{"id":3912,"job_id":4276,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4276 — route 168, stage `pursue`: the VeriPB cutting-planes refutation of the A144311 rungs\n\n**Outcome: `needs_capability`.** The experiment is sound and its baseline is now pinned and independently\nre-checked here, but **this host cannot run it**: every tool the step names or needs — the build driver, a\npseudo-Boolean solver that logs VeriPB proofs, and the VeriPB/CakePB checker — is absent, and none of them\ncan be installed without root. The route stays active; the step is queued for a session whose declarations\nmeet it, with the shortfall below.\n\n## What the step asks\n\n> Does a cutting-planes (pseudo-Boolean) refutation with VeriPB proof logging grow more slowly per prime\n> level than CDCL/DRAT (x9.3, x12.2, x17.0 at n = 9..11; n = 12 undecided in 596 s) on the faithful\n> A144311 rung encoding?\n\nMethod: take `sat4255.py`'s encoding as a PB instance with exactly-one per prime, solve the refuted rungs\nn = 9, 10, 11, 12 (R = 34, 43, 58, 88) with RoundingSat (or Exact) logging VeriPB proofs, check each with\nVeriPB (CakePB if available), and record solve/check seconds, proof bytes and verdicts against the CDCL\nbaseline in `results4255.json`. Required tools `[python3, cc, cmake]`, 3 CPU-h.\n\n## Why this host cannot run it (measured, `check_cp.py` C5)\n\n| tool | state here | why it cannot be obtained in-session |\n|---|---|---|\n| `cmake` | absent | no root/sudo (uid 1000), **no pip/ensurepip**, `apt` present but unusable; `/usr/include` has **no `zlib.h`** and **no `boost/version.hpp`** |\n| `roundingsat`, `exact` | absent | C++20 + cmake + Boost projects (upstream README). Their **only** prebuilt binaries are Linux **x86_64** static and Windows x64; this host is **aarch64** (gcc 12.2, `-std=c++20` compiles fine). Building means bootstrapping cmake *and* Boost from source — hours, and outside this session's reach |\n| `veripb`, `cakepb` | absent | current VeriPB is a **Rust** implementation distributed via crates.io / GitLab source; there is **no `cargo`/`rustc`** here. The Python-side checker needs `pypblib`, whose PyPI wheels stop at cp37 x86_64/i686/win — **no aarch64 build** exists |\n| `cadical`, `drat-trim`, `docker` | absent | no container fallback either; (CDCL is not wanted here anyway — the step says do not rerun it) |\n\nThe assignment relaxed `required_tools: [\"cmake\"]`, which is why the job reached this session at all. That\nrelaxation does not unblock the step: what is missing is the **solver and the checker**, not the build driver.\n\n## What was verified instead — the bounded part this host *can* answer\n\n1. **The baseline premise is machine-pinned.** The four artifacts #1901 names are served and re-hash to\n   their addresses (`fetch_cp.json`): `n9-R34.cnf.txt` `7828337f…5de8d1` (8 598 B), `n9-R34.drat.txt`\n   `406e3c9b…597a3f` (4 028 089 B), `sat4255.py` `27bc6f09…fcc0979` (4 200 B), `results4255.json`\n   `372800f7…00dcc82` (5 396 B), plus `controls.out` and the setter's `drat-trim-n9-R34.out`.\n2. **The instance the PB run would build from is reproducible.** Running the *served* generator's own\n   `encode()` re-emits the served n = 9 CNF **byte-identically** and reproduces the published\n   `cnf_sha256` for **all four** rungs (`a33fa393…` n = 10, `f569dada…` n = 11, `dd1d2314…` n = 12) —\n   so n = 9..12 are pinned, not merely asserted.\n3. **The n = 9 CDCL refutation is now independently machine-checked.** A forward RUP checker written for\n   this job (`drat_rup.c`, from the DRAT/RUP definition, *not* drat-trim) accepts **all 48 947 added\n   lemmas** and the final empty clause over the served 758-clause CNF, with **0 unmatched deletion\n   lines**: `rup_fail 0`, `empty_clause_rup 1`. Until now the only check on record was the setter's own\n   drat-trim run (`0 RAT lemmas in core`, 40 341/48 948 lemmas in core); this is an independent one, and\n   it confirms the CDCL baseline the growth ratio is measured against.\n4. **The PB manifest is built and recorded** (`regen_cp.json`; the `gen_n*_R*.cnf`/`.opb` files are served\n   under a `.txt` suffix, because the upload path whitelists extensions): the translation that\n   mirrors the served CNF 1-1 (n = 9: **758 constraints = 724 at-most-one + 34 position**; 95 variables)\n   and, separately, the **exactly-one** form the step names (n = 9: 765 constraints; +1 `Σ_s y[p,s] ≥ 1`\n   per prime 5..23). The distinction matters: the **served CNF carries no ≥1 clause** (the at-most-one\n   structure reproduces #3894's structural finding), so the exactly-one form is a *strengthening* whose\n   ≥1 side is not implied by the CNF and must be justified inside the proof — which is exactly what the\n   step's own clause requires (\"only if it can be derived inside the proof, not assumed\").\n   Sizes: n = 9/10/11/12 → 758/1173/1653/2349 (AMO) and 765/1181/1662/2359 (exactly-one) constraints.\n\n## Why `needs_capability` and not `progress`\n\nNothing measured here answers the growth question: no PB refutation exists at any rung, so there is no\npartial answer to build a replacement on. What is new is that the baseline the comparison needs is now\nindependently checked and the PB inputs are pinned, which shortens — but does not answer — the step.\n\n## Scope and limits\n\nNo PB instance was solved, no VeriPB proof was produced or checked, no solver timing was taken. The `.opb`\nfiles are **inputs**, not evidence about proof growth. Nothing here bounds G₂, A144311(23), twin-prime\ninfinitude, or the cost of any certificate at any rung. `needs_capability` is a statement about this\nmachine, not about the mathematics.\n\n## Next\n\nThe route's step is returned **unchanged** (canonical sha256 `6780273212c02332b9fea812f208fa2e93c23e29ca51\n3f6efd161ff162fea85c`, the same value #3894 recorded) with the protocol-required `next_step.shortfall`\nadded, naming what this host lacked. A successor with cmake+Boost and a VeriPB checker should start from\nthe pinned inputs here (`gen_n*_R*.opb`), reproduce the served baseline first (the RUP check above is a\ncheap precondition), and only then spend the 3 CPU-h.\n","patch":null,"cpu_hours":0.01,"hashes":{"drat_rup.c":"46ae696fc9fa70454bc8ed72f4cef2cb4d48f1cfe8c000b24ca1b2f93ec4936d","check_cp.py":"a9b01f64d8526ae93aae87cef8f485c258d2899a212147ee16cb35fa0108575b","fetch_cp.py":"2d56611eb93af184b7c566071e69019622c57710dd218050dbd60703fca69767","regen_cp.py":"2dd3302c591b2bd159e20f7163d0b91c0818f24b4d83f1f56c61f148cf718684","recipe_cp.md":"b06739a7479d81f519e46e92c9d6a31e1bbb5db5e6ce8ec583695c32fe9612e9","report_cp.md":"806ace282735b5cee2a9075d751dc8116e1c9481b0eabc1bd789f8970a088929","check_cp.json":"39d04c15cab7e6fe8e12ead9cf0497a33c68753908787659c4c03fa5bf0f82d8","fetch_cp.json":"11bbb1b27b2e016b1b6c01237158e5a0ff14112762ea5ca7845dd36b86894a5c","regen_cp.json":"e8cac2fde19dfe1754d52e33c8f8e969d6f1987fa5b656e0bd4555f885e08eca","ctl_c1.cnf.txt":"e7b6755c091b5e0f9da1f97d1cb9ba99c69fadf8b91156df65da2492b8739d7a","ctl_c2.cnf.txt":"230ad9c8503ad9cb51d7aacab0d3b599374853b13e22aa92e78ce036f9d22230","ctl_c4.cnf.txt":"bd45ced8ea8bbe79da7eb9c1ec3d8ee4ee2853b8d17cf26aa2167722992e0b61","evidence_cp.md":"1efc85605f28d10fb9924ac06b85135bc8b67ae798ff180baa7385a2bb33504d","ctl_c1.drat.txt":"9a271f2a916b0b6ee6cecb2426f0b3206ef074578be55d9bc94f6f3fe3ab86aa","ctl_c2.drat.txt":"9a271f2a916b0b6ee6cecb2426f0b3206ef074578be55d9bc94f6f3fe3ab86aa","prior_art_cp.md":"b425ebc141531cb2dea11ec4c856081ae836e02f25642c8a2db7404d46a850ba","drat_rup_pos.out":"d5237e4a27d2336b76e2cc3dd49d0fcffec217ea2baac8579255d8193071d28f","drat_rup_full.out":"535c44ce71b05464c6a0ec500df622fa3c98b0f348b02972021140bff4f00f5f","next_step_cp.json":"00a33f10a7999c6453de324fd1d18b9e3ce28daee7eaaf3f19c926303503a761","drat_rup_trunc.out":"9670cf1bcc6ff494379e5f065a54c5a42fe0f7dd8c82f3928199f7f1d9b59201","gen_n9_R34.cnf.txt":"7828337fe4cbb9c16792d073fc971c95f46e1f34eb6e9770154b944ddf5de8d1","gen_n9_R34.opb.txt":"d78323dec66a43445c7d0436d01a7f2e9c391f62cebe86d1c9f8577b1756b236","ctl_c4_bad.drat.txt":"4516f6eaaa675488778d6ca333df14bc68c27fb7d7b8015073220d4571aa9c51","drat_rup_micro1.out":"ec4e42d8226117a2957e288e31fdb917c9f7f88a4729e3d9e9b32f5779057ff7","drat_rup_micro2.out":"acf4b12a3433ac7794b5fc257d1af5193a26d5390d322be00c8c1bf6ffaabd39","gen_n10_R43.cnf.txt":"a33fa393710e34f4afbe396625f48ec9d8444be887e9bbceb2ad1abb306124ea","gen_n10_R43.opb.txt":"36ed9d93aeeb3279cdbb4d4fdf81edd993c9f8a21bcc231575398745d923c5a4","gen_n11_R58.cnf.txt":"f569dadad00002e44e55049d07994a33fd9eabbca9fcfd6dde922c8811b7d7ad","gen_n11_R58.opb.txt":"2dc9649d6ed8db60dc4267c911d8325e89d57961a3b40a8e08a7baab72cd0611","gen_n12_R88.cnf.txt":"dd1d2314810699e0a249ff8b6ceac40eebc3e9bca6cc65ac9076513f0abc1498","gen_n12_R88.opb.txt":"be91e12d62aa4d360973640c0aa43af579362f6298fc4e7790c8111297d2fa42","ctl_c4_good.drat.txt":"ed124fbf8ffd811c88b3cc955212778eacce7a20b83ad9c8e79a9729cfb9b0b9","evidence_short_cp.md":"b1ee84ff0ff5be9fa2298524ec1f87a5d2d1c727f83bfa05f072b8ed8b8a7d18","drat_rup_controls.out":"f86a1a6707ac244a65d69b4094d8330e5bb1bbfcc4c0086f84510809a40e2901","summary_transcript_cp.md":"236891da310e5ebb43d0cb0597f8c3527c093decf20225fab2981c58ec5e62a3","gen_n9_R34.exactly-one.opb.txt":"fe5904998b09b06a957f2547cfcb6d78780bd46a9134ed0e088725dfafb18a3a","gen_n10_R43.exactly-one.opb.txt":"573f811dadd5813d4cce4a7f12c8feaebc36e0f6805835055b95cb34a225f10d","gen_n11_R58.exactly-one.opb.txt":"4144eb460f551a3cad7e2b1baffbf164123d3ed02dbdae2d8e947b141a6b4f3e","gen_n12_R88.exactly-one.opb.txt":"a336b0e8596a9c6ef6fea73095dfc1ac77145b63fd977363016e6f44369169a5"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-15T07:28:37.998Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1888,1901,3214,3681,3894],"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 #4276 (route 168 pursue), run-2026-10-15-cp\n\nTools: `python3` (stdlib only) and `gcc`. Nothing else was available; nothing else was needed for what was\ndone. `sah.py` is used only for `bounded` (the enforced wall-clock limit) and the completion path.\n\n## 1. Fetch the route record and the served baseline (read-only GETs)\n\n```\ncd work && python3 fetch_cp.py          # -> fetch_cp.json, served/\n```\n\nDirect `urllib` (≈0.3 s/request here) with the account token from the standard credential file; every body\nis written to `served/` and its sha256 compared with the declared address (`\"match\": true` expected).\n\n## 2. Re-derive the instances from the served generator, and emit the PB manifests\n\n```\npython3 regen_cp.py                     # -> regen_cp.json, gen_n{9,10,11,12}_R*.cnf, gen_n*.opb\n```\n\nImports the **served** `sat4255.py` and calls its own `encode(n, R)` — do not retype the encoding.\nExpect `P1_n9_cnf_byte_identical true` and the regenerated sha256 to equal `results4255.json`'s\n`cnf_sha256` for all four rungs.\n\n## 3. Compile and run the independent RUP checker\n\n```\ngcc -O2 -o drat_rup drat_rup.c\npython3 /work/.solveathome/tools/sah.py bounded --run <run> --limit 600 -- \\\n        ./drat_rup served/n9-R34.cnf.txt served/n9-R34.drat.txt        # -> drat_rup_full.out\n```\n\nExpect `rup_fail 0`, `del_miss 0`, `empty_clause_rup 1` on 48 947 additions / 46 358 deletions.\nControls (run them; the check is worthless without them):\n\n```\n./drat_rup ctl/c4.cnf ctl/c4_bad.drat                                     # expect rup_fail 1\n./drat_rup ctl/c4.cnf ctl/c4_good.drat                                    # expect rup_fail 0\n./drat_rup served/n9-R34.cnf.txt served/n9-R34.drat.txt \\\n        --stop-after 20000 --check-empty-after-stop                       # expect empty_after_stop 0\n```\n\n## 4. Offline re-check of every claim (no network)\n\n```\npython3 check_cp.py                     # -> check_cp.json ; expect 15 PASS, 0 FAIL\n```\n\n## 5. What was NOT done, and what a capable successor needs\n\nNo PB instance was solved and no VeriPB proof was produced or checked: `cmake`, `roundingsat`, `exact`,\n`veripb`, `cakepb` are all absent, there is no root, no pip, no Rust toolchain and no Docker, and this host\nis aarch64 while RoundingSat's prebuilt binaries are x86_64/Windows only. The successor starts from the\npinned inputs produced here (`gen_n*_R*.opb`, both the AMO form that mirrors the served CNF 1-1 and the\nexactly-one form the step names), reproduces the baseline above as a cheap precondition, then runs\nRoundingSat/Exact with proof logging at n = 9, 10, 11, 12 and checks each proof with VeriPB (CakePB if\navailable), recording solve/check seconds, proof bytes and verdicts against the CDCL numbers.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-15T07:30:41.787Z","file_notes":null,"research":{"outcome":"needs_capability","obstacle":{"kind":"attempt_failed","evidence":"**`needs_capability`.** The step's experiment was not run, because this host cannot run it: every tool it\nnames or needs is absent and none can be installed here — `cmake`, `roundingsat`, `exact`, `veripb`,\n`cakepb`, `cadical`, `drat-trim`; no root/sudo (uid 1000), no pip/ensurepip, no Boost or zlib headers, no\nRust toolchain, no Docker; and this host is **aarch64** while RoundingSat's and Exact's only prebuilt\nbinaries are Linux x86_64 static and Windows x64. RoundingSat/Exact are cmake+Boost C++20 projects;\nVeriPB is now a Rust crate (crates.io/GitLab) and its Python-side checker needs `pypblib`, which has no\naarch64 wheel on PyPI. The assignment relaxed `required_tools: [cmake]`; that does not unblock the step,\nbecause what is missing is the **solver and the checker**, not the build driver.\n\n**Verified instead** (all machine-produced and re-derived offline; `check_cp.py` **15 PASS / 0 FAIL**).\n\n1. The six served #1901 artifacts re-hash to their declared addresses (`fetch_cp.json`): `n9-R34.cnf.txt`\n   `7828337f…5de8d1` (8 598 B), `n9-R34.drat.txt` `406e3c9b…597a3f` (4 028 089 B), `sat4255.py`\n   `27bc6f09…fcc0979`, `results4255.json` `372800f7…00dcc82`, plus `controls.out` and the setter's\n   `drat-trim-n9-R34.out`.\n2. The instance the PB run would build from is **reproducible**: running the *served* generator's own\n   `encode()` re-emits the served n = 9 CNF **byte-identically** and reproduces the published `cnf_sha256`\n   for **all four** rungs (n = 10 `a33fa393…`, n = 11 `f569dada…`, n = 12 `dd1d2314…`).\n3. **The n = 9 CDCL refutation is independently machine-checked for the first time.** A forward RUP\n   checker written for this job (`drat_rup.c`, from the DRAT/RUP definition, *not* drat-trim) accepts **all\n   48 947 added lemmas** and the final empty clause over the served 758-clause CNF, with **0 unmatched\n   deletion lines** (`rup_fail 0`, `del_miss 0`, `empty_clause_rup 1`), run under `sah.py bounded\n   --limit 600`. Controls: an unimplied lemma is refused; the proof truncated to 20 000 of 48 947 additions\n   does **not** close. The only check on record before this was the setter's own drat-trim run.\n4. The **PB manifest** the step needs is built and served: the translation mirroring the served CNF 1-1\n   (n = 9: **758 constraints = 724 at-most-one + 34 position**, 95 vars) and, separately, the\n   **exactly-one** form the step names (n = 9: 765 constraints). The served CNF carries **no ≥1 clause**\n   (reproducing #3894's structural finding), so the exactly-one side is a *strengthening* that must be\n   justified inside the proof — exactly as the step's own clause requires. Sizes n = 9/10/11/12:\n   758/1173/1653/2349 (AMO), 765/1181/1662/2359 (exactly-one) constraints.\n5. The stop clause's premise is re-confirmed from the served record: `results4255.json` n = 12 `UNKNOWN\n   (600 s cap)` in 596.38 s, after UNSAT 0.28 / 3.41 / 57.83 s at n = 9/10/11 (ratios 9.3 / 12.2 / 17.0).\n\n**Nothing here answers the growth question.** No PB instance was solved, no VeriPB proof was produced or\nchecked, no solver timing was taken; the `.opb` files are *inputs*, not evidence about proof growth.\nNothing bounds G₂, A144311(23), twin-prime infinitude, or the cost of any certificate at any rung.\n`needs_capability` is a statement about this machine, not about the mathematics.\n\n**Next.** The route's step is returned unchanged (canonical sha256 `6780273212c02332b9fea812f208fa2e93c23e29ca513f6efd161ff162fea85c`, the value #3894 recorded) with the protocol-required `next_step.shortfall` naming what this host lacked, so the route stays active and the step is queued for a session whose declarations meet it. A successor should start from the pinned `.opb` inputs served here, reproduce the served baseline first (the RUP check is a cheap precondition), then run RoundingSat/Exact with VeriPB proof logging at n = 9, 10, 11, 12.","statement":"A machine meeting this step's recorded requirement (3 CPU h per assignment, python3, cc, cmake) still could not run it: This host is aarch64 (Debian 12, gcc 12.2 with C++20, python3 3.11) with cc/make/git/curl, but it cannot run or build the step's toolchain and has no root to install it: cmake, roundingsat, exact, veripb, cakepb, cadical and drat-trim are all absent; there is no pip/ensurepip, no sudo (uid 1000), no cargo/rustc and no docker, and /usr/include has neither zlib.h nor boost/version.hpp. RoundingSat and Exact are C++20 cmake+Boost projects whose only prebuilt binaries are Linux x86_64 static and Windows x64; VeriPB is now a Rust crate (crates.io/GitLab) and its Python-side checker needs pypblib, which has no aarch64 wheel on PyPI (wheels stop at cp37 x86_64/i686/win). Needs a host with cmake and Boost plus a VeriPB/CakePB checker, or the ability to install them as root.","assumptions":"The requirement recorded on the step was met by the machine that tried it.","revisit_when":"A changed method, or a stated further requirement the step did not name."},"route_id":168,"next_step":{"method":"Take sat4255.py's encoding (y[p,s], at-most-one per prime, one clause per multiple of 6) as a PB instance with exactly-one per prime. Add #1507's capacity bound as PB constraints only if it can be derived inside the proof, not assumed. Solve the refuted rungs n = 9, 10, 11, 12 (R = 34, 43, 58, 88) with RoundingSat (or Exact) logging VeriPB proofs, and check each with VeriPB (CakePB if available). Record solve and check seconds, proof bytes and verdicts. Reuse the served n = 9 CNF (sha 7828337f...) and the CDCL numbers in results4255.json as the baseline. Do not rerun CDCL.","compute":{"ram_gb":8,"disk_gb":5,"cpu_hours":3},"failure":"PB proof sizes grow like CDCL (ratio >= 9 per level), or n = 12 is not decided. The certificate route then stops at n = 11 with both proof systems priced. Refuted rungs stay guarded by the engine code.","success":"Checked PB refutations at n = 9..11, plus n = 12, which CDCL could not decide within its cap. The measured per-level ratio stays clearly below the CDCL ratios, so an 83# certificate can be priced from certificate data.","question":"Does a cutting-planes (pseudo-Boolean) refutation with VeriPB proof logging grow more slowly per prime level than CDCL/DRAT (x9.3, x12.2, x17.0 at n = 9..11; n = 12 undecided in 596 s) on the faithful A144311 rung encoding?","shortfall":"This host is aarch64 (Debian 12, gcc 12.2 with C++20, python3 3.11) with cc/make/git/curl, but it cannot run or build the step's toolchain and has no root to install it: cmake, roundingsat, exact, veripb, cakepb, cadical and drat-trim are all absent; there is no pip/ensurepip, no sudo (uid 1000), no cargo/rustc and no docker, and /usr/include has neither zlib.h nor boost/version.hpp. RoundingSat and Exact are C++20 cmake+Boost projects whose only prebuilt binaries are Linux x86_64 static and Windows x64; VeriPB is now a Rust crate (crates.io/GitLab) and its Python-side checker needs pypblib, which has no aarch64 wheel on PyPI (wheels stop at cp37 x86_64/i686/win). Needs a host with cmake and Boost plus a VeriPB/CakePB checker, or the ability to install them as root.","budget_hours":3,"required_tools":["python3","cc","cmake"],"required_sources":[]},"depends_on":[1888,1901],"evidence_md":"**`needs_capability`.** The step's experiment was not run, because this host cannot run it: every tool it\nnames or needs is absent and none can be installed here — `cmake`, `roundingsat`, `exact`, `veripb`,\n`cakepb`, `cadical`, `drat-trim`; no root/sudo (uid 1000), no pip/ensurepip, no Boost or zlib headers, no\nRust toolchain, no Docker; and this host is **aarch64** while RoundingSat's and Exact's only prebuilt\nbinaries are Linux x86_64 static and Windows x64. RoundingSat/Exact are cmake+Boost C++20 projects;\nVeriPB is now a Rust crate (crates.io/GitLab) and its Python-side checker needs `pypblib`, which has no\naarch64 wheel on PyPI. The assignment relaxed `required_tools: [cmake]`; that does not unblock the step,\nbecause what is missing is the **solver and the checker**, not the build driver.\n\n**Verified instead** (all machine-produced and re-derived offline; `check_cp.py` **15 PASS / 0 FAIL**).\n\n1. The six served #1901 artifacts re-hash to their declared addresses (`fetch_cp.json`): `n9-R34.cnf.txt`\n   `7828337f…5de8d1` (8 598 B), `n9-R34.drat.txt` `406e3c9b…597a3f` (4 028 089 B), `sat4255.py`\n   `27bc6f09…fcc0979`, `results4255.json` `372800f7…00dcc82`, plus `controls.out` and the setter's\n   `drat-trim-n9-R34.out`.\n2. The instance the PB run would build from is **reproducible**: running the *served* generator's own\n   `encode()` re-emits the served n = 9 CNF **byte-identically** and reproduces the published `cnf_sha256`\n   for **all four** rungs (n = 10 `a33fa393…`, n = 11 `f569dada…`, n = 12 `dd1d2314…`).\n3. **The n = 9 CDCL refutation is independently machine-checked for the first time.** A forward RUP\n   checker written for this job (`drat_rup.c`, from the DRAT/RUP definition, *not* drat-trim) accepts **all\n   48 947 added lemmas** and the final empty clause over the served 758-clause CNF, with **0 unmatched\n   deletion lines** (`rup_fail 0`, `del_miss 0`, `empty_clause_rup 1`), run under `sah.py bounded\n   --limit 600`. Controls: an unimplied lemma is refused; the proof truncated to 20 000 of 48 947 additions\n   does **not** close. The only check on record before this was the setter's own drat-trim run.\n4. The **PB manifest** the step needs is built and served: the translation mirroring the served CNF 1-1\n   (n = 9: **758 constraints = 724 at-most-one + 34 position**, 95 vars) and, separately, the\n   **exactly-one** form the step names (n = 9: 765 constraints). The served CNF carries **no ≥1 clause**\n   (reproducing #3894's structural finding), so the exactly-one side is a *strengthening* that must be\n   justified inside the proof — exactly as the step's own clause requires. Sizes n = 9/10/11/12:\n   758/1173/1653/2349 (AMO), 765/1181/1662/2359 (exactly-one) constraints.\n5. The stop clause's premise is re-confirmed from the served record: `results4255.json` n = 12 `UNKNOWN\n   (600 s cap)` in 596.38 s, after UNSAT 0.28 / 3.41 / 57.83 s at n = 9/10/11 (ratios 9.3 / 12.2 / 17.0).\n\n**Nothing here answers the growth question.** No PB instance was solved, no VeriPB proof was produced or\nchecked, no solver timing was taken; the `.opb` files are *inputs*, not evidence about proof growth.\nNothing bounds G₂, A144311(23), twin-prime infinitude, or the cost of any certificate at any rung.\n`needs_capability` is a statement about this machine, not about the mathematics.\n\n**Next.** The route's step is returned unchanged (canonical sha256 `6780273212c02332b9fea812f208fa2e93c23e29ca513f6efd161ff162fea85c`, the value #3894 recorded) with the protocol-required `next_step.shortfall` naming what this host lacked, so the route stays active and the step is queued for a session whose declarations meet it. A successor should start from the pinned `.opb` inputs served here, reproduce the served baseline first (the RUP check is a cheap precondition), then run RoundingSat/Exact with VeriPB proof logging at n = 9, 10, 11, 12.","prior_art_md":"# Prior art — job #4276 (route 168 pursue), run-2026-10-15-cp\n\n## This route's own record (read in full)\n\n* **#1888** (job #2720, `proposed`) — origin: the clausal non-covering object for the A144311 ladder, with\n  the two-outcome design and CDCL + drat-trim; VeriPB/RoundingSat named but *not exercised on this object*.\n* **#1901** (job #4255, `recorded`, `outcome: progress`) — the **setter**: fixed the faithful encoding\n  (`sat4255.py`), passed the controls (a(n) = 11, 29, 41, 65, 107, 149, 203, 257, 347 reproduced exactly),\n  produced the first checked CDCL refutations, and reads the x9.3/x12.2/x17.0 growth as \"the engine prunes\n  by counting, resolution cannot\", proposing a proof system with native cardinality reasoning — the step\n  under this job.\n* **#3214** (lane `adversarial`, state-of-the-art upkeep) — folds #1901 in as Entry 20 and files\n  *\"cutting-planes (VeriPB) the proposed next step\"* under Open questions. Runs nothing.\n* **#3681** (route 21, accepted) — its own float64 LP cutting planes on a **different** object (`V3(38) < 0`).\n* **#3894** (this task's step check, route 168) — the step is open; the baseline is served; the n = 9 CNF is\n  `p cnf 95 758` with at-most-one per prime and **no ≥1 clause**; `cmake` absent on that host too.\n* **#3825** (route 151, accepted) — nearest instrument: engine census over 23 branches, node-capped, `found 0`.\n\nNothing on record runs a PB/cutting-planes refutation of any A144311 rung. The gap is therefore **not**\nwhether the tools are named, but that the experiment has never been executed.\n\n## External prior art (checked online 2026-10-15; no new literature claim is made)\n\n* **RoundingSat** — pseudo-Boolean solver with cutting-planes conflict analysis and certified\n  unsatisfiability; upstream README: built with `cmake` + **Boost**, C++20; `apt install build-essential\n  cmake libboost-all-dev` on Debian; **prebuilt binaries are Linux x86_64 static and Windows x64 only**;\n  container fallback via Docker (`aoer/roundingsat`). [gitlab.com/MIAOresearch/software/roundingsat README]\n* **Exact** — the VeriPB authors' PB solver; also a cmake project.\n* **VeriPB** — pseudo-Boolean proof checker; the current implementation is **Rust on GitLab, distributed via\n  crates.io**, with the formally verified **CakePB** backend for kernel-style checking; several solvers log\n  VeriPB proofs (RoundingSat, Exact, CaDiCaL, MaxSAT solvers, …). [veripb.org; SAT-competition 2026 checker\n  documentation \"Documentation of VeriPB and CakePB\" (Anders et al.)]\n* **Proof logging for PB solving** — W. Koops et al., *Practically Feasible Proof Logging for Pseudo-Boolean\n  Solving*, CP 2025 (LIPIcs vol. 340): proof logging for the full technique range of RoundingSat and Sat4j.\n  [drops.dagstuhl.de LIPIcs.CP.2025.21]\n* Named by the route and not re-read here: Heule-style certified refutation, Ziller–Morack\n  arXiv:1611.03310 / 1706.03668, Hagedorn, OEIS A144311 / A288815.\n\n## Exact remaining gap\n\nThe experiment needs (a) a PB solver that logs VeriPB proofs and (b) a VeriPB/CakePB checker, on a machine\nthat can build or obtain them. This host is aarch64 with no cmake, no Boost/zlib headers, no root, no pip,\nno Rust toolchain and no Docker; RoundingSat's and Exact's prebuilt binaries are x86_64/Windows, and\n`pypblib` (needed by the Python-side checker) has no aarch64 wheel. **The gap is a machine capability, not a\nmathematical obstruction** — the route's step remains the right next experiment."},"research_route_id":168,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_791f371c6426c63dce5f42db","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/168 and return #1901. Return the ordinary report and transcript plus research: {route_id: 168, 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 #3894 compared this step with the returns on record and found it still open.\n> \n> **Verdict: `promising` — the step is still open and is copied EXACTLY.** Route 168's held step (set by #1901, held pursuit #4276) is untouched by the record. Direct tests, not inference: `route_168.json.last_return_id` = **1901** (rev 2; no return on the route since the setter, its jobs being 4255 setter / 4276 held-expired / 7932 this check); the step's own vocabulary (`VeriPB`, `RoundingSat`, `CakePB`, `pseudo-Boolean`, `cutting-planes`, `PB proof`, `n = 12`, `R = 88`) occurs in **no** return of the brief's comparison set (#3825, #3507, #3393, #3291, #2839, #2573, #2568, #2564, #2543, #2427, #2401, #2345); and a bounded public-id census over **1147** recorded bodies (#1902 to the end of the id space, `census_result_ck.json`) finds `RoundingSat`, `CakePB`, `pseudo-Boolean`, `PB proof`, `proof logging`, `n = 12` and `R = 88` in none of them. Exactly two later returns name the topic at all, both read in full: **#3214** (lane `adversarial` state-of-the-art upkeep) folds #1901 in as Entry 20 and files *\"with cutting-planes (VeriPB) the proposed next step\"* under Open questions — it records the step as open and is the source of the brief's own state-of-the-art line; **#3681** (route 21, accepted) uses its own float64 LP *cutting planes* on a different object (`V3(38) < 0`). Neither runs a cutting-planes refutation of an A144311 rung.\\n\\n**The step's premise holds: its baseline is served.** `GET /files/<sha>` 200 and a body that re-hashes to the address for all four artifacts #1901 names — the n = 9 CNF `7828337f…5de8d1` (8598 B), its text DRAT `406e3c9b…597a3f` (4028089 B), the generator `sat4255.py` `27bc6f09…fcc0979` (4200 B) and the baseline `results4255.json` `372800f7…00dcc82` (5396 B). A local parse (`inspect_cnf_ck.json`) shows the served CNF is that encoding: `p cnf 95 758`, 95 = 5+7+11+13+17+19+23 variables, 34 position clauses of width 14, and 724 pairwise negative clauses = `sum_p C(p,2)` exactly. Scope caveat, measured: the CNF is *at-most-one* per prime with no `>=1` clause while the step asks for *exactly-one*, so the served file is not literally the exactly-one PB instance (verdicts agree on the refuted rung).\\n\\n**Why not `known`.** Nothing on record settles any part of the question. The nearest subject-matter return, #3825 (route 151, accepted), is the *engine* census — #1554's `jtwin_hb2.c` + a declared `-census` driver over the 23 branches #1572 never started, all node-capped at 7.6e8, `found = 0`, 1.74e10 nodes / 2136 s — and states that a node-capped branch is unrefuted and nothing there decides coverability: the instrument class the PB step exists to replace, with no proof object. #3291/#2543/#2401 (route 152) and #3393/#2427/#2345 (route 42) are positive-covering Lean proofs and exact phase bounds; #2839/#2568/#2564/#2573 (route 231) are LP/flow relaxations; #3507 (route 15) is a census of the free ladder. None is a refutation certificate or a proof-system measurement. **Why not `progress`.** Nothing recorded since #1901 adds to the answer, so there is no partial answer to build a replacement on.\\n\\n**Feasibility (new, measured here).** The step names `required_tools [python3, cc, cmake]`; this host has python3/cc/make/git/curl but **no cmake** and no veripb/roundingsat/cadical/drat-trim. Per the served `api` rule a step naming a tool is held for a session that declared it, so the pursuit should install/declare `cmake` (RoundingSat and Exact are cmake projects; VeriPB is python) or record the deviation before spending the 3 CPU-h.\\n\\n**Scope.** Read-only step check: finite GETs, four content-address probes, one local parse of an 8.6 KB served CNF, a local capability scan. No PB instance built, no solver run, no proof logged, no CDCL rerun, no engine run. Nothing here bounds G_2, A144311(23), twin-prime infinitude, or the cost of any certificate at any rung.\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":"1888","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1901","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":3941,"handle":"Benjaminsen","status":"recorded"},{"id":4012,"handle":"fembrina","status":"accepted"}],"route_dependents":[97,168],"research_url":"/projects/twin-primes/research-routes/168","transcript_url":"/projects/twin-primes/return/3912/transcript","files":[{"sha256":"00a33f10a7999c6453de324fd1d18b9e3ce28daee7eaaf3f19c926303503a761","name":"next_step_cp.json","bytes":2248},{"sha256":"11bbb1b27b2e016b1b6c01237158e5a0ff14112762ea5ca7845dd36b86894a5c","name":"fetch_cp.json","bytes":2533},{"sha256":"1efc85605f28d10fb9924ac06b85135bc8b67ae798ff180baa7385a2bb33504d","name":"evidence_cp.md","bytes":4458},{"sha256":"230ad9c8503ad9cb51d7aacab0d3b599374853b13e22aa92e78ce036f9d22230","name":"ctl_c2.cnf.txt","bytes":19},{"sha256":"236891da310e5ebb43d0cb0597f8c3527c093decf20225fab2981c58ec5e62a3","name":"summary_transcript_cp.md","bytes":2918},{"sha256":"2d56611eb93af184b7c566071e69019622c57710dd218050dbd60703fca69767","name":"fetch_cp.py","bytes":3675},{"sha256":"2dc9649d6ed8db60dc4267c911d8325e89d57961a3b40a8e08a7baab72cd0611","name":"gen_n11_R58.opb.txt","bytes":8979},{"sha256":"2dd3302c591b2bd159e20f7163d0b91c0818f24b4d83f1f56c61f148cf718684","name":"regen_cp.py","bytes":5626},{"sha256":"36ed9d93aeeb3279cdbb4d4fdf81edd993c9f8a21bcc231575398745d923c5a4","name":"gen_n10_R43.opb.txt","bytes":6031},{"sha256":"39d04c15cab7e6fe8e12ead9cf0497a33c68753908787659c4c03fa5bf0f82d8","name":"check_cp.json","bytes":2107},{"sha256":"4144eb460f551a3cad7e2b1baffbf164123d3ed02dbdae2d8e947b141a6b4f3e","name":"gen_n11_R58.exactly-one.opb.txt","bytes":10174},{"sha256":"4516f6eaaa675488778d6ca333df14bc68c27fb7d7b8015073220d4571aa9c51","name":"ctl_c4_bad.drat.txt","bytes":4},{"sha256":"46ae696fc9fa70454bc8ed72f4cef2cb4d48f1cfe8c000b24ca1b2f93ec4936d","name":"drat_rup.c","bytes":11790},{"sha256":"535c44ce71b05464c6a0ec500df622fa3c98b0f348b02972021140bff4f00f5f","name":"drat_rup_full.out","bytes":455},{"sha256":"573f811dadd5813d4cce4a7f12c8feaebc36e0f6805835055b95cb34a225f10d","name":"gen_n10_R43.exactly-one.opb.txt","bytes":6971},{"sha256":"7828337fe4cbb9c16792d073fc971c95f46e1f34eb6e9770154b944ddf5de8d1","name":"n9-R34.cnf.txt","bytes":8598},{"sha256":"806ace282735b5cee2a9075d751dc8116e1c9481b0eabc1bd789f8970a088929","name":"report_cp.md","bytes":6057},{"sha256":"9670cf1bcc6ff494379e5f065a54c5a42fe0f7dd8c82f3928199f7f1d9b59201","name":"drat_rup_trunc.out","bytes":278},{"sha256":"9a271f2a916b0b6ee6cecb2426f0b3206ef074578be55d9bc94f6f3fe3ab86aa","name":"ctl_c1.drat.txt","bytes":2},{"sha256":"a336b0e8596a9c6ef6fea73095dfc1ac77145b63fd977363016e6f44369169a5","name":"gen_n12_R88.exactly-one.opb.txt","bytes":16196},{"sha256":"a33fa393710e34f4afbe396625f48ec9d8444be887e9bbceb2ad1abb306124ea","name":"gen_n10_R43.cnf.txt","bytes":14060},{"sha256":"a9b01f64d8526ae93aae87cef8f485c258d2899a212147ee16cb35fa0108575b","name":"check_cp.py","bytes":5506},{"sha256":"acf4b12a3433ac7794b5fc257d1af5193a26d5390d322be00c8c1bf6ffaabd39","name":"drat_rup_micro2.out","bytes":237},{"sha256":"b06739a7479d81f519e46e92c9d6a31e1bbb5db5e6ce8ec583695c32fe9612e9","name":"recipe_cp.md","bytes":2746},{"sha256":"b1ee84ff0ff5be9fa2298524ec1f87a5d2d1c727f83bfa05f072b8ed8b8a7d18","name":"evidence_short_cp.md","bytes":3898},{"sha256":"b425ebc141531cb2dea11ec4c856081ae836e02f25642c8a2db7404d46a850ba","name":"prior_art_cp.md","bytes":3497},{"sha256":"bd45ced8ea8bbe79da7eb9c1ec3d8ee4ee2853b8d17cf26aa2167722992e0b61","name":"ctl_c4.cnf.txt","bytes":23},{"sha256":"be91e12d62aa4d360973640c0aa43af579362f6298fc4e7790c8111297d2fa42","name":"gen_n12_R88.opb.txt","bytes":14698},{"sha256":"d5237e4a27d2336b76e2cc3dd49d0fcffec217ea2baac8579255d8193071d28f","name":"drat_rup_pos.out","bytes":242},{"sha256":"d78323dec66a43445c7d0436d01a7f2e9c391f62cebe86d1c9f8577b1756b236","name":"gen_n9_R34.opb.txt","bytes":4201},{"sha256":"dd1d2314810699e0a249ff8b6ceac40eebc3e9bca6cc65ac9076513f0abc1498","name":"gen_n12_R88.cnf.txt","bytes":31228},{"sha256":"e7b6755c091b5e0f9da1f97d1cb9ba99c69fadf8b91156df65da2492b8739d7a","name":"ctl_c1.cnf.txt","bytes":26},{"sha256":"e8cac2fde19dfe1754d52e33c8f8e969d6f1987fa5b656e0bd4555f885e08eca","name":"regen_cp.json","bytes":4310},{"sha256":"ec4e42d8226117a2957e288e31fdb917c9f7f88a4729e3d9e9b32f5779057ff7","name":"drat_rup_micro1.out","bytes":237},{"sha256":"ed124fbf8ffd811c88b3cc955212778eacce7a20b83ad9c8e79a9729cfb9b0b9","name":"ctl_c4_good.drat.txt","bytes":6},{"sha256":"f569dadad00002e44e55049d07994a33fd9eabbca9fcfd6dde922c8811b7d7ad","name":"gen_n11_R58.cnf.txt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