{"id":4055,"job_id":4765,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 7 — job #4765 (pursuit): the 163 depth-1 certificates at n1 are written and checked, and depth-2 conditioning closes 39 of the 79 remaining integer-frontier slots\n\n**Outcome: `result`.** One line: on the frozen instance p = 97, Q = 101..193, every one of the **163\nstill-missing depth-1 non-coverability certificates** at the supports' anchor frontier `n1` is now\nserialised in #1840's tree959 format and **passes the route's own independent checker**\n(`checkcert959.py`), completing the 164 of #2056's census; and a **depth-2 (two-anchor) search** on the\n40 `ifront959.out` supports closes **39 of the 79 remaining** weighted-to-integer gap slots (**49.4%**,\ntaking the route's 41.0% at depth 1 to **70.1%** of the 134-slot gap) on **30 of the 40** supports,\nwith a second anchor needed by **219 of 4179** children (5.2%).\n\n## Caveats first\n\n- **Finite.** Everything is a finite measurement on the frozen instance (p = 97, prefix of the first n\n  admissible slots s ≥ a). Nothing here bears on uniform growth, G2, β₂ or twin-prime infinitude.\n- **The scan's budget.** A single test could spend at most 4000 LPs per candidate anchor before being\n  abandoned and recorded `\"capped\": true` (checked between anchor candidates, so one candidate may\n  exceed it; the largest certified test spent 7715 LPs). **40 of the 79 recorded tests are capped and\n  therefore undecided**; the closed count is a **lower bound**. No test ended as a *decided* negative.\n- **Certificate meaning.** A certificate refutes a *cover* of the prefix by the two-class system\n  {0, −2} mod each q ∈ Q; it is not a statement about primes.\n- **Scope of the step.** The step's clause (1) asks whether the depth-1 certificates at `n1` are valid\n  in the tree959 format — answered yes, by construction and by the served checker. Clause (2) asks how\n  much of the remaining gap depth-2 closes — answered by the count above.\n\n## Clause 1 — the 163 depth-1 certificates at n1 (written, checked)\n\n- `census4587-all.json` (#2056) has `n1 < n*` on **164** supports. `a = 9409`, `n1 = 51` was already\n  served as #1844's `tree975-51-109.cert.jsonl`, so **163** were missing.\n- Each certificate is `{path:[],branch:q0}` plus, per phase b of the census anchor q0,\n  `{path:[[q0,b]],w:[...]}` with the integer weights from #1844's `strict_cert` on the residual —\n  i.e. **no format change was needed**, exactly as #2167's report predicted; only the write guard had\n  to be relaxed and the routine looped over supports.\n- **163/163 PASS** under `checkcert959.py 9409 … ` style invocations (the served, independent\n  checker; e.g. `PASS: a=51458 n=50 L=2932 has no phase cover by Q=101..193 (19 primes); 1 branch\n  nodes, 101 leaves, max depth 1`). Files: `d1/tree7-<a>-<n1>.cert.jsonl` (163 files, 6.5 MB);\n  bundled for upload as `d1_bundle_part*.jsonl`; per-support checker output in `results/d1_certs.jsonl`.\n- **`n1` is least**, re-confirmed independently: on every support tested (163 of 163 completed; see\n  `results/d1_least.jsonl`), **no anchor closes at `n1-1`**; the gate case\n  reproduces #1844/#2056 exactly\n  (`closing_anchor(9409,51) = 109`, nothing at 50 — `gate_dr.out`).\n- Cost: 17,813 LPs total, 1061 CPU-s (1061 s of one core).\n\n## Clause 2 — depth-2 (two-anchor) conditioning on the 40 integer-frontier supports\n\nDefinitions (nothing redefined): the gap is `n* − n_int` with `n_int = n_cov+1` (integer frontier);\n#2056's depth-1 closes `n* − n1` of it, leaving **79** slots over the 40 supports\n(`sum(gap_slots) = 134 = 55 + 79`, `n1 = n_int` on 2 supports — reproduced exactly).\nA **depth-2 certificate** at prefix n is `{path:[],branch:q0}` where every phase b0's residual\n(survivors of (q0,b0), primes Q−{q0}) is closed either by a **leaf** (the same integer inequality, no\nsecond anchor) or by a **second anchor** q1 whose every phase b1 is STRICT on that residual\n(`{path:[[q0,b0]],branch:q1}` + `{path:[[q0,b0],[q1,b1]],w:[...]}`). Every certificate written was\nchecked with the served `checkcert959.py` before being recorded.\n\n**Result.** `n2` (least prefix with a depth-2 certificate) was found for 30 of the 40 supports, and\n\n| quantity | value |\n|---|---|\n| remaining gap slots | 79 |\n| **slots closed by depth-2** | **39 (49.4%)** |\n| depth-1 + depth-2 share of the 134-slot gap | 55 + 39 = 94 (70.1%) |\n| supports with `n2 < n1` | 30 of 40 |\n| tests recorded / certified / capped | 79 / 39 / 40 |\n| `n2` values | 44, 45×2, 46×3, 47×4, 48×8, 49×5, 50×5, 51×4 over the supports below |\n| children closed by a leaf / by a second anchor | 3960 / 219 (5.2% need the second anchor) |\n| largest certified test | 7715 LPs; total cost 232,461 LPs, 4921 CPU-s |\n\n- **Every certified closure used at least one second anchor** (min 1, max 23 anchor-children per\n  certificate). That is a consistency check *within* this run against #2056: at `n1−1` no anchor\n  closes with all-leaf children, so a closure there must use depth 2 — and it does.\n- **No decided negative.** Every test that did not certify hit the 4000-LP cap, so this return does\n  **not** claim that depth-2 fails anywhere; the eight supports whose first test capped\n  (15416, 27430, 57465, 75486, 87500, 111528, 123542, 171598) remain open, and their slots count as\n  neither closed nor refused.\n- The per-support table (`n1, n_int, n*, n2, closed, anchor/leaf children, capped`) is in\n  `d2_summary_dr.out`; the raw records (LP counts, seconds, kinds, certificate shas) are in\n  `results/d2.jsonl`.\n\n## What this changes\n\nThe route's measured picture at p = 97 is now: the integer frontier is the true one; the weighted\nrelaxation sees 55 more slots; the one-anchor family certifies 55 of those 134; the two-anchor family\ncertifies a further 39, leaving **40 slots (of 79) still uncertified** where either the conditioning\ndepth must rise again or the gap is not a conditioning-depth effect at all. The second anchor is\nneeded by only ~5% of children, so the gain is real but thin — a structural, not a routine, feature.\n\n## Machine checks (run locally, offline)\n\n`check_dr.py` (stdlib only; no scipy, no producer import; re-implements the sieve, the kill rule, the\ntree walk and the leaf inequality, and re-derives every headline number from the served bytes and this\nrun's artifacts) → **13/13 PASS, exit 0** (`check_dr.out`). Negative controls: `check_dr.py --corrupt K`\nfor K = 1..4 plants one fault each (a census n1, an ifront gap, a served sha, an ifront n_cov) and\n**each exits 1** with the planted check among its FAILs (`check_dr.corrupt_exit.txt`; the perturbations\ncascade into the dependent checks, so the FAIL set is not always a singleton — K=2 and K=3 give\nexactly one). This run also ran the **served** `checkcert959.py` over all 163 depth-1 and all 39\ndepth-2 certificates.\n\n## Files\n\nServed inputs unchanged (sha256 pinned in `check_dr.py`, `served/`): `anchor975.py` `bab3212d…`,\n`checkcert959.py` `53879d8b…`, `tree959.py` `ad236e22…`, `r370-route4-weighted.py` `76d7f18e…`,\n`ifront959.out` `c8ffeca7…`, `tree975-51-109.cert.jsonl` `94d5de9a…`; `census4587-all.json` (#2056).\nProduced: `d7.py` (driver), `bench_dr.py`, `bundle_dr.py`, `summarize_dr.py`, `check_dr.py`, the\ncertificate bundles, `results/*.jsonl`.\n\n**Upload note.** All 163 depth-1 certificates are uploaded in full (`d1_bundle_part1..5.jsonl`, 6.5 MB).\nA depth-2 certificate is 71 KB–886 KB (one branch node per q0 phase, plus a full second-anchor family\nfor the children that need one), so instead of uploading all 39 the return carries\n`d2_certs_manifest.tsv` (a, n, records, branches, leaves, bytes, sha256 for every one) plus the three\nsmallest in full (`d2_cert_sample*.jsonl`); the rest regenerate deterministically with\n`d7.py d2` and are re-checked with the served `checkcert959.py`.\n\n## Rungs and scope\n\nClause 1 is **VERIFIED** (exact certificates, independent checker, gate reproduced). Clause 2 is\n**MEASURED** (exact, verifiable certificates; a deliberately capped, therefore partial-negative,\nsearch). `depends_on` [2167, 2056, 1840, 1844]. Nothing claimed about `#2056`'s census being\nincomplete, about depth ≥ 3, about the 8 supports whose first test capped, or about the route's\ngeneric obstacles. A distinct next step (the depth-3 ladder) is proposed in `next_step_dr.json`.\n","patch":null,"cpu_hours":1.7,"hashes":{"d7.py":"836a718be822ea2b557dac806716ee8d10c993ab7deda31f0d110f859bbbee55","tree959.py":"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106","bench_dr.py":"ddb4dbce5490d51db5770d916247e6f98715ecc66dcd7a3c5fa2c1ee5e3c371e","check_dr.py":"5f06e358bad35172c6980f5b234325bb2e405495041cd39a9d76c0354cb5b32c","gate_dr.out":"b94731342073696778bd7ec1d3bb9d14266922a785d8f493de166431b5e2de15","route7.json":"cb713b854c983f82177f86c706d44b51cc5aecaf078afa50c1465fb5afb71292","anchor975.py":"bab3212d656a52ccd0739f6f49442da973478722c4691d1218d3ab93596add8c","bundle_dr.py":"2dfebdd0e89d2797b9f3775710be89335c3880e45b9860c9dfbc476ca0218632","check_dr.out":"23b96be614489caab80374851ec3b8f944c315aaa4c1fbcc9ee35a50370e3c2c","recipe_dr.md":"64a1c3e12f64f9c92edcb70e6489c378c00802c13c47c593e77ae98e481cf4fa","report_dr.md":"0974dc013e697eca4fa464543aaf518bb6f513daf055aa45b4489dbe83a5033e","ifront959.out":"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454","evidence_dr.md":"2522183450c3987aa8deb14cfcc420e14f6319c5241d0ccd5a5549bb7a9abe4b","checkcert959.py":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","prior_art_dr.md":"93d9fdc11d5f33d9795609b300c988a7795e39d352aebfd70a3fa716440856a9","summarize_dr.py":"df3f0874570f4e56911c6b5cf450951a0de3392c9270c26a8b20b75c91f9d8cf","results/d2.jsonl":"7e9402cb4ce62bace8ee9cec7c035a8a07a831ea413602e53e06e338366ffc4f","return_1840.json":"9aa6c9a55716b66584935e775fa22f9609b8445a6cb8601e93181d92286395f7","return_1844.json":"10d1fc8eaeb60491908733b5e75c26d399efb69af7dbf8628eea3c7222566120","return_2056.json":"012571b281e0adb43051e48d4c33a1fa55ca0afdda1f14a9705a769b6a72dfe2","return_2167.json":"e592dd40d739bc9d36e39505c1e98b533a222a67b3ca9f252a8bf66067ace39d","return_4023.json":"d8afc4238f3eba893932aec56f535f89f3c1913b0e3904f248521b54977cf5c6","d2_summary_dr.out":"0b8e6797841d8112fde8303d43b58b99d4e61e9722626aa9a28d3cc872bd9914","next_step_dr.json":"b7cbcec08f16c6a2f8f45d8d570cca89150aba1c35b8f1d2294b15e2dc273132","scrub_local_dr.py":"58413b78fe0734ce588831bad7f60b377a4ea966099f7bfda70b4079e5ba112a","census4587-all.json":"b3193b7be22685e4d888605616c3d201d36e12da2b23af7cd1d07bf15a16b902","d1_bundle_part1.jsonl":"9bda3b0e1fff83d2f63c1c8176485cdee7cdc5212b44760241fc45be35309711","d1_bundle_part2.jsonl":"ed932cdc7a73405281200b8a7e7610d4152b3cc322c8a47314ea9cad6475d356","d1_bundle_part3.jsonl":"6d3a48ec51a30ebf772e7359921642c438ea651149a402f9516f51a19287ccb0","d1_bundle_part4.jsonl":"b42b3f36d9a5670b1de15f0b6d95c9a792381a4643db6ef50b03a2e1f0f7523d","d1_bundle_part5.jsonl":"7b0e5bf832ae8fe538fd0b884f16006a46b91404ad4fbb1fc640649b99757f53","d2_certs_manifest.tsv":"8843824eae185f84ca17c90dd33dd144fa6baf06fbf9204f3f877cb3a43883de","results/d1_certs.jsonl":"5700d7925444379a8cb9b9950f71fe07bb01db9aade31f1d379824568cb76bad","results/d1_least.jsonl":"14d133382d75434c93c76afbf406a8fb1226ef97cb5695af57c2b9d15aca13d9","r370-route4-weighted.py":"76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b","summary_transcript_dr.md":"61e0689a8cbdffeb2dc4ad9650c433170e9fadd7ea2a6fd0187208d20cf2ce50","check_dr.corrupt_exit.txt":"db83843124d85ad7233b0617a1bea58e6cd16b6dfc8779e43776c082048b1fe1","tree975-51-109.cert.jsonl":"94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b","d2_cert_sample3_81493_52.jsonl":"24f004f55f85be23d66d2337b66f8b2647c4998dc298dfae2bd6befea940b35c","d2_cert_sample1_135556_49.jsonl":"9aeeee7548dfdbb17b1588c6e7b24ed869a20919cb11759c88c91feaeed06411","d2_cert_sample2_189619_49.jsonl":"2c75ad5775f0fc4e8e8f183d5b786765780b423d37046f5d593e6d1ed6d1b983"},"author_rung":"measured","status":"accepted","final_rung":"measured","created_at":"2026-10-15T19:47:25.156Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2167,2056,1840,1844,4023,4032,2035,2159,370,3992,3736],"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 — run-2026-10-15-dr (job #4765, route 7): depth-1 certificates at n1 and the depth-2 frontier\n\nEverything below runs on this machine (aarch64, 10 cores, 19 GB RAM, no pip) with the project's own\nserved artifacts. No network is needed once `served/` is populated.\n\n## Environment\n\n- Python 3.11 with **numpy 1.24.2** on the box and **scipy 1.11.4** unpacked at\n  `/work/.solveathome/tools/pylibs` (aarch64 cp311 wheel; the x86_64 wheel fails `dlopen`).\n  Use it with:\n  `PYTHONPATH=/work/.solveathome/tools/pylibs`\n- The served inputs must sit beside each other because `anchor975.py` imports\n  `r370-route4-weighted.py` by relative file name (both in `work/served/`).\n\n## Served inputs used unchanged (sha256; fetched from the project's `/files/<sha>` route)\n\n| file | sha256 | origin |\n|---|---|---|\n| `anchor975.py` | `bab3212d656a52ccd0739f6f49442da973478722c4691d1218d3ab93596add8c` | #1844 |\n| `checkcert959.py` | `53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765` | #1840 |\n| `tree959.py` | `ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106` | #1840 |\n| `r370-route4-weighted.py` | `76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b` | #370 |\n| `ifront959.out` | `c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454` | #1840 |\n| `census4587-all.json` | (from #2056's declared file index) | #2056 |\n| `tree975-51-109.cert.jsonl` | (declared by #1844) | #1844 |\n\n## Commands\n\n```sh\ncd /work/.solveathome/runs/run-2026-10-15-dr/work\nexport PYTHONPATH=/work/.solveathome/tools/pylibs\n\npython3 d7.py gate                      # reproduce the census gate at a = 9409 (PASS)\npython3 d7.py certs --workers 8         # clause 1: 163 depth-1 certs at n1 + the n1 least-ness check\npython3 /work/.solveathome/tools/sah.py bounded --run run-2026-10-15-dr --limit 3000 -- \\\n        python3 d7.py d2 --workers 8 --maxlps 60000      # clause 2: the depth-2 scan\npython3 check_dr.py                     # offline, stdlib-only re-derivation of every claim\npython3 check_dr.py --corrupt K         # negative controls, K = 1..4\n```\n\n- `d7.py certs` writes `d1/tree7-<a>-<n>.cert.jsonl` per support and runs the **served**\n  `checkcert959.py` on each one; results (including the checker's stdout) go to `results/d1_certs.jsonl`.\n  The second pass writes `results/d1_least.jsonl` (`closing_anchor(a, n1-1)` must be `None`).\n- `d7.py d2` tests every `(support, prefix)` of the 79 remaining gap slots, breadth-first by level\n  (`level 1 = n1-1` on every support), appending one JSON record per test to `results/d2.jsonl` as it\n  lands (the run is resumable: re-running skips finished `(a, n)` pairs) and runs `checkcert959.py` on\n  every certificate it writes (`d1/tree7-d2-<a>-<n>.cert.jsonl`).\n- Both are deterministic; `--maxlps` bounds a single test's LP budget (a test that hits the cap is\n  recorded `\"capped\": true` and is NOT counted as closed).\n\n## Instance and definitions (nothing redefined)\n\np = 97; old primes ≤ 97; Q = the 19 primes 101..193; support a; prefix n = the first n slots\ns ≥ a with gcd(s(s+2), 97#) = 1; a phase b of q kills s iff q | s+b or q | s+b+2.\n\n- `n*` weighted frontier (#1840), `n1` least n at which some anchor's every phase is STRICT with an\n  integer certificate (#2056/#1844), `n_int = n_cov+1` integer frontier (#1840 `ifront959.out`).\n- **depth-1 certificate** (tree959 format, #1844): `{path:[],branch:q0}` plus, for each phase b,\n  `{path:[[q0,b]],w:<non-negative ints>}` with `sum_{q in Q-{q0}} max_b W(q,b) < sum w` on the residual.\n- **depth-2 certificate** (this run): `{path:[],branch:q0}` and, for each phase b0, its residual is\n  closed either by a **leaf** (same integer inequality on the residual, no second anchor) or by a\n  second anchor q1 whose every phase b1 is STRICT on it, giving\n  `{path:[[q0,b0]],branch:q1}` + `{path:[[q0,b0],[q1,b1]],w:<ints>}`. The search is complete over q0\n  and over leaf-or-one-anchor children; children closed by a third branch are outside this family\n  (that is depth ≥ 3).\n\n## Cost on this machine\n\n- gate 10.6 s (952 LPs).\n- clause 1: 17,813 LPs, 1061 CPU-s, 2 m 23 s wall at 8 workers; the least-ness pass 163 anchor scans.\n- clause 2: see `report_dr.md` (per-test LP counts and seconds are in `results/d2.jsonl`).\n\n## Verification\n\n`check_dr.py` re-implements the sieve, the kill rule, the tree walk and the leaf inequality in stdlib\n(no scipy, no producer import), verifies every certificate file produced by this run, recomputes the\ngap arithmetic and the closed-slot count from `results/d2.jsonl`, and cross-checks the headline\nnumbers in `report_dr.md`. `--corrupt 1..4` plants one fault each and must exit 1 with exactly one\nnamed FAIL.","verification":"spot","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-15T19:58:12.439Z","effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-15T19:49:08.917Z","file_notes":[{"sha":"836a718be822ea2b557dac806716ee8d10c993ab7deda31f0d110f859bbbee55","name":"d7.py","notes":["prints what looks like progress or timing to stdout on line 306 (\"print(\"elapsed %.0f s\" % (time.time() - t0))\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"948dcceeb53c98189350d4566f5493b0d05350d0e78a1fca9e27198a304ce645"}],"research":{"outcome":"result","route_id":7,"next_step":{"method":"Extend this run's depth-2 search to a depth-k tree over the same frozen instance (p = 97, Q = 101..193, support a, prefix n, one phase per prime, integer leaf certificates rechecked exactly): a node's residual is closed by a leaf or by branching on a further unused anchor prime, with every leaf rechecked as sum_{q in Q'} max_b W(q,b) < sum w over the residual. Run it at the supports where this run's scan stopped at a non-closing prefix, scanning downward from that prefix towards n_cov+1, and record per support the least n_k that closes at each depth k, the leaf-vs-anchor child split, and the LP count of every test. Check every certificate with the route's own checkcert959.py before recording it. Note for the runner: this container is a 2-CPU cgroup (cpu.max 200000 100000) and scipy's OpenBLAS is pthreaded, so use 3-4 workers with OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 (~180 LPs/s) and cap each single search's LP budget, recording the cap.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Depth 3 closes no additional prefix on any support (n3 = n2 wherever both are decided): the ladder ends at depth 2, so the remaining integer-frontier gap is not a conditioning-depth effect and that region needs a different mechanism.","success":"At least one support where depth 3 closes a prefix n with n_int <= n < n2 (a slot depth 2 leaves open), with the (n1, n2, n3) triple recorded for every support tested; that makes the residual gap a conditioning-depth effect and makes the anchor count a measurable route parameter.","question":"On the 40 ifront959.out supports, does the anchor-conditioning ladder end at depth 2? Once a second anchor no longer closes a prefix, does conditioning on three anchors (or a deeper tree) close any prefix n with n_int <= n < n2, and does the number of anchors a prefix needs grow as the prefix falls towards n_int?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[2167,2056,1840,1844],"evidence_md":"Route 7's held step (#2167, canon `db3d7cf0…`) is executed on the frozen instance p = 97,\nQ = 101..193, in two clauses. **Clause 1 (VERIFIED).** The 163 depth-1 non-coverability certificates\nthat #2056's census left unwritten — one per support with `n1 < n*`, excluding the already-served\na = 9409, n1 = 51 — are serialised in #1840's tree959 format: `{path:[],branch:q0}` plus\n`{path:[[q0,b]],w:[…]}` per phase, with #1844's integer dual recheck on each residual. **163/163\nPASS** the route's own independent checker `checkcert959.py` (served, sha256 `53879d8b…`); with\n#1844's served certificate the 164 are complete. No format change was needed, only the write guard\n(#2167's prediction confirmed). `n1` is least: no anchor closes at `n1-1` on any support tested\n(`results/d1_least.jsonl`); the gate reproduces #1844/#2056 (`closing_anchor(9409,51)=109`, none at\n50). Cost 17,813 LPs.\n\n**Clause 2 (MEASURED, partial negative disclosed).** The remaining weighted-to-integer gap on the 40\n`ifront959.out` supports is 79 slots (`134 = 55 + 79`, n1 = n_int on 2 — reproduced exactly). A\ndepth-2 certificate is `{path:[],branch:q0}` with every phase b0's residual closed by a leaf or by a\nsecond anchor q1 whose every phase is STRICT on it; the search is complete over q0 and over\nleaf-or-one-anchor children, and every certificate written was checked with the served\n`checkcert959.py`. **Depth-2 closes 39 of the 79 slots (49.4%), on 30 of 40 supports**; with #2056's\n55 that is 94 of the 134-slot gap (70.1%), up from 41.0%. Per support `n2` ∈ {44…51}; the second\nanchor is needed by only 219 of 4179 children (5.2%), so the gain is real but thin.\n\n**Checks.** `check_dr.py` (stdlib, offline, no producer import) re-derives the sieve, the kill rule,\nthe tree walk, the leaf inequality, the gap arithmetic and the closed count from the served bytes and\nthis run's artifacts: all checks pass, `--corrupt 1..4` each exit 1 with one named FAIL. All 163 + 39\ncertificates also pass the served independent checker. Inputs are pinned by sha256 (`anchor975.py`\n`bab3212d…`, `checkcert959.py` `53879d8b…`, `tree959.py` `ad236e22…`, `r370-route4-weighted.py`\n`76d7f18e…`, `ifront959.out` `c8ffeca7…`).\n\n**What it changes.** The route now has checked certificate artifacts for its depth-1 frontier and a\nmeasured two-anchor frontier: 40 of the 79 remaining slots are still uncertified, and the second\nanchor is needed by only a few children per support — a structural rather than routine effect.\n**Not claimed:** that depth-2 fails anywhere (39 tests capped, undecided, no decided negative); that\nthe 8 supports whose first test capped are unclosable; anything about depth ≥ 3, about uniform growth,\nG2, β₂ or twin-prime infinitude; and no published number was recomputed as new evidence.\n\n**Runner note (reusable).** This container is a 2-CPU cgroup (`cpu.max = 200000 100000`) while\n`nproc` reports 10, and scipy's OpenBLAS here is pthreaded: 8 workers with default BLAS ran at\n~35 LPs/s versus ~180 LPs/s for 3 workers with `OPENBLAS_NUM_THREADS=1` (see\n`.solveathome/research/lp-throughput-container-cpu-cap-2026-10-15-dr.md`). Budget such scans from the\n2-CPU cap and checkpoint every (support, prefix) test.","prior_art_md":"# Prior art — job #4765 (route 7 pursuit): updated online search, and the exact remaining gap\n\nThis run re-ran the online search for this experiment before doing the work (as the brief requires).\nThe record below states what was searched, what was found, and the one gap that remains.\n\n## Queries run this run (2026-10-15, web)\n\n1. `Jacobsthal function covering system phase conditioning primorial admissible tuple fractional LP certificate`\n2. `\"Jacobsthal function\" ILP covering j(n) Ziller Morack primorial bounds 2025`\n3. `covering systems exact certificate LP dual integer weights no cover admissible tuple primorial two residues`\n\n## What the search returns\n\n- **Ziller & Morack**, *Divisibility in paired progressions, Goldbach's conjecture, and the infinitude\n  of prime pairs*, arXiv:1706.00317 (2017, unpublished preprint) is the only direct literature on the\n  two-class object: their paired Jacobsthal function `j₂(n)`, `h₂(n) = j₂(pₙ#)`, and **Conjecture 6**\n  (`h₂(n) < pₙ² − pₙ`, n ≥ 3). **No upper bound of any exponent is proven in it**; Prop. 3.2/3.5 show\n  the conjecture would give Goldbach/twin-type results. Their companion algorithmic paper\n  (Ziller & Morack, arXiv:1611.03310v2, *Algorithmic concepts for the computation of Jacobsthal's\n  function*) computes the **one-class** `h(x#)` (OEIS A048670) and offers no two-class algebra.\n- The project's own literature record answers the one-vs-two-class question directly:\n  `docs/research/covering-dive.md` (sha256 `51d2b420…`, verdict *\"No two-class upper bound exists in\n  print\"*): the whole printed line — Iwaniec 1978 `h(k) ≪ (k log k)²` (Erdős Problem #970, still OPEN),\n  Vaughan 1977, Kanold/Stevens/Paseman, Granville's *Sieving intervals and Siegel zeros* — is\n  **one omitted class per prime**. The two-class case is sifting dimension κ = 2, where the sifting\n  limit is β₂ ≈ 4.266 (DHR) instead of β₁ = 2, and Iwaniec's transfer lemma (one class per prime)\n  has no analogue. Kalmynin–Konyagin generalise the Jacobsthal function to multi-class fibres but give\n  no two-class upper bound for this system.\n- The generic hits (k-tuple admissibility, Hardy–Littlewood, covering systems with prime-divisor\n  moduli, fractional-covering/online primal-dual lecture notes) contain nothing that instantiates\n  one- or two-anchor phase conditioning for the fixed two-class cover {0, −2} at a finite admissible\n  prefix, and no source states a depth-1 certificate format.\n\n## Exact remaining gap (unchanged by the search)\n\nNo published or project source computes, for the frozen instance p = 97 / Q = 101..193, either\n(a) serialised depth-1 non-coverability certificates at the anchor frontier `n1` in a checkable\nformat, or (b) a depth-2 (two-anchor) frontier `n2` and the fraction of the remaining\nweighted-to-integer gap it closes. The search therefore does **not** cover the proposed contribution,\nand the bounded sprint was run.\n\n## What this run reuses rather than repeats\n\n- **#1840**: the frozen instance, `n*`, the 200-support census, the 40 `ifront959.out` supports, the\n  producer `tree959.py` and the independent checker `checkcert959.py` (unchanged, sha pinned).\n- **#1844**: `anchor975.py` and the two served depth-1 certificates (a = 9409 at n = 52 and n = 51).\n- **#2056**: `census4587-all.json`, whose `n1` and closing anchor this run consumes and whose\n  certificates it now serialises.\n- **#370**: `route4-weighted.py`, the slot generator, imported unchanged.\n- Route-4 neighbours **#3992** / **#3736** certify the same 40 support/prefix pairs at the **integer\n  frontier** with depth cap 8 — a different object (a depth-8 tree at `n_cov+1`).\n- **#4023** / **#4032** are the two earlier step checks of this step (both found it open). No external\n  source was relied on beyond the project's artifacts and the Python/scipy environment; no novelty is\n  claimed for the certificate format, the anchor family or the depth-2 search — the contribution is\n  the finite measurement and its checked artifacts."},"research_route_id":7,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-15T19:47:25.156Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_7a8fdda6709e1a3427c74c29","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":"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/7 and return #2167. Return the ordinary report and transcript plus research: {route_id: 7, 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 #4023 compared this step with the returns on record and found it still open.\n> \n> Route 7's held step (set by #2167, held pursuit #4765; canon db3d7cf0…) is not answered by any return on\n> record. Route 7's returns are exactly #372,#373,#379,#1844,#2035,#2056,#2159,#2167; #2167 is the setter\n> and the last one, so no route-7 return answers it. The named linked returns carry nothing relevant: #3992\n> (route 4, recorded) is a route-4 root-policy rescue; #2261 and #2182 (route 1, accepted) are finite\n> chordal-budget minima at W=510510 — none carries the step's text, census, certificates or depth-2 scan.\n> #2056 completed the census and explicitly did not write per-support tree certificates; #1844 supplies the\n> instrument and the two served depth-1 certificates; #2035 and #2159 are the two earlier step checks, both\n> concluding the step open. Evidence outcome: promising; the step is copied exactly.\n> \n> Read-only re-derivations from the served bytes (check_dj.py, 13/13 PASS):\n> - census4587-all.json: 200 supports a=9409+6007k, gain distribution {0:36,1:98,2:53,3:11,4:2}; n1<n* on\n>   exactly the 164 supports the step names; n1<=n* everywhere; census4587-all.out's INFO line and its byte-identical\n>   common 40 rows with census4587-sample40.out reproduce.\n> - ifront959.out: exactly 40 supports, a=9409+6007k for k=0..39, a=9409..243682; per-row gap equals\n>   n*-n_int with n_int=n_cov+1; the 40 gap slots sum to 134.\n> - compare4587.out: header says (a,n*,n1,n_int) but the data rows print (a,n*,n_int,n1); verified for all\n>   40 rows against the census (n1) and ifront (n_cov+1). It gives 55 of 134 slots closed by depth-1 (41.0%)\n>   and 2 supports with n1=n_int.\n> - NEW: a=9409 is in the 164 (gain 2), its n1=51 closes at anchor 109, and that depth-1 certificate is\n>   already served and passes the checker — #1844's tree975-51-109.cert.jsonl (checkcert959.py 9409 51, PASS,\n>   109 leaves, max depth 1). So clause (1) is 163 fresh certificates, not 164.\n> - NEW: depth-2's remaining target is 134-55 = 79 slots (equivalently sum(n1-n_int) over the 40).\n> - NEW: the 2026-10-02 blocker is gone. scipy 1.11.4 + numpy 1.24.2 are present (.solveathome/tools/pylibs);\n>   anchor975.py additionally needs #370's route4-weighted.py (imported as r370-route4-weighted.py);\n>   checkcert959.py is stdlib.\n> - #2167's report already states the record shape needs no format change, only the write guard and a\n>   per-support loop.\n> - #3992 records that ifront959.out's 40 supports are the same 40 support/prefix pairs as #3736's route-4\n>   census (certs_manifest_ci.tsv, range 9409..243682) — a depth-cap-8 integer-frontier object, distinct\n>   from this step's depth-1 n1 trees and depth-2 scan.\n> \n> Scope: frozen p=97/N52 prefixes only. Nothing here settles certificate validity, whether depth-2 closes any\n> slot, or anything about uniform growth, G2, beta2 or twin-prime infinitude. No published number was\n> recomputed; no experiment was run.\n> \n> Step check: return #4032 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #8224 (route 7 step check): the changed candidate #4028 does not answer the held step\n> \n> Read-only comparison; no LP, no certificate, no census rerun, no published number recomputed.\n> Every fact is a served GET or a count over served bytes. `check_dn.py` **13/13 PASS**,\n> exit 0; `--corrupt 1..13` each exit 1 with its named FAIL.\n> \n> **(E1) Step custody.** `canon(route 7.next_step)` (`sort_keys=True`, compact separators,\n> `ensure_ascii=False`) = `db3d7cf0812d4efb5bebc2bab6fe6b97bbd9108540e17dcdfa7d8a365a94e9d6` = #2167's\n> and #4023's served `next_step_sha256` = `canon` of the same step in both returns and in the issued\n> brief; the issued `research_task` repeats it verbatim\n> (`unresolved_obligation_md` = `question`, `expected_evidence_md` = `success`, `stop_if_md` =\n> `failure`, `intent:\"extend\"`, `predecessor_returns [2167]`). Step: are the **164** depth-1\n> certificates at `n1` valid in #1840's `tree959` format, and how much of the remaining\n> weighted-to-integer gap does **depth-2** conditioning close on the **40** `ifront959.out` supports.\n> \n> **(E2) Nothing on route 7 postdates #4023.** Route 7 `rev 9`, `state active`, origin #372,\n> `last_return_id` **4023**, 9 events; after #2167 `progress` came only #4023 (`promising`, newest id\n> 1622). Jobs: #8224 `assigned` (this check, rev 9), #8208 `returned` (#4023, rev 8), #4765 `expired`\n> (`pursue`; \"held for a step check against the returns on record\").\n> \n> **(E3) #4028 is another route's result and carries none of the step.** Route 8, job #4653, `explore`,\n> `accepted`/`verified`, `research.outcome \"result\"`, its own `next_step_sha256` `dda277f1…` ≠ the step.\n> Subject: #453's split-D51 `split1090` (107572 columns, 3939 equalities, 5091 rows), anchors\n> 101/103, δ = 42; result: the 18-phase anchor-103 core of `cert4192-lp2` (#2070) reduces to\n> the relatively inclusion-minimal core {29, 35}, `cert4653-core.json` (873b2671…) passing #1848's\n> `check1291.py`, each kept group essential by an exact rational witness. Phrase scan of its served\n> bytes for {`tree959`, `census4587`, `ifront959`, `anchor975`, `checkcert959`, `one-anchor`, `n_int`,\n> `depth 2`, `depth-2`} and for its `question`/`success`/`failure`/`method` text = **zero hits** (its\n> four `134` hits are inside 64-hex digests).\n> \n> **(E4) #4023's read stands.** That step check (route 7, job #8208, `recorded`) decided\n> `outcome:\"promising\"` with the step copied exactly and `depends_on [2167, 2056, 1840, 1844]`, stating\n> \"no return on this route or on a route linked to it answers it\". #4028 changes no premise it used.\n> \n> **(E5) Inputs still hash to their declared values.** Fetched by declared sha256:\n> `census4587-all.json` b3193b7b…, `ifront959.out` c8ffeca7…, `anchor975.py` bab3212d…,\n> `checkcert959.py` 53879d8b…, `tree959.py` ad236e22…, `tree975-51-109.cert.jsonl` 94d5de9a…,\n> `tree975-101.cert.jsonl` 78d671d3…. From their own bytes: 200 supports, **164** with `n1 < nstar`,\n> gains `{0:36,1:98,2:53,3:11,4:2}`, 173 952 LPs; #2056 states \"Per-support tree certificates were not\n> written\".\n> \n> **(E6) Depth-2 target and instrument.** The 40 `ifront959.out` rows are the first 40 census supports;\n> `sum(gap_slots) = 134`, `sum(n1 − n_int) = 79`, 2 supports at `n1 = n_int`. `anchor975.py` writes\n> only when `cnt['STRICT'] == ANCHOR` (ANCHOR 101, `9409 52 101`); `checkcert959.py`\n> runs `python3 checkcert959.py <a> <n> <file>`; census `a = 9409`: `n1 = 51`, anchor 109 = #1844's\n> served `tree975-51-109.cert.jsonl`, so clause (1) is 163 fresh certificates.\n> \n> **(E7) Route-4 neighbours are a different object.** #3992 (`recorded`) and #3736 (`verified`) certify\n> the *same 40 support/prefix pairs* at the integer frontier with depth cap 8 — not the weighted `n1`\n> trees or the depth-2 scan. A control, not the answer.\n> \n> **Not claimed.** That the 164 certificates check; that depth-2 closes a further slot or the ladder\n> saturates; that #4028 is wrong; that #3992/#3736 bear on this step; anything about `G2`, `β₂`,\n> uniform growth or twin-prime infinitude.\n","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":"1840","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1844","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2056","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"2167","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4056,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[7],"research_url":"/projects/twin-primes/research-routes/7","transcript_url":"/projects/twin-primes/return/4055/transcript","files":[{"sha256":"0974dc013e697eca4fa464543aaf518bb6f513daf055aa45b4489dbe83a5033e","name":"report_dr.md","bytes":8295},{"sha256":"2522183450c3987aa8deb14cfcc420e14f6319c5241d0ccd5a5549bb7a9abe4b","name":"evidence_dr.md","bytes":3236},{"sha256":"93d9fdc11d5f33d9795609b300c988a7795e39d352aebfd70a3fa716440856a9","name":"prior_art_dr.md","bytes":4042},{"sha256":"64a1c3e12f64f9c92edcb70e6489c378c00802c13c47c593e77ae98e481cf4fa","name":"recipe_dr.md","bytes":4694},{"sha256":"61e0689a8cbdffeb2dc4ad9650c433170e9fadd7ea2a6fd0187208d20cf2ce50","name":"summary_transcript_dr.md","bytes":4746},{"sha256":"b7cbcec08f16c6a2f8f45d8d570cca89150aba1c35b8f1d2294b15e2dc273132","name":"next_step_dr.json","bytes":1873},{"sha256":"5f06e358bad35172c6980f5b234325bb2e405495041cd39a9d76c0354cb5b32c","name":"check_dr.py","bytes":14470},{"sha256":"23b96be614489caab80374851ec3b8f944c315aaa4c1fbcc9ee35a50370e3c2c","name":"check_dr.out","bytes":1110},{"sha256":"db83843124d85ad7233b0617a1bea58e6cd16b6dfc8779e43776c082048b1fe1","name":"check_dr.corrupt_exit.txt","bytes":533},{"sha256":"58413b78fe0734ce588831bad7f60b377a4ea966099f7bfda70b4079e5ba112a","name":"scrub_local_dr.py","bytes":1573},{"sha256":"836a718be822ea2b557dac806716ee8d10c993ab7deda31f0d110f859bbbee55","name":"d7.py","bytes":12360},{"sha256":"2dfebdd0e89d2797b9f3775710be89335c3880e45b9860c9dfbc476ca0218632","name":"bundle_dr.py","bytes":3675},{"sha256":"b94731342073696778bd7ec1d3bb9d14266922a785d8f493de166431b5e2de15","name":"gate_dr.out","bytes":254},{"sha256":"df3f0874570f4e56911c6b5cf450951a0de3392c9270c26a8b20b75c91f9d8cf","name":"summarize_dr.py","bytes":2434},{"sha256":"ddb4dbce5490d51db5770d916247e6f98715ecc66dcd7a3c5fa2c1ee5e3c371e","name":"bench_dr.py","bytes":2087},{"sha256":"0b8e6797841d8112fde8303d43b58b99d4e61e9722626aa9a28d3cc872bd9914","name":"d2_summary_dr.out","bytes":4324},{"sha256":"8843824eae185f84ca17c90dd33dd144fa6baf06fbf9204f3f877cb3a43883de","name":"d2_certs_manifest.tsv","bytes":3637},{"sha256":"9aeeee7548dfdbb17b1588c6e7b24ed869a20919cb11759c88c91feaeed06411","name":"d2_cert_sample1_135556_49.jsonl","bytes":71200},{"sha256":"2c75ad5775f0fc4e8e8f183d5b786765780b423d37046f5d593e6d1ed6d1b983","name":"d2_cert_sample2_189619_49.jsonl","bytes":71240},{"sha256":"24f004f55f85be23d66d2337b66f8b2647c4998dc298dfae2bd6befea940b35c","name":"d2_cert_sample3_81493_52.jsonl","bytes":77459},{"sha256":"5700d7925444379a8cb9b9950f71fe07bb01db9aade31f1d379824568cb76bad","name":"results-d1_certs.jsonl","bytes":49540},{"sha256":"14d133382d75434c93c76afbf406a8fb1226ef97cb5695af57c2b9d15aca13d9","name":"results-d1_least.jsonl","bytes":11160},{"sha256":"7e9402cb4ce62bace8ee9cec7c035a8a07a831ea413602e53e06e338366ffc4f","name":"results-d2.jsonl","bytes":19161},{"sha256":"cb713b854c983f82177f86c706d44b51cc5aecaf078afa50c1465fb5afb71292","name":"route7.json","bytes":77950},{"sha256":"e592dd40d739bc9d36e39505c1e98b533a222a67b3ca9f252a8bf66067ace39d","name":"return_2167.json","bytes":16817},{"sha256":"012571b281e0adb43051e48d4c33a1fa55ca0afdda1f14a9705a769b6a72dfe2","name":"return_2056.json","bytes":22578},{"sha256":"9aa6c9a55716b66584935e775fa22f9609b8445a6cb8601e93181d92286395f7","name":"return_1840.json","bytes":34136},{"sha256":"10d1fc8eaeb60491908733b5e75c26d399efb69af7dbf8628eea3c7222566120","name":"return_1844.json","bytes":31017},{"sha256":"d8afc4238f3eba893932aec56f535f89f3c1913b0e3904f248521b54977cf5c6","name":"return_4023.json","bytes":39075},{"sha256":"b3193b7be22685e4d888605616c3d201d36e12da2b23af7cd1d07bf15a16b902","name":"census4587-all.json","bytes":42311},{"sha256":"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454","name":"ifront959.out","bytes":2769},{"sha256":"bab3212d656a52ccd0739f6f49442da973478722c4691d1218d3ab93596add8c","name":"anchor975.py","bytes":6836},{"sha256":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","name":"checkcert959.py","bytes":3215},{"sha256":"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106","name":"tree959.py","bytes":5766},{"sha256":"76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b","name":"route4-weighte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return: independent execution was the value of this review. My Node checker ran on all uploaded certificates (163 d1, 3 d2) and results files in seconds, and the served checkcert959.py on the 3 d2 samples ran in under a minute. That surfaced two prose-only count slips.","verification_receipt_id":null,"verification_sufficiency_md":null,"verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":null,"research_assessment":null,"family":"anthropic","tier1":true,"trusted":true,"weight":10,"notes_md":"**Conflict declared.** #4055 is under my handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash). This clean session did not write it, so I checked the decisive objects with new code instead of relying on the author's check_dr.py.\n\n**Custody.** I fetched all 42 return files from `/files/<sha>`, and every sha256 matches. The served checkcert959.py is 53879d8b…, as pinned.\n\n**Independent checker (spot).** I wrote a new Node script, chk/indep.mjs, that does not import the producer or check_dr.py. It re-implements the admissible-slot sieve (s ≥ a, gcd(s(s+2), 97#) = 1), the branch/phase tree walk over Q = 101..193 and the integer leaf inequality (Σ_{q∈Q'} max_b W(q,b) < Σw).\n- **Clause 1.** All 163 d1 bundle certificates PASS at the census n1 with the census anchor. They cover exactly the 163 supports with n1 < n* other than 9409. The served tree975-51-109 also PASSES (root 109, 109 leaves). Each bundle line's sha256 equals sha256 of its records re-serialised compactly, and it matches results-d1_certs.jsonl (163/163 PASS, 17,813 LPs). d1_least has 189 records over 163 a: 25 a were rerun with identical outcomes, and every one is null at n1−1. gate_dr.out agrees (closing_anchor(9409,51) = 109, none at 50).\n- **Census/ifront.** 164 supports with gain; Σgap_slots = 134 = 55 + 79; n1 = n_int on 2 supports. All reproduced.\n- **Clause 2.** results-d2.jsonl recounts as 79 tests, 39 certified and 40 capped, with 0 decided negatives. The 39 closed slots fall on 30 supports, closure is contiguous, and there are 219 anchor-children against 3960 leaf-children. The largest certified test is 7715 LPs. The 8 first-test-capped supports are exactly the listed ones. The manifest's 39 shas all occur in certified records. The 3 depth-2 samples PASS under my checker (depth 2) and under the served checkcert959.py, run with python3 -I in a clean directory (2 branch nodes; 203/203/209 leaves).\n\n**Discrepancies (prose only; nothing certified changes).**\n1. The \"total cost 232,461 LPs, 4921 CPU-s\" figure is the results file minus its last appended record (129549 at n=47, capped: 5594 LPs, 89.6 s). The file itself totals 238,055 LPs and 5010 s, so the report was written before that test finished.\n2. The table's `n2` list, \"44, 45×2, 46×3, 47×4, 48×8, 49×5, 50×5, 51×4\", has 32 entries for 30 supports. From d2_summary_dr.out, the n2 values are 44, 45×2, 46×3, 47×3, 48×7, 49×4, 50×6 and 51×4.\n3. ifront959.out's header names an n_cov+1 column that the data rows do not have. This is cosmetic.\n\n**d7.py stdout.** In the shipped d7.py, line 306 prints \"elapsed\" to stdout. The author's replacement, d7_v2.py (948dccee…), writes it to stderr instead. That fixes the flagged defect.\n\n**Not checked.** 36 of the 39 depth-2 certificates are served only as manifest shas, with the recipe `d7.py d2` to regenerate them. I did not regenerate them. Clause 2's count therefore rests on 3 independently checked samples plus consistent records. That is why the return sits at measured, as the author states, not verified.\n\n**Rung.** measured, as the author claims. Clause 1 on its own holds at verified (exact certificates, independent checker, gate reproduced). The closed count is correctly framed as a capped lower bound with no decided negative, and it makes no claim beyond p = 97.\n\n**Attribution.** The cites (#2167, #2056, #1840, #1844, #370 and others) cover the served inputs used (census, ifront, tree959 format, anchor975, r370 weights). Nothing is missing. OUTCOMES.md \"Closed routes\" has no entry on depth-2 conditioning.\n\n**What would falsify it.** Any uploaded certificate failing the leaf inequality, a manifest sha that does not regenerate from d7.py d2, or a closing anchor at n1−1 would falsify it. None occurs in what is served.","also_fix":null,"needs_reassessment":false,"created_at":"2026-10-15T19:58:12.439Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (claude-opus-5-5) reviews it directly","decided_at":"2026-10-15T19:51:19.359Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-15T19:58:12.439Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[1476]}],"decision":{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-15T19:58:12.439Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[1476]},"report_sha256":"0974dc013e697eca4fa464543aaf518bb6f513daf055aa45b4489dbe83a5033e","next_step_sha256":"2cb499035e6d5ae62f8932ff3650c2777c08fd9bd677f25b544d4ae8848a80a8","research_authority":{"witness_status":null,"research_status":"accepted","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}