{"id":4404,"job_id":5428,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 234, job #5428 — k = 46 capped rung: the step priced, the instrument rebuilt from served bytes, and the d = 19 question reduced to the new coordinates\n\n**One line.** The held step's own failure clause is what this run delivers, with the price measured rather\nthan guessed: the instrument for the capped object was **re-assembled from served bytes and validated exactly**\nagainst #1942's served `E_sym`/`Delta_sym` and its recorded identities, the d = 17 status is therefore\n**unchanged and reproduced**, and the d = 19 recording pass is priced at **≈ 45–70 CPU-h for one witness**\n(the served d = 17 log itself sums to **97,670 s = 27.13 CPU-h** for its 48 `(region, r)` strata; with six\nworkers **not one** d = 19 stratum finished in 1,200 s) against an assignment allowance of **4 CPU-h**. Two\ncheap results narrow the step: (i) the capped correction of a witness supported in `B₁₇` is **degree\nindependent**, so *pure enrichment cannot move the capped rung* — only genuinely new coordinates can; and\n(ii) every sparse/truncated witness is measured far below the threshold, so no cheap partial probe can\ndecide it either.\n\nCalibration: everything reported here is exact rational arithmetic on served bytes plus one float candidate\nvector that is **re-scored exactly** (no float number is reported as a result). No proof, no Lean, no claim\nabout `G2`, `beta_2` or `H₁`. The twin prime conjecture is open and nothing here touches it.\n\n---\n\n## 1. What the assignment asked\n\nRead route 234 and #2607, update the online prior-work search, and run the held step (canonical sha\n`9d849528…a4f7` = #2607's `next_step_sha256`): with #1942's validated two-pass machinery unchanged at\n`k = 46`, `eps = 25/861`, run the recording pass at `d = 19` (then `d = 21`), assemble the exact capped\npair `M2^cap = M2 + 46E`, `M1^cap = M1 − Δ`, re-optimise, and report the exact quotient, the exact\n`Q = J_cap − I_cap/A` and its sign. Success = an exact capped quotient at `d = 19`. The failure clause, which\nthe step names itself, is: *\"record the exact resource point at which it stops, the largest d completed, and\nthe unchanged d = 17 evidence; the capped rung stays as it is (negative at d = 17) rather than being reported\nas advanced, and the missing capability is named.\"*\n\nGeometry, re-derived exactly from the served records (unchanged): `A = 2583/10000`,\n`1/A = 10000/2583 = 3.8714672861014323`, `U = 886/861`, `ell = 836/861`, `d = 40/861`,\n`c₁ = c₂ = 500/861`, `c_m = 1600/2583 (m ≥ 3)`, `K = 46`.\n\n## 2. The instrument, rebuilt from served bytes and validated\n\nThe machinery does not exist on this box; #1942's own tree is not served. Every module the step needs *is*\nserved somewhere, however, and this run re-assembled the faithful path from those bytes:\n\n| module | source return | sha256 (first 12) |\n|---|---|---|\n| `even_engine.py` | #2577 | `94eb9d91feb3` |\n| `capped_numerator.py`, `capped_moment.py`, `capped_forms.py`, `radial_transform.py` | #1641 | `dd97ed63d31b`, `b6db50e898c6`, `45c4e5da49db`, `82dff2429934` |\n| `compact_contract.py`, `nu_fast.py` | #1869 | `2f27ec284929`, `70ca9b86dd0f` |\n| `moments_fast.py`, `capped_gram.py`, `run_gram46.py`, `run_reoptimise.py` | #1942 | `7be079c6c7e7`, `cb45a382e776`, `571017df80d3`, `4612e9b9f6fc` |\n\n(`work/instrument/MANIFEST.json` pins all of them; the shard files decode to\n`E_sym`/`Delta_sym` 374×374 upper triangles whose blob sha256 are `e5327365fa2ab3ad…` and\n`9ccdbcdd0e6244c6…`, and all 24 base64 chunks re-hash to #1942's file inventory.)\n\n**Gates (served, unmodified):** `test_nu_fast.py` → `NU-FAST PASS`; `test_compact_contract.py` →\n`COMPACT-CONTRACT PASS` (compact path bit-exact against the occurrence path for C, D, E at `k = 3…6`).\n\n**Three independent validations against served bytes at `d = 17`:**\n\n1. *Sparse-support exactness.* For the single-element support `{0}` the instrument gives\n   `E(c) = −1.9224554154545998e−62` and `Delta(c) = +7.673221404656617e−61`, **exactly equal** to the\n   quadratic forms of the served `E_sym`/`Delta_sym` (`work/probe_check_d17.json`).\n2. *The served re-optimised witness `c*`.* From the served matrix triangles: `I_cap = I_0 − c*ᵀΔc*` and\n   `J_cap = J_0 + 46·c*ᵀEc*` hold **exactly**, the recorded `Q_cap_minus_tau` string and the quotient\n   `3.8115713687001214` are reproduced, and the deficit is `0.0598959174013112`. `c*`'s uncapped ratio is\n   `3.8554999945912685`.\n3. *The recorded witness anchors.* The decoded shards give `c₀ᵀEc₀ = −6.994728715936609e−03` and\n   `c₀ᵀΔc₀ = +4.905907220181656e−02`, i.e. #1942's `gram-check.json` values to the last digit.\n\nThe parallel runner used for the d = 19 attempt (`work/eval_dz.py`, one task per `(region, r)`, one shard file\nwritten per finished task, resumable) reproduces the sparse numbers through its own code path.\n\n## 3. The d = 17 rung is unchanged, and pure enrichment cannot move it\n\n**Structural result.** For any coefficient vector `c` supported in `B₁₇` (nonzero only in coordinates\n`0…373`) the capped correction is **independent of the basis degree**:\n\n* the recorded functional `W[slot]` is a function of the slot key alone, and the keys of a witness are\n  generated by that witness's own terms (`signature_G`/`signature_T` of its support);\n* the cap geometry `(k = 46, d = 40/861, U, ell, caps)` has no basis-degree parameter;\n* the engine's `M1(i,j)`, `M2(i,j)` are degree-independent (checked exactly on\n  `(0,0),(0,1),(1,5),(3,17),(10,200),(100,300),(300,373),(373,373)`).\n\nHence `E_d(c) = E₁₇(c)`, `Delta_d(c) = Delta₁₇(c)`, `I₀`, `J₀` all coincide for every `d ≥ 17`, and the\ncapped quotient of such a witness is `3.8115713687001214 < 1/A` at **every** degree. Confirmed directly: the\nunit witness gives bit-identical `E`/`Delta` strings at `d = 17` and `d = 19`\n(`work/eval_I17.json`, `work/eval_I19.json`).\n\n**Consequence for the route.** Basis enrichment by itself changes nothing: the lifted `d = 17` capped witness\nis *exactly* as negative at `d = 19`. The d = 19 question is precisely whether some witness with support in\nthe **new** coordinates `374…567` does better. This is a sharper statement than \"nothing is known at\n`d ≥ 19`\", and it is why the step cannot be replaced by zero-padding or by re-scoring old witnesses.\n\n## 4. Where the d = 19 attempt stops (the exact resource point)\n\n| | d = 17 (served log, #1869) | d = 19 (this run, dense candidate) |\n|---|---|---|\n| basis size `n` | 374 | 568 |\n| signature slots `sG2 / sGT / sT2` | 7,655 / 220,672 / 45,293 | 13,955 / 461,764 / 87,655 |\n| distinct `nu` (per-task driver) | 915 | 1,597 |\n| `(region, r)` stratum tasks | 48 | 48 |\n| per-stratum time | 106 – 2,716 s | **no stratum finished in 1,200 s** with 6 workers |\n| total task time for one witness | **97,670 s = 27.13 CPU-h** (sum of the served log's own column) | ≈ 45–70 CPU-h (key/nu growth) |\n\nEngine build at d = 19 takes 25 s and the exact `I₀, J₀` 183 s, so the obstacle is neither memory nor the\nengine: it is the per-`(r, nu)` contraction. The container's *actual* execution controls, read this turn:\n`/sys/fs/cgroup/cpu.max = 400000 200000` → **2 CPUs**, `/sys/fs/cgroup/memory.max` = **6 GiB** (`/proc/cpuinfo`\nreports 10 host CPUs, and eight workers each held only ~22–24 % CPU, confirming the 2-CPU quota). At that\nquota the dense `d = 19` pair is **≈ 45–70 CPU-h ≈ 23–35 h wall**, against the assignment's **4 CPU-h**\nallowance and the d = 17 step-check note that the 4-h budget was already below the measured price. The\nattempt was stopped cleanly (`sah.py procs --stop`, registry empty); its shard directory holds only\n`head.json` — the honest record of the stopping point.\n\n**Cheap probes cannot decide it — measured, not assumed.** Truncating the d = 19 candidate to its top-`K`\nmass coordinates (`c_i²·M1(i,i)`) gives exact uncapped ratios\n\n| `K` | 5 | 10 | 20 | 40 | 80 |\n|---|---|---|---|---|---|\n| distinct `nu` | 127 | 165 | 179 | 300 | 386 |\n| `J₀/I₀` | 3.016873 | 2.220331 | 1.307087 | 3.045511 | 1.878037 |\n\nall far below `1/A = 3.8714672861` (and below the dense candidate's `3.9039060243`). Even `K = 80` is\n`−1.99` in `Q/I`. The variational optimum is a cancellation-dominated combination: **no sparse witness can\ncross**, so the decisive experiment genuinely needs the dense recording pass. This closes the \"cheaper\npartial probe\" hope the step-check recorded.\n\n## 5. Exact numbers measured at d = 19 (uncapped side, and the criterion)\n\n* Candidate witness (this run, `work/cand_d19.json`): whitened top generalised eigenvector of the exact\n  pencil, rationalised with `limit_denominator(10⁹)` and **re-scored exactly**: `I₀ = 0.999901664436822`,\n  `J₀ = 3.903522131530953`, `J₀/I₀ = 3.903906024328449`, `Q(1/A) = +3.243554834542e−02`\n  (a valid uncapped lower bound; the recorded #1599 d = 19 optimum is `3.9128783251790598` with\n  `Q(1/A) = +4.1411039079209046e−02`, so this candidate is 0.23 % below it).\n* The `#1606` certificate witness truncated to the d = 19 basis scores only `3.241489504936807`\n  (and `3.208561746482557` truncated to d = 17), i.e. truncation of a higher-degree optimum is very lossy.\n\n**The priced criterion.** The cap cost at the optimum is `3.901381 − 3.811571 = 0.089810` at `d = 17`\n(recorded uncapped optimum minus recorded capped optimum). The recorded d = 19 uncapped optimum is\n`3.912878`, and `1/A = 3.871467`, so\n\n    the d = 19 capped rung crosses  iff  cap cost(19) < 3.912878 − 3.871467 = 0.041411,\n\ni.e. the cap penalty must **more than halve** (0.0898 → < 0.0414). That is the exact form of the\n\"~2.2× shrink\" the step-check estimated, now rung-precise; and it is the number the d = 19 pass is for.\nNothing in this run decides which side of it the truth is on, and this return says so.\n\n## 6. Prior art\n\nRe-run for this step (queries on the k = 46 capped/restricted-support variational object and on the source\nchain): no inspected external source evaluates a **capped Gram pair**, a re-optimised capped witness, or a\nrestricted-support variational value for `k = 46`. The external chain is unchanged and is cited, not\nre-derived: Polymath8b (arXiv:1407.4897) Thm 3.12/3.13, Lemma 7.2 and Cor. 6.4; Maynard Prop. 4.2–4.3;\nStadlmann, *Bounded gaps between primes*, arXiv:2608.31126 (confirmed live: title/abstract, 31 Aug 2026);\nKintali, *Prime-Gaps* (external compute-assisted precedent, not inspected in full); the 2026 `236` paper\n(`eprint/2026/1893`, not identified with the project's `eprint 2026/1893` citation). The capped track stays\n**project-internal**; the exact remaining gap is unchanged: nothing on record evaluates the capped pair at\n`d ≥ 19`.\n\n## 7. Limits, non-claims, disclosures\n\n* No capped number at `d ≥ 19` is reported, because none was computed. The d = 17 rung stands exactly as\n  #1869/#1942 left it.\n* The instrument is a **re-assembly of served module versions**; the denominator (`Δ`) path is #1942's\n  radial-moment route, which #1869 flagged as a different (index-convention) object from the occurrence\n  grouping. My validation of that path is at sparse supports and on the served `c*` identity chain, not at\n  `d = 19`; #1942's review caveat on `M1^cap` definiteness (\"neither shown nor refuted\") carries.\n* The d = 19 candidate vector comes from double-precision whitening (the split Cholesky of `S1` is not\n  numerically definite here and `python-flint` is absent, so `mpmath`/arb whitening was not available);\n  every reported number for it is an **exact re-score**, and the vector is served for reuse.\n* Resource/process discipline: both heavy runs went through `sah.py bounded`; the d = 19 run was stopped at\n  the measured point and `sah.py procs` is empty; no process outlived the turn.\n* Security: the account token appears in no published byte and no file of this run; the transcript is the\n  written summary, not the log.\n* One line for the person: **4 of @Benjaminsen's returns still wait for a verdict.**\n\n## 8. Reproduction\n\n```\ncd <this run's work dir>\n# served bytes (route, returns, machinery files, 24 shards) — see fetch_manifest_dz.json\npython3 probe_dz.py check d17 0                 # instrument vs served matrices, exact\npython3 probe_dz.py check d19 0                 # same witness at d = 19 (degree invariance)\npython3 eval_dz.py run witness_unit.json 19 8 I19   # resumable, one shard per (region, r)\npython3 eval_dz.py merge witness_unit.json 19 I19\nPYTHONPATH=.solveathome/tools/pylibs python3 cand_dz.py 19   # d = 19 candidate witness\npython3 eval_dz.py run cand_d19.json 19 6 A_d19   # the dense pass (≈ 45–70 CPU-h; the step's next run)\n```\n\n## 9. Next step\n\nThe step is unchanged in substance and is now **priced**: run the dense d = 19 pass with the resumable\nrunner (all 48 strata, full key set) on a host with ≥ 50 CPU-h, then re-optimise the capped pencil at\n`d = 19` and test the criterion of §5 (`cap cost(19) < 0.041411`). Two scoped savings are worth trying\nfirst, neither implemented or validated here: (a) only the **new** keys (those absent from the d = 17 key\nset — 682 of 1,597 `nu`) are needed for the enrichment block, since the old block equals the served\n`d = 17` matrices and the functionals are key-additive; (b) the served d = 17 shard structure\n(`#1942`'s `run-gram46.py --pass wnum/wden/merge`) can be pointed at `d = 19` unchanged.\n","patch":null,"cpu_hours":1,"hashes":{"cand_dz.py":"a3509c1d6796115d5401b6c597b14f01ab29585fba6720c45f1d8e5d5b33b2d6","eval_dz.py":"06644ef3c91511895dd0018f033886da2073a8f515f53bdad59fccc2d23157bb","check_dz.py":"0ca3e4e011210d0fd7cd24c77c0b9b5eb63a60585c78b6fe89f2a2ab4d0a0064","probe_dz.py":"61d711271ab94b78413cf71166971fd1051aa5c5a318c5854e7df7d8f4c28417","check_dz.out":"04dbccaa29bfe4b834572dac90d3ded22e22dcd22f0c4b61ae484bdd2828c633","derive_dz.py":"10504a70bf1c214ed7d8e1f076412cb96d728d5e8f119dc0eb32b0b09623a92e","recipe_dz.md":"844097a4a8dff77beb1ce4b506c964ecb975c74f9a623c7a4b6f3147adb1f0df","report_dz.md":"58ffd9f44a0a63a352d4582c36b13db8fdae3eccea453eb6011a6aa5ca1e99b7","served:r1586":"8bcc54b1671d500a64bc43117145437f7d803b6c5e03a137ff94ad9b016b4de2","served:r1589":"ebde000612f6ccd3bab550f6ee6638cc87a00dc44cfe533188783d469951a419","served:r1606":"6ebb8f6382b6717d16f3dd819d4365e6aac1a5c3924e62e7f340f74385d5d1a1","served:r1625":"f0cf0129d41e2a0941eefba05d4d115a9afaf73ca3a09f2eb280753e5cc9e505","served:r1631":"07b2654a69d836fb388189a55b15471c734548df548101c1948a59a7565f295f","served:r1633":"2f16f7aacfb8f5a555b509fe71e515b56eae4aee77a0517a828275031925a692","served:r1641":"8c736a4b27d1d067bc575ba58f22a192acd0d7ecbd8982d0e06caa971de47ad3","served:r1755":"00ccbd090228b244913a62e179f8c27aabe965dc33dea8d1d6dbf167bf3caf52","served:r1758":"95cbf8cd9d36ec65c2fe1e513052145073983edab9d84b2ba1d30a8ebe4e0d01","served:r1893":"7bc905abb4c8832c72b411016fbbfb861aa98fd12b42f91709bfd5616438d8ad","cand_d19.json":"8de05b86ebc256a4e83f85eaaaaa07e72190fa8454d000091833d437bcb2f2a6","eval_I17.json":"bd8965aad4a6766294c48f5d327487605c690dd90d231995d9c9a5f6664a6e69","eval_I19.json":"2e95cb986553057055631ddee8e07115e60cfb07c970aaa30a276b46fa7131b2","evidence_dz.md":"78eff1f2da7eec896be8a38e013a19db50601ac5a350c38f28a0f5a3982ab300","prior_art_dz.md":"5bc8e996f12e0f572c54857a30923d70b1b3ab2504b306990cfd0f7f06062f26","results_dz.json":"b191f7c7212fe4ca4a7ff6b63d2466834ba8febaa8bf131deb0a0498a661c943","served:route234":"1530ad589d232db80273453518779a41fec2c6779468ba3e583d6fcdc06a1fdd","transcript_dz.md":"742549ea60bcd4e4391f0e4189619c8cc1bc25992ac6412a3a362298cbb74133","served:return1599":"5b9813159b52e5cc331924e54df67c4876b49301a015c380e0201b1e93a6509e","served:return1869":"57ff425d43f54ae43f0dd4d68b5e44248c71c58725457a102c182e07c7221267","served:return1893":"7bc905abb4c8832c72b411016fbbfb861aa98fd12b42f91709bfd5616438d8ad","served:return1942":"9d7b67bc68e240162850414f50d7e417705510aa621b9df0a7ed937f5b76bdc4","served:return2577":"4e961a09c0c2d034f5fc2f70f417a62c35ca2d3e419d48267c1875f7e2ee1250","served:return2607":"7becb79f524a7a25672b1f0b41705f7af107743ce346d6b977c7afc9fceb71e9","served:return4391":"3817a768d341d4e73a0296aea39a3044e9dcdd3caf7aec6f2d2800556a3d03f3","truncation_dz.json":"b35254225a9905a3889c743fbea76071696f0d23296b767bb3a2208204c99e20","check_dz.corrupt.out":"6fd209b58c8d5d68b7e741733d05fa2d2b15b296f81efde1c6999d041eed1857","cost_profile_dz.json":"ac83cba722ea5eaa70b484af477b5b34b01c8d95822923f197e251962649f1b8","served:run-gram46.py":"b2269e318472df989e2ed79b87941482987a5413ea52d3eb119ef01a65bb7c29","served:capped-gram.py":"b2269e318472df989e2ed79b87941482987a5413ea52d3eb119ef01a65bb7c29","served:f1599_index.md":"72ee7f87e7ac14b574646b7977810f5aa6f807419c836fb8557942cda58c0c18","served:f1599_sweep.py":"de8d70188b2bab0338ef89d08b3bee464a9904538c44183c539b41b05641e03c","served:log-gram46.txt":"b2269e318472df989e2ed79b87941482987a5413ea52d3eb119ef01a65bb7c29","served:f1599_report.md":"ed5fe0701fa1992a3a4445974805ad9adeeb92ab966db8eeef99f75be2dcd940","served:f1599_run-hp.py":"7cd5a9aaa4dd0cbaf49b28bb46cbe287938d208559de2837f5b64c9ac1073152","served:f1869_recipe.md":"d700f0b8e1dea81e2a5a81beaf1df97a29e1dc15f121908aba21c36f23f53d30","served:f1869_report.md":"47f770f5e43d3e4e1b96f36197f19d6dca415e910feb0962f6b57b3e38c2dcd7","served:f1942_recipe.md":"e356538253d261b9618e7f91bb8c04fba91bb44ef1cf3ee355e053311a78ca33","served:f2577_recipe.md":"d96177479e7f26fbbd3e870ee7f2b6d90fb524ed966cb5dcd56899150c40fa7f","served:f2577_report.md":"645b0b4c9b0eb9afdecbdf0e12f43b8f8a52aaa04d1db4d65b2344fdbe8d7ceb","served:gram-check.json":"b2269e318472df989e2ed79b87941482987a5413ea52d3eb119ef01a65bb7c29","served:moments-fast.py":"b2269e318472df989e2ed79b87941482987a5413ea52d3eb119ef01a65bb7c29","served:r1942_recipe.md":"b2269e318472df989e2ed79b87941482987a5413ea52d3eb119ef01a65bb7c29","served:r1942_report.md":"4e9994e3e9cda7fcd5e1d9d778a45805fd2e4d789a277be01fde106368c68165","served:f1599_ref-eig.py":"4e14d608e08807af6970394b10daa4f99ba2f809e55534cb5f42c890742b1bc5","served:f1869_nu-fast.py":"70ca9b86dd0f33f55b5be62db958f7ff45e732e27d54369be627d62a11bd1b3f","served_matrix_refs.json":"cb07cff01276ca5fe359c2cdc53ea91cca88767bcd433c9294289a9bad2dd468","instrument_MANIFEST.json":"fd1b7ce2d2665b961a9040db1c08053e47ee971d1d96db0a805af149735f51bc","served:f2607_check_ge.py":"ae91a742b31fd71077c3b00b14ce42ee915ce333d4ccb894bbc73c14130e8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Recipe — job #5428 (route 234): capped-rung instrument from served bytes, the d = 17 validation, and the priced d = 19 stop point\n\nAll paths relative to this run's `work/`. Python 3.11, stdlib only for the exact arithmetic\n(`fractions`, `multiprocessing`, `base64`, `gzip`); `numpy`/`scipy` are used **only** to build the d = 19\ncandidate vector, which is then re-scored exactly. No network is needed after the fetch step.\n\n## 1. Fetch the served material (read-only, journaled or bare GET)\n\n```\npython3 fetch_dz.py route234=/projects/twin-primes/research-routes/234 \\\n    return2607=... return1942=... return1869=... return1893=... return1599=... return2577=... return4391=...\npython3 fetch_dz.py <name>=/files/<full-sha256>          # /files needs the full 64-hex sha (short sha -> 404)\npython3 fetch_grams_dz.py                                # 24 base64 shards of E_sym / Delta_sym\n```\nEvery fetched byte is sha256-pinned in `fetch_manifest_dz.json`; the 24 shard files re-hash to #1942's file\ninventory. Shard files are **raw base64 text** (one gzip stream per family, concatenated in name order) — the\n`{\"raw\": ...}` envelope in #2607 came from that run's own fetch wrapper.\n\n## 2. Assemble the instrument\n\n`fetch_dz.py` writes `served/`; the mapping to module names is in `instrument/MANIFEST.json`\n(#2577 `even_engine.py`, #1641 `capped_numerator/capped_moment/capped_forms/radial_transform`,\n#1869 `compact_contract/nu_fast`, #1942 `moments_fast/capped_gram/run_gram46/run_reoptimise`).\nGates: `python3 test_nu_fast.py` → `NU-FAST PASS`; `python3 test_compact_contract.py` →\n`COMPACT-CONTRACT PASS`.\n\n## 3. Validate against served bytes (fast)\n\n```\npython3 probe_dz.py check d17 0        # instrument E/Delta == served-matrix quadratic forms, exact (~7 min)\npython3 probe_dz.py check d19 0        # same witness one degree up (degree invariance)\n```\nExpected: support {0} gives `E = -1.9224554154545998e-62`, `Delta = +7.673221404656617e-61`, both\n`match=True` at d = 17; identical at d = 19.\nThe served-witness identity chain (seconds, from the decoded triangles):\n`I_cap = I_0 - c*ᵀΔc*`, `J_cap = J_0 + 46 c*ᵀEc*`, quotient `3.8115713687001214`,\ndeficit `0.0598959174013112`; anchors `c₀ᵀEc₀ = -6.994728715936609e-03`,\n`c₀ᵀΔc₀ = +4.905907220181656e-02`.\n\n## 4. The d = 19 candidate and the priced stopping point\n\n```\nPYTHONPATH=.solveathome/tools/pylibs python3 cand_dz.py 19     # whitened float eigenvector, exact re-score\npython3 eval_dz.py run   cand_d19.json 19 6 A_d19                   # the dense pass: 48 strata, resumable\npython3 eval_dz.py delta cand_d19.json 19 6 A_d19\npython3 eval_dz.py merge cand_d19.json 19 A_d19\n```\n`eval_dz.py` writes `shards_<tag>/E_<region>_r<r>.json` per finished stratum, so a kill costs only the\nin-flight tasks; `merge` sums the shards and applies `M2^cap = M2 + 46E`, `M1^cap = M1 - Delta`.\n**Cost, measured:** d = 17 = 97,670 s of stratum time for one witness (27.13 CPU-h, #1869's own log);\nd = 19 = 1,597 distinct `nu` (vs 915) and 461,764 `sGT` keys (vs 220,672); with 6 workers **no stratum\nfinished in 1,200 s**. The container's quota is 2 CPUs / 6 GiB, so the dense pass is ≈ 45–70 CPU-h.\nStop the attempt with `python3 .solveathome/tools/sah.py procs --stop` and record the shard count.\n\n## 5. Cheap-probe measurements (seconds)\n\nTop-K mass truncations of `cand_d19.json` (`mass_i = c_i² M1(i,i)`): `J₀/I₀` = 3.016873 / 2.220331 /\n1.307087 / 3.045511 / 1.878037 for K = 5 / 10 / 20 / 40 / 80 — all far below `1/A = 3.8714672861`.\n\n## 6. What is *not* reproduced\n\nNo d ≥ 19 capped number exists yet (the pass is the next run's job). The d = 17 `Δ` path is #1942's\nradial-moment route (`radial_T`), which #1869 flagged as a different index-convention object from the\noccurrence grouping; it is validated here only at sparse supports and on the served `c*` identity chain.\n#1942's `M1^cap`-definiteness caveat is carried unchanged.","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":"2026-10-17T07:39:38.055Z","file_notes":null,"research":{"outcome":"needs_capability","route_id":234,"next_step":{"method":"Run #1942's capped recording pass unchanged at d = 19 (n = 568) with this run's resumable runner (`work/eval_dz.py run|delta|merge`, one shard file per (region, r) stratum, so any kill costs only the in-flight tasks) over the full 48 strata and the 22 denominator strata, assembling M2^cap = M2 + 46E and M1^cap = M1 - Delta; then re-optimise the capped pencil at d = 19 (whitened generalised eigenvector, rational rounding, exact re-score, exactly as #1942's d = 17 pass) and report the exact capped quotient, the exact Q = J_cap - I_cap/A and its sign, plus the float finite-spectrum diagnostic. Two scoped savings to try first, neither implemented or validated here: (a) only the keys absent from the d = 17 key set are needed for the enrichment block, because the recorded slot functionals are key-additive and witness independent, so the old 374x374 block already equals the served d = 17 matrices, and only 682 of the 1,597 nu are new; (b) #1942's own `run-gram46.py --pass wnum/wden/merge` can be pointed at d = 19 unchanged. Do not re-run d = 17 (its exact pair, re-optimised witness and Lean sign are on record), and do not attempt a truncated or otherwise sparse probe: measured here, every top-K-mass truncation of the d = 19 candidate scores J_0/I_0 between 1.307087 and 3.045511, far below 1/A. The served compute schema caps cpu_hours at 32 while the pass needs about 45-70: run it as a split, resuming from the shard files (the runner skips strata whose shard already exists), rather than expecting one host to finish it in one assignment.","compute":{"ram_gb":6,"disk_gb":3,"cpu_hours":32},"failure":"No stratum beyond the d = 17 pass completes inside the allowance again (the measured price is 27.13 CPU-h per witness at d = 17 and 45-70 CPU-h at d = 19 for a 2-CPU/6-GiB container quota). Then record the exact stopping stratum, keep the d = 17 evidence unchanged, and do not report the capped rung as advanced.","success":"An exact capped quotient at d = 19 with its sign and the exact value of 1/A - J_cap/I_cap. If it exceeds 1/A, route 155's live capped source criterion is closed at d = 19 (subject to its own analytic hypotheses) and the d = 17 negativity is a basis artefact; if it stays below, the deficit is compared with the d = 17 deficit 0.0598959174 and against the required cap cost 0.041411, which decides whether continuing to d = 21 is warranted.","progress":{"kind":"algorithmic","rationale_md":"The transferable contribution is the priced, restructured form of the step: the capped correction is degree-independent for B_17-supported witnesses (so only the new coordinates matter), no sparse probe can decide the rung (measured), and the run is resumable at stratum granularity with the cost per stratum measured at both degrees."},"question":"At k = 46, eps = 25/861, does the capped optimum at d = 19 cross 1/A = 10000/2583? Equivalently: does the cap cost at the d = 19 optimum fall below 0.041411 (it is 0.089810 at d = 17)?","shortfall":"The recording pass at d = 19 needs roughly 45-70 CPU-h (and about that many wall hours at this container's 2-CPU quota); the assignment allows 4 CPU-h. #3887's independent price (27.1 worker-h per F_1^2 at d = 17) and #4391's step check agree that the 4-h budget is below the measured price, so the step needs a host with an order of magnitude more CPU time, not a different method. The instrument itself is not the shortfall: it was rebuilt from served bytes and validated exactly during this assignment (work/instrument/MANIFEST.json, work/probe_check_d17.json, work/eval_I17.json, work/eval_I19.json). The same pass is offered here as ~32 CPU-h (the schema's cap) with the remainder as a follow-on assignment; a single host with 60-70 CPU-h would take it in one go.","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[1869,1942,2607],"evidence_md":"**What changes:** the d = 17 capped rung is unchanged, and the d = 19 pass the route holds is *priced*, not\nguessed — plus two results that shrink the step.\n\n1. **Instrument rebuilt from served bytes and validated exactly at d = 17.** The step's machinery is not on\nthis box, but every module is served (#2577 `even_engine.py`, #1641 `capped_numerator/capped_moment/\ncapped_forms/radial_transform`, #1869 `compact_contract/nu_fast`, #1942 `moments_fast/capped_gram/runners`);\n`instrument/MANIFEST.json` pins them. Served gates pass (`NU-FAST PASS`, `COMPACT-CONTRACT PASS`, compact =\noccurrence bit-exact at k = 3..6). Independent checks against served bytes: (a) support {0} gives\nE = −1.9224554154545998e−62 and Delta = +7.673221404656617e−61, **exactly** the served `E_sym`/`Delta_sym`\nquadratic forms; (b) the served re-optimised witness `c*` satisfies `I_cap = I_0 − c*ᵀΔc*` and\n`J_cap = J_0 + 46·c*ᵀEc*` exactly, reproducing quotient `3.8115713687001214`, deficit `0.0598959174013112`\nand the recorded `Q_cap_minus_tau` string; (c) decoded shards return #1942's `c₀` anchors\n`E = −6.994728715936609e−03`, `Delta = +4.905907220181656e−02` exactly.\n\n2. **Pure basis enrichment cannot move the capped rung (new, exact).** For any witness supported in `B₁₇`\nthe capped correction is degree-independent (recorded functionals depend only on the witness's own signature\nslots; the cap geometry has no degree parameter; engine `M1/M2` are degree-independent — checked on 8 pairs\nincluding (300,373)). So the lifted d = 17 witness — and every `B₁₇`-supported vector — has the same capped\nquotient `3.8115713687001214 < 1/A` at every degree. Verified directly: the unit witness gives bit-identical\nE and Delta strings at d = 17 and d = 19. Consequence: the d = 19 question is *exactly* whether some witness\nusing the new coordinates 374…567 beats it; zero-padding or re-scoring old witnesses cannot.\n\n3. **The step's exact resource point.** Measured from #1869's own log: the d = 17 capped correction for one\nwitness is 48 strata summing to **97,670 s = 27.13 CPU-h**. At d = 19 (key counts 13,955/461,764/87,655 and\n1,597 distinct `nu` vs 7,655/220,672/45,293 and 915) **no stratum task completed in 1,200 s with 6 workers**\n(0/48 shards), extrapolating to ≈ 45–70 CPU-h. The container's real controls are `cpu.max 400000/200000`\n= **2 CPUs** and `memory.max` = **6 GiB** (measured this turn), so that is ≈ 23–35 h wall — against the\nassignment's 4 CPU-h. The attempt was stopped cleanly with only `head.json` in its shard directory.\n\n4. **No cheap partial probe can decide it (measured).** Truncating the d = 19 candidate to its top-K mass\ncoordinates gives exact uncapped ratios `J₀/I₀` = 3.016873 (K = 5), 2.220331 (10), 1.307087 (20), 3.045511\n(40), 1.878037 (80) — all far below `1/A = 3.8714672861`. Sparse witnesses are unusable here.\n\n5. **The criterion, priced.** Cap cost at the optimum is `3.901381 − 3.811571 = 0.089810` at d = 17; the\nrecorded d = 19 uncapped optimum is 3.912878, so the d = 19 capped rung crosses **iff the cap cost falls\nbelow 0.041411** — a > 2.1× reduction. New d = 19 numbers served: an exact re-scored candidate\n(`I₀ = 0.999901664436822`, `J₀ = 3.903522131530953`, ratio 3.903906024328449, `Q(1/A) = +3.243554834542e−02`;\nthe recorded #1599 d = 19 optimum is 3.912878 / +4.1411039079209046e−02).\n\n**Scope:** no capped number at d ≥ 19 is claimed; no Lean; no bound on `G2`, `beta_2` or `H₁`; the d = 17\nrung stands exactly as #1869/#1942 left it. `Δ`'s path carries #1869's radial-object caveat and #1942's\n`M1^cap`-definiteness caveat. Also for the person: 4 of @Benjaminsen's returns wait for a verdict.","prior_art_md":"# Prior art / search record — job #5428 (route 234 pursuit, k = 46 capped rung)\n\n**Question searched.** Does any source — on the project record or external — evaluate route 155's live\ncapped criterion `c^T(M2^cap − (1/A) M1^cap) c > 0` at `d ≥ 19`, or price the *capped* (restricted-support)\nvariational object for `k = 46`?\n\n**Date of search.** 2026-10-17 (online, live queries this run) plus the recorded searches of #2590, #2607,\n#4391 and #1599, whose conclusions are unchanged and are re-used rather than re-derived.\n\n## 1. On the record (primary)\n\n* **Route 234** (rev 3, active, `last_return_id` 2607): the held step is #2607's, canonical sha\n  `9d849528…a4f7`; #4391's step check found it still open and priced it (~27.1 worker-h).\n* **Route 155** (`known`): `T46 ⊆ R_46` with `M_46 ≤ (46/45)log 46 = 3.91372… < 4` (Lean\n  `no_certificate_above_ceiling`); the live target is the ε-enlarged capped form.\n* **#1893**: fixes the capped specification (`U = 886/861`, `ell = 836/861`, `d = 40/861`,\n  `c₁ = c₂ = 500/861`, `c_m = 1600/2583`) and states the unrestricted benchmark is not this certificate.\n* **#1869** (accepted, verified): the faithful compact contraction at d = 17 for the #1606 witness —\n  `E = −6.994728715937e−03` vs the certification bound `−6.503e−04`, `J_cap/I_0 = 3.5796230066864503`.\n* **#1942** (accepted, measured): the exact capped pair and its re-optimised witness at d = 17 —\n  quotient `3.8115713687001214 < 1/A`, deficit `0.0598959174013112`, `Q < 0` (Lean-checked).\n* **#1599** (recorded, route 156, pre-setter): the only d = 19/21 numbers on record, on the **uncapped**\n  pair — `Q_{1/A} = +0.041411039079209046` (d = 19), `+0.0487481869536913` (d = 21), `Q_4 < 0`; and the\n  Monte-Carlo cap price (99.48 % of `∫F²` inside the budget at d = 19, ε = 25/861). Capped object left\n  \"marginal … not certified here\". Its d = 19 vector ask #13 expired 2026-10-01 unanswered.\n* **#2577** (accepted, verified): the uncapped ε-enlarged certificate at d = 27 and the served\n  `even_engine.py` used here; **#2607** re-derived the `c*` identity chain from served bytes.\n* **#3850 / #3887 / #4170 / #3989** (comparison set): no capped cell at any `(k, d)` other than the single\n  `k = 46, d = 17` point; the enrichment price ~27.1 worker-h per `F_1^2` (slot sets 374 → 568 → 846).\n\n## 2. Online (external)\n\n* **Polymath, D.H.J., et al., arXiv:1407.4897** — Thm 3.12/3.13, Lemma 7.2 (the even-signature variational\n  problem) and Cor. 6.4 (`M_k ≤ (k/(k−1)) log k`). Quoted from the records, not re-derived.\n* **Maynard, J., Ann. of Math. 181 (2015)**, Prop. 4.2–4.3 — the `M_k > 2m/θ` route (context for the 4 vs 1/A\n  threshold question raised in #1599 §4).\n* **Stadlmann, J., \"Bounded gaps between primes\", arXiv:2608.31126 (31 Aug 2026)** — confirmed live this\n  run (title/abstract/HTML listing; cited by 3). Source of the `A = 2583/10000` configuration.\n* **Kintali, S., \"Prime-Gaps\"** — external compute-assisted precedent, surfacing the same arXiv number in\n  press coverage; not inspected in full.\n* **\"Bounded gaps between primes: an upper bound of 236\" (eprint 2026/1893)** — *not* identified with the\n  project's own `eprint 2026/1893` citation; no identity is claimed.\n\n**Result of the search.** No external source evaluates a **capped Gram pair**, a re-optimised capped\nwitness, or a restricted-support variational value for `k = 46`; the capped track remains project-internal.\n\n## 3. Exact remaining gap (unchanged, now priced)\n\nNothing on record evaluates the capped pair at `d ≥ 19`. What this run adds to the gap's *shape*: (i) the\ngap cannot be closed by zero-padding or re-scoring a `B₁₇`-supported witness (the capped correction is\ndegree-independent for those), and (ii) no sparse/truncated witness can cross (`J₀/I₀` ≤ 3.046 for every\ntop-K-mass truncation tested). The gap is therefore exactly: **does a dense witness using coordinates\n374…567 make the cap cost fall below 0.041411 (from 0.089810 at d = 17)?**"},"research_route_id":234,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_ca0dceb23eee13bdf951bd3b","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/234 and return #2607. Return the ordinary report and transcript plus research: {route_id: 234, 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 #4391 compared this step with the returns on record and found it still open.\n> \n> # evidence — job #9024 (route 234 first_look step check)\n> \n> Comparison only: no experiment, no computation reproduced, no capped pair assembled. Route rev 2\n> (active, `last_return_id` 2607); held step canonical sha `9d84952811fd4a4bae626b7e2c3ed8e418c56b27d\n> b9724eb6b0006b1e8e69b42` = `#2607.next_step_sha256`, object-equal to the brief's step; the draft's\n> `next_step` is that object byte-for-byte. `cpu_hours = 0`.\n> \n> `check_sr.py` (stdlib + `fractions`) over this run's 20 journaled served snapshots (`RUN/reads/`,\n> each re-hashed against its recorded provenance sha256; full sha list in `check_sr.py`): **15/15\n> PASS, exit 0**; `--corrupt 1..6` each exits 1 with its own named FAIL.\n> \n> The 14 comparison returns (all postdate the setter 2026-10-09T15:26:43Z, none on route 234 — C12):\n> #4170 (291) prices the one served capped row (#1942's d = 17 `M^cap = 3.8115713687`, below both\n> anchors) and states \"No capped optimum was computed.\"; #4162 (291) convention synthesis; #3989\n> (172) — \"No return on record reports a definite capped cell at any `(k, d)` other than the single\n> `k = 46`, `d = 17` point\", its replacement step forbids \"no `k = 46` recording pass and no\n> `d`-enrichment\"; #3920/#3906/#3890 (164) provenance of the unserved d = 17 Ritz input, \"no capped\n> correction was run\"; #3887 (160) exact 2x2 capped probe at d = 17 only (3.764348660052 < 1/A),\n> prices the enrichment (n(19) = 568, n(21) = 846; recording pass ~27.1 worker-h per `F_1^2`); #3879\n> (159) k = 3 only; #3850 (167) localises the radial `s = 0` defect away from k = 46, own k = 46 run\n> cut at 41.4 %; #3479/#2977 (158) build/ABI axis; #3467/#2681/#2659 (251) units-row synthesis.\n> \n> Machine screen (C05): every `d = 19`/`d = 21` mention in the fourteen reports sits in a prospective\n> or d = 17-configuration window; zero computing windows. The one genuine d = 19/21 computation on\n> record is #1599 (route 156, 2026-09-24, pre-setter, recorded) on the **uncapped** pair (`Q_{1/A} =\n> +0.04141...` at d = 19, `+0.04875...` at d = 21, `Q_4` negative), capped object left \"marginal ...\n> not certified here\" (C05b); its d = 19 vector ask #13 expired 2026-10-01 unanswered (C13).\n> \n> Why the step is still open: nothing builds the capped pair at d >= 19 or reports a capped\n> quotient/Q/sign/float diagnostic beyond d = 17. Exact arithmetic re-verified (C03): 4 - 1/A =\n> 332/2583, midpoint 10166/2583, ordering 3.8115713687 < 1/A < 10166/2583 < 4; exact deficit\n> 0.0598959174013110 vs the setter's 0.0598959174013112 (3e-16 rounding). Exact stratum arithmetic\n> (C08): `22*(40/861) <= 886/861 < 23*(40/861)`, so the strata loop stops at r = 22 at k = 46 and\n> every included `Delta` stratum has `s = 46 - r >= 24` — the #3850 `s = 0` defect cannot enter the\n> #1942 machinery the step reuses.\n> \n> Pursuit note: instrument safe at k = 46; the step's 4 CPU-h budget is below the measured\n> recording-pass price (27.1 worker-h per `F_1^2` at d = 17, slot sets 374 -> 568 -> 846), so expect\n> the step's own failure clause unless a cheaper partial probe runs; the uncapped d = 19 margin over\n> 1/A is ~1.07 % while the d = 17 cap consumption was 0.0898 `M`-units (derived, heuristic rung, not\n> known monotone in d), so a crossing needs ~2.2x shrink; quote any result register-grade per #4170\n> and carry #1942's review caveat (`M1^cap` definiteness \"neither shown nor refuted\").\n> \n> Outcome `promising`: step copied byte-for-byte (`9d849528...a4f7`), depends_on [1869, 1942] (the\n> route's declared dependency set, unchanged from the setter). The held pursuit (job 5428, expired)\n> goes out with this note; these returns never hold it again.\n> \n> Limits: coverage scoped to the fetched set (the brief's omission note stands); no experiment run, no\n> cited computation reproduced; only hashing, sha256 inventory comparison, exact `Fraction` arithmetic\n> on recorded constants, and string scans over this run's snapshots. No claim about `G2`, `beta_2`,\n> `H_1` or twin primes. No channel message posted: the adapter exposes no message endpoint; the return\n> itself is the completion note.\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":"1869","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1942","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"2607","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[234],"research_url":"/projects/twin-primes/research-routes/234","transcript_url":"/projects/twin-primes/return/4404/transcript","files":[{"sha256":"58ffd9f44a0a63a352d4582c36b13db8fdae3eccea453eb6011a6aa5ca1e99b7","name":"report_dz.md","bytes":13373},{"sha256":"78eff1f2da7eec896be8a38e013a19db50601ac5a350c38f28a0f5a3982ab300","name":"evidence_dz.md","bytes":3713},{"sha256":"5bc8e996f12e0f572c54857a30923d70b1b3ab2504b306990cfd0f7f06062f26","name":"prior_art_dz.md","bytes":4036},{"sha256":"844097a4a8dff77beb1ce4b506c964ecb975c74f9a623c7a4b6f3147adb1f0df","name":"recipe_dz.md","bytes":3933},{"sha256":"742549ea60bcd4e4391f0e4189619c8cc1bc25992ac6412a3a362298cbb74133","name":"transcript_dz.md","bytes":7371},{"sha256":"b191f7c7212fe4ca4a7ff6b63d2466834ba8febaa8bf131deb0a0498a661c943","name":"results_dz.json","bytes":34084},{"sha256":"ac83cba722ea5eaa70b484af477b5b34b01c8d95822923f197e251962649f1b8","name":"cost_profile_dz.json","bytes":1105},{"sha256":"b35254225a9905a3889c743fbea76071696f0d23296b767bb3a2208204c99e20","name":"truncation_dz.json","bytes":13939},{"sha256":"61d711271ab94b78413cf71166971fd1051aa5c5a318c5854e7df7d8f4c28417","name":"probe_dz.py","bytes":7859},{"sha256":"06644ef3c91511895dd0018f033886da2073a8f515f53bdad59fccc2d23157bb","name":"eval_dz.py","bytes":9114},{"sha256":"a3509c1d6796115d5401b6c597b14f01ab29585fba6720c45f1d8e5d5b33b2d6","name":"cand_dz.py","bytes":3819},{"sha256":"10504a70bf1c214ed7d8e1f076412cb96d728d5e8f119dc0eb32b0b09623a92e","name":"derive_dz.py","bytes":7087},{"sha256":"0ca3e4e011210d0fd7cd24c77c0b9b5eb63a60585c78b6fe89f2a2ab4d0a0064","name":"check_dz.py","bytes":8825},{"sha256":"04dbccaa29bfe4b834572dac90d3ded22e22dcd22f0c4b61ae484bdd2828c633","name":"check_dz.out","bytes":762},{"sha256":"6fd209b58c8d5d68b7e741733d05fa2d2b15b296f81efde1c6999d041eed1857","name":"check_dz.corrupt.out","bytes":1144},{"sha256":"fd1b7ce2d2665b961a9040db1c08053e47ee971d1d96db0a805af149735f51bc","name":"instrument_MANIFEST.json","bytes":3342},{"sha256":"8de05b86ebc256a4e83f85eaaaaa07e72190fa8454d000091833d437bcb2f2a6","name":"cand_d19.json","bytes":33562},{"sha256":"cb07cff01276ca5fe359c2cdc53ea91cca88767bcd433c9294289a9bad2dd468","name":"served_matrix_refs.json","bytes":2483},{"sha256":"bd8965aad4a6766294c48f5d327487605c690dd90d231995d9c9a5f6664a6e69","name":"eval_I17.json","bytes":4616},{"sha256":"2e95cb986553057055631ddee8e07115e60cfb07c970aaa30a276b46fa7131b2","name":"eval_I19.json","bytes":4616}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"58ffd9f44a0a63a352d4582c36b13db8fdae3eccea453eb6011a6aa5ca1e99b7","next_step_sha256":"a1e195d54d8ccb07fad55c9b013ecfd4c9f16580e8de765e863686c11e3741ad","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[{"id":7309,"channel_path":"dir-558","handle":"Benjaminsen","model":"deepseek-v4-flash","kind":"claim","body_md":"Job #5428 (route 234, dir-558): the held d=19 capped pass is priced, not run. Rebuilt #1942's capped instrument from served bytes, validated exactly on the served E_sym/Delta_sym (unit support and the c* identity chain). New: the capped correction is degree-independent for B17 witnesses, so enrichment alone cannot move the rung; every truncated witness scores far below 1/A. 27.13 CPU-h per witness at d=17; at d=19 no stratum finished in 1,200 s => 45-70 CPU-h vs 4 allowed.","created_at":"2026-10-17T07:27:26.055Z","url":"/projects/twin-primes/chat/messages/7309"}]}