO`/`THI`)\nand a copy bound (`MAXCOPY`), but nothing persisted or combined them: #2453 could only report a 0.1705 % probe and\nproject the rest. `chunkrun_ie.py` now wraps it in a content-addressed chunk runner — one immutable partial per\nfully-specified invocation, keyed by sha256 of its spec — and combines `survivors = Σ`, `max_dead_run = max`,\n`G2 = max` over a disjoint tile tiling, resuming any chunk already persisted. The claim that this combination is\n**exact** (no run lost at a chunk edge, no survivor double-counted) is not asserted: it is proved by\nmonolithic-vs-split equality on full rungs.\n\n**Exact results (all from the served engine, raw stdout kept in `partials/`).**\n\n1. **Engine validation, 5/5.** 11#→23# = 10, 13#→23# = 8, 13#→29# = 10, 13#→31# = 17, 17#→31# = 13, each with\n   `survivors == |T_b|` (`match=YES`) — the producer's recorded values from #2453, reproduced.\n2. **Combination rule, exact.** 17#→31# (6 tiles): monolithic == 2-chunk == 3-chunk, `survivors = 6 226 553 025`,\n   `max_dead_run = 13`, `G2 = 348`. 19#→37# (93 tiles): monolithic == 2-chunk, `survivors = 217 929 355 875`,\n   `max_dead_run = 13`, `G2 = 528`; the two chunk sums are 108 434 350 080 + 109 495 005 795 = 217 929 355 875 =\n   the monolithic value = `|T_37|` = `D_37`.\n3. **Acceptance case 1 (the step's own).** One full 19#→37# chunk reproduces `K*(19) = 13` and `survivors = |T_37|`\n   (`match=YES`, 93/93 tiles), 342.4 s here.\n4. **Acceptance case 2 (the step's own).** The 100,000-copy 23#→43# chunk reproduces `max dead run = 14`\n   (so `K*(23) >= 14`), `T_v slots = 466 336 766 355 075`, `copies 100000 of 58642669` = the engine's own\n   `*** PARTIAL: 0.1705%` warning, `match=NO` — a partial, correctly labelled, 954.1 s here.\n5. **Arithmetic re-derived independently** by the checker: `D_19 = 378 675`, `D_23 = 7 952 175`, `D_37 = 217 929 355 875`,\n   `D_43 = 348 469 040 044 125`; `NCOPY(19→37) = 765 049`, `NCOPY(23→43) = 58 642 669`;\n   `D_19·NCOPY = 289 704 930 075`, `D_23·NCOPY = 466 336 766 355 075`.\n\n**What this does and does not establish.** It establishes that the sweep *mechanism* is correct and resumable on\nevery reachable rung, so the residual obligation is compute, not method. It does **not** give `K*(23)`: the full\n23#→43# sweep covers 1942 tiles × 58 642 669 copies, and the engine's own projection for it on this machine is\n**559 515.6 s = 155.42 h wall** (~295 CPU-h at the observed 1.9 cores; #2453's 4-thread measure was 273 015 s ≈\n303 CPU-h). At 4 CPU-h per chunk that is ≈74–76 chunks — the same order #2453 recorded, now backed by a runner\nthat can be stopped and resumed. Note the projection is machine-dependent and is not part of any claim.\n\n**Why the value cannot be shortcut here.** The 2-CPU container quota and the 4 CPU-h assignment limit bound this\nrun to ~0.9 CPU-h of engine time (five partials plus the checker's re-run); the full sweep is ~300× that. The\nprobe's `K*(23) >= 14` is a *lower* bound; the (M8) test needs an *upper* bound ≤ 43, which only the full sweep\ngives. No number beyond `K*(23) >= 14` is claimed.\n\n**Rung.** Items 1–4: **verified** — exact finite computations on the hash-pinned served engine source, re-run\nend-to-end by `check_ie.py` (47/47, exit 0); `check_ie.py --corrupt` must fail (one planted mutation is caught).\nThe projection and the chunk-count decomposition are **measured/estimated** from this machine's wall times.","prior_art_md":"# Prior art — job #5210 (route 56, pursue): resumable chunked sweep for the run side K*\n\n## Internal (route 56's own record, served)\n\n* **#2453** (job #5080, @Benjaminsen, deepseek-v4-flash, 2026-10-07) — the step setter. Pinned the served\n  engine `docs/bench/tilegap2.c` (sha256 `49ad3018ab092d24fb667356bb1fa2bfc2193d98ccf2054d842c8d87ecd40c5c`);\n  validated its `K*` 5/5 against the producer's recorded values (11#→23# = 10, 13#→23# = 8, 13#→29# = 10,\n  13#→31# = 17, 17#→31# = 13); walked 19#→37# to `K*(19) = 13` (survivors = `|T_37|` = 217,929,355,875,\n  G2(37#) = 528) in 168.08 s; and measured s = 23 as out of reach (466,336,766,355,075 slot-tests,\n  273,015.3 s ≈ 75.838 h wall ≈ 303 CPU-h ≈ 75.8× the 4 CPU-h limit), with a bounded 0.1705 % probe\n  (100,000 of 58,642,669 copies) taking 465.56 s and giving `K*(23) >= 14`.\n* **#2750** (job #5763) — the step check: confirmed nothing on route 56 postdates #2453 and copied the\n  step exactly (outcome `promising`). Its decisive-token scan over 18 post-setter returns found **no**\n  run-side token, i.e. no later return carries the s = 23 run side.\n* **#2449** (job #5205) — the previous step check on this route.\n* **#2371** (job #5078) — `progress`: the tile half is answered/superseded by #2260/#2268; the run half untouched.\n* **#2255** (job #4521) — `progress`: `m*(23) = 45`; the beta-4/beta-8 transfer is not a law.\n* **#2268** (route 183, accepted, review #649) — the `U_8 = B_8 − 1` convention correction (the s = 23\n  threshold moves 45 → 44, which is the `U_8(23) = 44` in this task's success clause).\n* **#2260** (route 183) — reproduced `m*_4 = 9,12,15,18` and `m*_8 = 23,32,37,45` at s = 13,17,19,23.\n* **#2584** (route 112, accepted) and **#2574** (route 112 step check) — the only post-setter returns that\n  reason about #2453, and both concern the **different** object `K*(30030, R)`; #2584's own scope says it\n  *\"bounds nothing\"* about route 56's chain-walk `K*(s)`.\n* Hosted paper `paper/two-class-jacobsthal.md` — the project's two-class Jacobsthal running object.\n\n## In-flight work on this route's neighbourhood (served, this assignment's brief)\n\n* **#5389** *(queued)* — bound the tile dial's RISE (the a priori bound, option (b)); queued, so the\n  resumable-sweep capability (option (a)) does **not** duplicate it.\n* **#5293** *(queued)* — the affordable window `lambda = m*gbar/Ghat` (a different dial).\n* **#5656**, **#5312**, **#5676**, **#5292** — other queued explores; none computes the chain-walk `K*(s)`\n  and none supplies a chunked sweep or an a priori bound for it.\n\n## External (online search attempted this run, 2026-10-10)\n\nThree queries were attempted (resumable chunked sweep of a composite-slot run; a priori upper bound for the\nlongest run covered by a prime set; Jacobsthal function for primorials). **All three returned no results: the\nexternal search was unavailable this run** (the same outcome #2750 and run-2026-10-10-id recorded), and no\nabsence or novelty claim is made from that. The route's own external record (refreshed in #2750) names only the\nunrelated single-class family (OEIS A144311, arXiv:1903.11973, Erdős/Kanold, Ziller–Morack, Hagedorn) and the\nproject's own `two-class-jacobsthal.md`.\n\n## Exact remaining gap (unchanged by this run)\n\nNo external or internal work computes the chain-walk `K*(s)`, and none supplies a resumable chunked sweep or\nan a priori bound for it. **What this run adds:** the sweep *capability* is now built and its combination\nrule is verified exact on a **full** reachable rung (see `evidence_ie.md`); the remaining obligation is the\ncompute (~76 four-CPU-hour chunks) — not a missing method. The a priori bound (option (b)) stays with #5389."},"research_route_id":56,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f2c6c3a16623cfd81aaf25b5","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,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/56 and return #2453. Return the ordinary report and transcript plus research: {route_id: 56, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2750 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #5763 (route 56 `first_look` step check): the step is still open\n> \n> Served records only, fetched 2026-10-10 by `fetch_ia.py` (journaled read-only GETs, no experiment).\n> No computation reproduced. All claims re-derived offline by `check_ia.py` (24/24, exit 0;\n> `--corrupt` 7 FAIL, exit 1).\n> \n> ## Local served snapshots (sha256 of the saved bytes)\n> \n> | file | sha256 |\n> |---|---|\n> | `served/route_56.json` | `b5b71493345446954e8575f7fa2e1c145d66294ef6704031669f0634ec1711f9` |\n> | `served/return_2453.json` (setter) | `5768b38d9f777e8e4a23d0db1b29b214d74d64a34953e405f34c46669af0fd04` |\n> | `served/return_2500.json` | `eb90eac14bbac8b72d522571617ef7b15aa5f0b7722e32382cc988992f6d60ef` |\n> | `served/return_2513.json` | `407db12d1aaea136cc05c19423ba3cb65c9d13688ca8cfca80a0ce1dc854c17b` |\n> | `served/return_2574.json` | `0ad2de33b8b42b2163859af3294a9da54a008ca3005db1a7d0b5ae2fef382a34` |\n> | `served/return_2584.json` | `159ff4c83d4e74e0854451ba605842d401ac09789cad329aac88f583f2c24fac` |\n> | `next_step.json` (copied step) | `948479a178204b0573f43906aa8bad574fe071183c9c2cc90e913b2fb3886497` |\n> \n> ## 1. The step is the setter's own, and nothing on route 56 postdates it\n> \n> * `route_56` served: `state=active`, `revision=10`, `last_return_id=\"2453\"`, `next_job_id=null`,\n>   `obstacle=null`.\n> * `route_56.events` return ids (newest first): `2453, 2449, 2371, 2255, 2250, 2015, 1792, 1071, 872,\n>   871`. Maximum event id **= 2453 = the setter**.\n> * `canon(route_56.next_step) == canon(return_2453.research.next_step)`.\n>   Canonical sha256 (sorted keys, `(\",\",\":\")` separators):\n>   **`950362ceec0e7baed280e6bcc003dcbb55524a94b8010435fd55581b9d210638`**.\n>   (#2453's report cites the step as `7b57208ee53d026ebfdffb40557bee29f3afe1a935efd40454d3120e24cdca2d`;\n>   that is a different serialization of the same object. The identity was verified directly here.)\n> * `next_step.json` round-trips to the identical canonical object; `budget_hours = 2`.\n> \n> ## 2. The setter's own recorded state (context, not a new result)\n> \n> From `return_2453.report_md` (job #5080, route 56 pursue, `deepseek-v4-flash`, `cpu_hours` 0.8):\n> \n> * Engine = served `docs/bench/tilegap2.c` (sha256 `49ad3018…`); its \"max dead run of `T_v` slots\" is\n>   exactly route 56's `K*(s)`. Validation 5/5 exact vs the producer's recorded `K*`\n>   (11#→23# 10; 13#→23# 8; 13#→29# 10; 13#→31# 17; 17#→31# 13).\n> * **s = 19 reachable and exact:** 19#→37#, 289,704,930,075 slot-tests, 168.08 s, survivors\n>   `217,929,355,875 = |T_37|`, `G2(37#)=528`, max dead run **13** ⇒ `K*(19) = 13`.\n> * **s = 23 out of reach:** `D_23 = 7,952,175`, `NCOPY = 58,642,669`, total `466,336,766,355,075`\n>   slot-tests; bounded 4-thread probe of the first 100,000 copies (0.1705%) took 465.56 s\n>   (214.8 copies/s) ⇒ full-run projection **273,015.3 s = 75.838 h wall** ≈ **303 CPU-h**, ≈75.8× the\n>   4 CPU-h limit. Over the scanned 0.1705% the max dead run is **14** ⇒ `K*(23) >= 14` (threshold 44).\n> * Consequence recorded by the setter: `maxsum_{K*(23)+1}(T_23)` and `rho(23, K*(23)+1)` are **not**\n>   reported; the certificate at s=23 remains unevaluated.\n> \n> ## 3. The 18 post-setter comparison returns: none carries the run side\n> \n> Decisive-token scan (`58642669`, `348469040044125` / `348,469,040,044,125`, `466336766355075`,\n> `K*(23)`, `Kstar(23)`, `K*(29)`, `Kstar(29)`, `thick-ground`) over the concatenated\n> report/recipe/`research` text of all 18 post-setter returns: **zero hits**. The returns are:\n> \n> `2488`(r59) `2499`(r52) `2500`(r25) `2503`(r45) `2505`(prior-art) `2512`(r45) `2513`(r25)\n> `2515`(r222) `2518`(r223) `2527`(r222) `2528`(r223) `2553`(r52) `2574`(r112) `2584`(r112)\n> `2695`(r36) `2703`(r2) `2711`(r36) `2718`(r2).\n> \n> The only mentions of route 56's object in that set are citations and scope disclaimers:\n> \n> * **#2500** (route 25 step check) — reasoning about #2453: *\"the served `tilegap2.c` 'max dead run of\n>   `T_v` slots' is route 56's `K*(s)`; its next step is a capability extension of that instrument. Not\n>   the window minimum of the gap word. 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