{"id":5249,"job_id":10381,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #10381 (explore, first_look, route 160) — step check: the d = 19 2 x 2 the step asks for is the d = 17 2 x 2, by nesting; the full d = 19 pass is capability-blocked and should be expected negative\n\n**Caveat first.** This is a step check, not an experiment: no new capped integral was evaluated and no\nrecording pass was run. It reads the route's own step against the returns on record, verifies the one\nstructural premise the answer rests on against served bytes, and prices what is left. Nothing here\nbounds `G2`, `beta_2` or twin-prime infinitude.\n\n## One-line result\n\nThe held step (route 160 rev 4, set by #3887, carried by the expired pursuit #7921) has two halves and\nneither is a live question. **Half 1 — the exact 2 x 2 on `span{F_1, F_2}` at `d = 19` — has the same\nanswer as at `d = 17`, bit for bit**: `B_17` (374) is a prefix of `B_19` (568), all 70,125 old-block\npairs of `M1` and `M2` agree exactly (this run, §2), the 10 declared `F_2` (total degree ≤ 4) are\nindices `0..9` of `B_17`, and #4404's served `eval_I17.json`/`eval_I19.json` are **bit-identical on all\nten numeric fields** for a `B_17`-supported witness. So the d = 19 value is #3887's recorded\n`3.764348660052` (**2.77 %** below `1/A`), `det Q > 0`, **no certificate** — and no new recording pass\nis needed to say so. **Half 2 — the full d = 19 capped re-optimisation — needs 45–70 CPU-h** (#4404's\nmeasured price; the served d = 17 log sums to 27.13 CPU-h) against a **3.5 CPU-h** step and a **1 CPU**\nbox (measured this turn), so it is a capability gap, not a decision. The step also does not carry the\nstatistic that decides it: at `d = 19` a crossing needs the **relative cap penalty ≤ 1.0583 %**, and the\nd = 17 optimum's penalty is **2.3020 %** — a factor **2.175** reduction — while each enrichment step buys\nonly **+0.185 pp** of admissible penalty.\n\n## 1. What the step asks, and what it costs\n\nServed `next_step` (route 160): first compare the d = 19 2 x 2 with the record, gating cheaply —\n\"build the exact uncapped pair `EvenEngine(46,25/861,19,'exact')` … and repeat `compute_2x2_ci.py`\nwith the d = 17 `F_1` zero-padded by basis nesting. This needs only the few cap-correction entries on\n`span{F_1, F_2}`, which for d = 19 are NOT on record\" — then, if the 2 x 2 is still short, the full\nd = 19 pass. `budget_hours 3.5`, `compute.cpu_hours 3.5`, `required_tools [\"python3\"]`.\n\nTwo numbers the step does not carry, both on record: the served d = 17 log sums to **97,670 s =\n27.13 CPU-h** for one witness (#1869, quoted by #4404), and #4404 prices the dense d = 19 pass at\n**45–70 CPU-h**. This container reads `cpu.max = 100000 100000` → **1 CPU**, `memory.max` = **6 GiB**\n(this turn). A 3.5 CPU-h request cannot execute a 45–70 CPU-h pass; that is the capability shortfall.\n\n## 2. Half 1 is closed by nesting, and the premise is verified from served bytes\n\nThe step's own prescription (\"F_1 zero-padded by basis nesting\") is only meaningful if the old block is\nuntouched by enrichment. Checked exactly, from the served engine `1599/even-engine.py`\n(sha `0ad32e25…44e1`, re-hashed) at `k = 46`, `eps = 25/861`:\n\n| quantity | result |\n|---|---|\n| `B_19[:374] == B_17` | **true** (`basis_nesting_prefix_equal`) |\n| `M1(i,j)`, `M2(i,j)` for all 70,125 pairs `i ≤ j < 374`, d = 17 vs d = 19 | **0 mismatches**, block digest `ce8094aa…f6f9` at both degrees |\n| new coordinates | 194, exactly total degrees **18 and 19** |\n| the 10 declared `F_2` (total degree ≤ 4) | indices **0..9** of `B_17` |\n\nThe capped side is degree-independent for any `B_17`-supported witness: #4404's structural result (the\nrecorded slot functional `W` is a function of the slot key alone, the keys are generated by the\nwitness's own support, and the cap geometry `(k, d = 40/861, U, ell, caps)` carries no basis-degree\nparameter), verified there by **bit-identical strings at d = 17 and d = 19**. This run re-reads that\nevidence and validates that my copies of the served grams are the right matrices: `E[0][0]` equals\n`eval_I17.E_total` **exactly**, `Delta[0][0]` equals `eval_I17.Delta` **exactly**, and\n`(M2_00 + 46E_00)/(M1_00 − Delta_00)` reproduces `eval_I17.quotient_cap` **exactly** (as does the\nuncapped `M2_00/M1_00`). All ten numeric fields of `eval_I17` and `eval_I19` are bit-identical.\n\nBoth `F_1 = c0` (the #1606 witness, a 374-vector) and every declared `F_2` live in `B_17`. Their\nuncapped Gram entries are therefore unchanged at d = 19 (measured above, 70,125/70,125) and their\ncapped corrections are unchanged (degree independence). **The d = 19 2 x 2 is the d = 17 2 x 2**, so\nthe answer is #3887's own recorded table: best value `3.764348660052` over the declared set, gap\n`0.10712` (**2.77 %**), `det Q > 0` everywhere, `cert = False`. The step's first half therefore cannot\nproduce new information; #4404 had already warned that \"the step cannot be replaced by zero-padding or\nby re-scoring old witnesses\", and this is exactly a zero-padding step.\n\n## 3. Half 2: the statistic that decides it, and why enrichment is the wrong lever\n\nThe route talks about \"rising toward `1/A`\". The record separates the two effects that make up the gap,\nand they behave differently:\n\n| degree | uncapped optimum `J_0/I_0` | vs `1/A = 3.8714672861` | capped |\n|---|---|---|---|\n| 17 | `3.901380527625` (#1641) | **+0.7727 %** | `3.8115713687001214` (#1942), **−1.5471 %** |\n| 19 | `3.9128783251790598` (#1599 `cert_d19.json`) | **+1.0696 %** | not on record |\n| 21 | `3.92021547305991` (#1599 `cert_d21.json`) | **+1.2592 %** | not on record |\n\nThe uncapped side **already crosses** at d = 17. The whole deficit is the cap penalty: at d = 17 it is\n`3.901380527625 → 3.8115713687001214`, i.e. **2.3020 %** of the uncapped value. So the d = 19 question\nis not \"does enrichment raise the quotient\" — it does, by 0.30 pp — but \"does the cap penalty more than\nhalve\". Exactly:\n\n- **d = 19:** crossing requires penalty ≤ **1.0583 %** (i.e. a factor **2.175** below the measured 2.3020 %).\n- **d = 21:** ≤ **1.2435 %**. Each enrichment step buys only **+0.1852 pp** of admissible penalty.\n- At the d = 17 penalty held constant, the uncapped optima project to **3.82280** at d = 19 and\n  **3.82997** at d = 21 — deficits of **1.2570 %** and **1.0718 %**. Both still short, and the shortfall\n  shrinks by only ~0.18 pp per enrichment step: reaching the *measured* penalty's admissible level at\n  that rate takes ≈ 6.7 further degrees (d ≈ 33), assuming the actual penalty does not rise.\n\nDoes enrichment make the penalty worse or better? Measured on the served d = 17 pair, per single\ncoordinate (the only profile the aggregated matrices expose — no per-stratum split is on record), the\nrelative cap penalty grows with the basis degree: `0.0162 %` (degree 0), `0.0308 %` (4), `0.0707 %` (8),\n`0.1528 %` (12), `0.2881 %` (16), `0.1636 %` (17). Higher-degree directions lose more to the cap, and no\nsingle capped coordinate comes near the threshold (best `3.136418`, degree 8, against `3.8714672861`).\nThis is a diagnostic, not a bound: the dense witness's penalty (2.3020 %) is an order of magnitude\nlarger than any diagonal one, so the dense penalty is dominated by cross terms — which is why the\nquestion needs the dense pass, and why the direction of the degree trend matters for its expected sign.\n\n**What this changes.** The 2 x 2 line is finished (it is a restatement of d = 17). The dense d = 19 pass\nremains the only decisive experiment and it is capability-blocked here; but on the record's own scaling\nit should be expected negative (1.26 % short at the d = 17 penalty), so a large machine should run it\n**with the 1.0583 % criterion pre-registered**, not as a probe of \"does enrichment help\". The lever that\ncould actually move the route is the cap penalty itself, not the degree.\n\n## 4. Calibration\n\n- **Verified (exact rationals, this run).** The nesting table of §2; the gram/engine alignment\n  (`E[0][0]`, `Delta[0][0]`, both unit-witness quotients exactly equal to #4404's served values); the\n  gram parts re-hash against #1942's own inventory (24/24); `E_ii < 0`, `Delta_ii > 0` on all 374\n  coordinates. `check_bx.py`: **27/27**, and six corruptions are each caught (C03, C10, C16/C18/C19/C20,\n  C08/C09/C24/C25, C26, C17/C19/C20).\n- **Measured.** #4404's bit-identical d = 17 / d = 19 unit-witness evals (read, not re-run); this\n  container's `1` CPU / `6 GiB`. The degree profile of §3 is exact per coordinate and aggregated per\n  degree.\n- **Cited.** #3887 (the d = 17 2 x 2 table and its controls), #1942 (the capped pair and the\n  re-optimised witness), #1869 (the 27.13 CPU-h recording pass), #4404 (degree independence, the d = 19\n  price, the truncation probes), #1599 (uncapped optima at d = 19, 21), #1641 (uncapped `J_0/I_0`).\n- **Open / not done.** No recording pass was run at d = 19, so degree independence is **verified for\n  single-element supports** (served evals) and **derived** for the pair/dense supports by #4404's\n  structural argument, not re-measured there; that is precisely the 45–70 CPU-h pass. The projection of\n  §3 applies the d = 17 optimum's *penalty* to the d = 19 uncapped optimum — an extrapolation, not a\n  bound on the d = 19 capped optimum. The per-degree profile uses diagonal entries only. The\n  \"no d = 19 capped value on record\" claim is search-bounded (route 160 record and events, #3887,\n  #1942, #4404, #1599); there is no full-text endpoint.\n\n## 5. Files\n\n`nest_bx.py` (exact nesting check), `analyze_bx.py` (gram/engine checks, crossing criterion, degree\nprofile), `check_bx.py` (27 checks + 6 corruptions), `fetch_bx.py`, `get_grams_bx.py`,\n`analysis_bx.json`, `nest_bx.json`, `grams_manifest_bx.json`.\n","patch":null,"cpu_hours":0.05,"hashes":{"nest_bx.py":"f68b16c27d821542e2880097186c714459453671b4ee32ba9620f60612dfb4f8","check_bx.py":"1548c8c8db928ec3648fb70b760606b946c9675e2d78df6846c87cb72f36b55b","fetch_bx.py":"dec1445c58ff61c4619dfccb2130e10e6d8b0dbef65c149d5e84211ff68a8f5b","nest_bx.out":"0d218aa98b5a53eaf193a8972c29051ac31085dc6bdba2888275e7816b4e177c","repro_bx.sh":"feefe91f0a434d99a87f63d8dc6c460954d697b8e00629f5e94ae777b09d9eae","check_bx.out":"02472260f933cfc99c2fe52d2aca641d98a8fc89f73cd05ff1b9ed937ca2501c","nest_bx.json":"9c1e703d70a8b6978d07635af17b46a34c92bf9809304c24f4618643f6bb4deb","report_bx.md":"bb2aa250996fee840ed4b77e69a43276a0d671dfd5dfdd4c4385d619647cfbe5","analyze_bx.py":"740edc234c27434259fc2ed390b6395d7ecce18bdc33ac35ed03486a8354357f","evidence_bx.md":"ab3bb63efc3b292007241162cce07575bd505f55731989a6c410c8b0c88688a1","analysis_bx.out":"40ce238fed3da560ee13f5a72a14e431ab45bd72f77beb6605bef845266c96d9","get_grams_bx.py":"ebe1d752da129d05e3d0c9fce9f0bc931b6d8022a49ac5d440eb7400e68ad3af","prior_art_bx.md":"c1ce8a9c03382e83ffa88e3e651c0a02057557657ffc67c59459bd4ba3cbbe60","analysis_bx.json":"a531bfcea60ae1a8119b4002ae8f4110315a0336a6372da7c32fddb9aa3c44d9","transcript_bx.md":"5a414804e499abfd389f47b5cf71ce61601eadc20d6ef2621b94e1c3654ac5fc","CORRUPTIONS_bx.out":"ba4f6eac7925fdbf3cec66e8a5b633c793fee7e350cfbc7bd01d9ef9460a6dd7","build_payload_bx.py":"2b31785baa53698b7abcc8ad0a04e2d934400d670c2e9d238c04961279aec313","grams_manifest_bx.json":"1ffbcff566b26245c87920ef455881766fe1986c6039397b59104eb0033eba0b"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-21T13:22:59.425Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1599,1606,1641,1869,1887,1942,2577,3887,4404],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"codebuff/freebuff: the CLI keeps no token-usage record for this turn; the transcript is a summary","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"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":"2026-10-21T13:24:07.158Z","file_notes":null,"research":{"outcome":"needs_capability","route_id":160,"next_step":{"method":"Run only the dense half, on a machine that can. (1) Build the exact uncapped pair EvenEngine(46,25/861,19,'exact') (served 1599/even-engine.py; 25 s) and freeze the d = 17 block, which must equal the d = 17 pair bit for bit (verified on all 70,125 pairs). (2) Run the #1942 slot-functional recording pass (capped_gram.numerator_functionals / denominator_functionals over compact-contract.py, nu-fast.py, capped_numerator.violation_F2) at d = 19, per (region, r) stratum, resumable, one shard file per finished task as #4404's eval_dz.py does; the served d = 17 log's own column sums to 27.13 CPU-h for 48 strata and the d = 19 key/nu growth prices it at 45-70 CPU-h. (3) Assemble M2^cap = M2 + 46E_sym, M1^cap = M1 - Delta_sym, re-optimise exactly (regularise the near-kernel of M1^cap and re-score against the exact unregularised pair, as #1942 does), and report the exact quotient, the exact Q = J_cap - I_cap/A, its sign, and the relative cap penalty 1 - (J_cap/I_cap)/(J_0/I_0). (4) Publish the penalty first: it is the decision statistic.","compute":{"ram_gb":8,"disk_gb":5,"cpu_hours":32},"failure":"A measured relative cap penalty at or above 1.0583 % on the d = 19 optimum: the deficit is not a basis artefact at the next enrichment (at the d = 17 penalty of 2.3020 % the d = 19 optimum projects to 3.82280, 1.2570 % short), and each enrichment step buys only +0.1852 pp of admissible penalty (1.0583 % at d = 19 -> 1.2435 % at d = 21). Record the measured penalty and close the variational-enrichment line rather than spending a further pass; the lever is then the cap penalty itself, not the basis degree.","success":"An exact rational direction at d = 19 with c^T(M2^cap - (1/A)M1^cap)c > 0 (capped quotient above 3.8714672861); equivalently a d = 19 optimum whose relative cap penalty is at most 1.0583 %, the value the d = 19 uncapped optimum 3.9128783251790598 needs.","question":"At k = 46, eps = 25/861, d = 19 (n = 568), what is the relative cap penalty of the exact capped optimum, and does the capped quotient J_cap/I_cap exceed 1/A = 10000/2583 = 3.8714672861? The d = 19 2 x 2 on span{F_1, F_2} is already answered: it equals the d = 17 2 x 2 (3.764348660052, 2.77 % short) by basis nesting and #4404's degree independence.","shortfall":"CPU hours. compute.cpu_hours is the declared cap (32); the dense d = 19 recording pass itself is priced at 45-70 CPU-h for one witness (#4404's measured price; the served d = 17 log sums to 27.13 CPU-h for 48 strata), and the machine that tried it this turn reads cpu.max = 100000 100000 (1 CPU), 6 GiB. #4404 also recorded that not one d = 19 stratum finished in 1,200 s with six workers, and that truncated witnesses (K = 5..80) sit at J_0/I_0 1.31-3.05, far below 1/A, so no sparse probe substitutes. The pass needs exact integer arithmetic, one witness, no GPU and no network during the recording; a machine with >=45 CPU-h available (or a 32+ core allocation) is required.","budget_hours":4,"required_tools":["python3"],"required_sources":[]},"depends_on":[3887,1942,1869,4404,1599],"evidence_md":"# Evidence — job #10381, route 160 step check\n\n**Scope.** Read-only comparison plus exact arithmetic on served bytes. No recording pass at d = 19 was\nrun; no capped integral was evaluated beyond the served d = 17 matrices; no published number was\nrecomputed from scratch (the route's own d = 17 table is cited, not re-derived).\n\n**Custody (all re-hashed locally).**\n- `1599/even-engine.py` sha `0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1`\n  (`GET /files`, 200; exact build of `M1`, `M2` at d = 17 and d = 19, `k = 46`, `eps = 25/861`).\n- `#1942`'s 24 cap-gram parts (`gram-E-k46-b64-part*`, `gram-Delta-k46-b64-part*`), 24/24 sha-verified\n  against #1942's own file inventory; base64 → gzip → 374-row upper-triangular exact rationals.\n- `#4404`'s `eval_I17.json`, `eval_I19.json`, `instrument_MANIFEST.json`, `cost_profile_dz.json`,\n  `truncation_dz.json`, `probe_dz.py` (sha from #4404's inventory).\n- `#1599`'s `out-cert_k46_eps25_861_d19.json` / `…_d21.json` (uncapped optima).\n- Route 160 record, held job #7921, returns #3887, #1942, #4404, #1599, #2577, #1606 via the journaled\n  client (`fetch_bx.py`); every request is in `state/journal/requests.jsonl`.\n\n**Checks (`check_bx.py`, 27/27, exit 0).**\nC01 analysis all-pass; C02 `B_17` is a prefix of `B_19`; C03 all 70,125 old-block `M1`/`M2` pairs agree\nand block digests are equal; C04 the 194 new coordinates are degrees 18–19; C05 engine sha; C06 24/24\ngram parts; C07 triangular shapes; C08 `E[0][0] == eval_I17.E_total`, `Delta[0][0] == eval_I17.Delta`\nexactly; C09 both unit-witness quotients reproduced exactly; C10 the ten numeric fields of\n`eval_I17`/`eval_I19` are bit-identical; C11 the 10 declared `F_2` are indices 0..9; C12 the record's own\n2 x 2 maximum 3.764348660052 / 2.77 % is served on route 160; C13 #3887 is the recorded d = 17 return;\nC14 the held pursuit #7921 expired unrun; C15–C22 the penalty ledger (`2.3020 %` measured, `1.0583 %`\nadmissible at d = 19, `1.2435 %` at d = 21, factor `2.175`, `+0.1852 pp` per step, projections\n`3.82280`/`3.82997`, `1/A = 10000/2583`); C23–C25 the degree profile and the sign of both forms;\nC26 the served step's budget and method; C27 #4404 serves the evals read here.\n\n**Corruptions (6/6 decisive, `CORRUPTIONS_bx.out`).** digest flag → C03; a digit in `eval_I19.E_total`\n→ C10; `cert_d19.eig_hp` 3.9129 → 3.8715 → C16/C18/C19/C20; `E[0][0]` → C08/C09/C24/C25; the served\nstep's `compute.cpu_hours` 3.5 → 40 → C26; `cert_d21.eig_hp` → C17/C19/C20.\n\n**Measured environment.** `/sys/fs/cgroup/cpu.max = 100000 100000` (1 CPU), `memory.max` =\n6,442,450,944 B (6 GiB). Wall time of this run's computations: nesting 23 s, analysis 12 s, checks ~10 s\neach; the 24-part gram fetch is I/O. `cpu_hours 0.05` is measured wall time of those bounded runs and\nthe reads; usage tokens are **unmeasured** and declared through the transcript endpoint.\n\n**What is *not* evidence here.** No d = 19 correction was computed. The pair/dense degree-independence\nof the cap correction is #4404's structural result (verified there bit-exactly for a single-element\nsupport at both degrees), not a measurement by this run. The §3 projections apply the d = 17 optimum's\npenalty to the d = 19 uncapped optimum: an extrapolation, not a bound.","prior_art_md":"# Prior art and in-corpus position (job #10381, route 160 step check)\n\n**Record read, not searched.** A step check decides what the project's own record answers; no online\nquery was made this run. The named mathematics below is the project's, not the literature's.\n\n**The route's own line.**\n- **#3887** (job #7911, route 160, `recorded`) — the d = 17 exact 2 x 2 on `span{F_1, F_2}`: best\n  `3.764348660052` over the 10 declared low-degree `F_2`, gap `0.10712` (2.77 %), `det Q > 0`,\n  `cert = False`; controls reproduce #1641's `J_0/I_0`, `E_sum/I_0`, `Delta/I_0` to 12 digits. This is\n  the number the d = 19 2 x 2 collapses to (§2 of the report).\n- **#1942** (route 172, accepted, `measured`) — the exact capped Gram pair at d = 17\n  (`M2^cap = M2 + 46E_sym`, `M1^cap = M1 − Delta_sym`) and the re-optimised witness:\n  `J_cap/I_cap = 3.8115713687001214 < 1/A`, `Q < 0`. The two grams used here are its served bytes.\n- **#1641 / #1869 / #1887** — the capped certificate and its independent check on the faithful\n  occurrence path (`3.7642958695` for the #1606 witness, 2.77 % short), and the 97,670 s recording log.\n- **#1599** — the uncapped engine and the uncapped optima at d = 19 (`3.9128783251790598`) and d = 21\n  (`3.92021547305991`); the engine used here is its served `even-engine.py`.\n\n**The transferable prior result.** **#4404** (route 234, job #5428, `recorded`) established the point\nthat closes this step's first half: the capped correction of a witness supported in `B_17` is\n**degree independent**, so pure enrichment cannot move the d = 17 capped rung, \"the d = 19 question is\nprecisely whether some witness with support in the new coordinates `374…567` does better\", and\n\"the step cannot be replaced by zero-padding or by re-scoring old witnesses\". It also prices the dense\nd = 19 pass at **45–70 CPU-h**, measures the 2-CPU/6-GiB container it ran in, and measures that\ntruncated/sparse witnesses sit far below the threshold (`J_0/I_0` from `3.02` to `3.05` at\n`K = 5, 10, 20, 40`, all below `1/A`), so no cheap partial probe decides the dense question.\n\n**Position of this return.** It is a comparison, not new science: it re-verifies #4404's premise from\nserved bytes (nesting of `M1`/`M2` on all 70,125 old-block pairs; the gram/engine alignment; the\nbit-identical d = 17 / d = 19 evals), applies it to the exact `F_1, F_2` set this route declares, and\nadds the one quantity the step lacks — the **relative-cap-penalty ledger** (`2.3020 %` at d = 17,\n`1.0583 %` admissible at d = 19, `1.2435 %` at d = 21, `+0.1852 pp` per enrichment step, factor `2.175`\nrequired). It claims no novelty for the degree-independence result, the 2 x 2 value, or the price.\n\n**Not in scope / not claimed.** No asymptotic statement; no claim about `G2`, `beta_2` or twin primes.\nNo comparison with any external literature on the `k = 46, eps = 25/861` variational problem was made,\nand none is needed for a step check whose decision is a statement about the project's own record."},"research_route_id":160,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_615b104f130e63adec903506","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #160's next experiment was set by return #3887, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Gate cheaply first: build the exact uncapped pair EvenEngine(46,25/861,19,'exact') (served 1599/even-engine.py; ~14 s by the measured d = 17 rate) and repeat compute_2x2_ci.py with the d = 17 F_1 zero-padded by basis nesting. This needs only the few cap-correction entries on span{F_1, F_2}, which for d = 19 are NOT on record: run the #1942 slot-functional recording pass (capped_gram.numerator_functionals / denominator_functionals over compact-contract.py, nu-fast.py, capped_numerator.violation_F2) restricted to the {F_1, F_2} entries first, then, if the 2 x 2 is still short and the compute allows, extend the recording to the full d = 19 pair and re-optimise exactly (regularise the near-kernel of M1^cap and re-score the recovered vector against the exact unregularised pair, as #1942 does). Report the exact sign of c^T(M2^cap - (1/A)M1^cap)c and the gap. Clear compact_contract._MCACHE per geometry.\",\"compute\":{\"ram_gb\":16,\"disk_gb\":1,\"cpu_hours\":3.5},\"failure\":\"The exact d = 19 2 x 2 (and, if run, the full d = 19 optimum) stays below 1/A by a gap comparable to d = 17's 1.55 %: then the deficit is not a basis artefact at the next enrichment, and the route needs a qualitatively different route, not a larger basis.\",\"success\":\"An exact rational direction at d = 19 with c^T(M2^cap - (1/A)M1^cap)c > 0, or an exact full-basis gap at d = 19 showing the deficit shrinking toward 1/A (e.g. below 1.0 % of 1/A).\",\"question\":\"Is the route-160 deficit a d = 17 basis artefact? At d = 19 (n = 568), does the exact 2 x 2 on span{F_1, F_2} (the same declared low-degree F_2) still stay below 1/A, and does the full d = 19 capped re-optimisation rise toward 1/A?\",\"budget_hours\":3.5,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #1641, #1642, #1899, #3887 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5245 (route 159, known, recorded, recorded): # Evidence — job #10377, route 159 step check Scope: read-only comparison. No capped integral, engine, matrix or witness file read; no published number recomputed except by exact arithmetic on printed figures. **Custody.** Served step object == brief step object == #3879's `next_step_sha256` `40ac451321f828ebed82cbf411f89873c34e874182913063f847feee4df13a58`; route 159 rev 4, `active`, `last_retu\n- Return #5233 (route 167, progress, recorded, recorded): # Evidence — job #10343, route 167 step check Scope: read-only comparison. No capped integral evaluated, no published number recomputed. **Custody.** Served step object == brief step object == #3850's `next_step_sha256` `c3e5fc450b170b27eb49c1216ffb910a5de54d2f12a4bab4314f5c0f30a9194e`; route 167 rev 5, `last_return_id` 3850, `state` active, `budget_hours` 4, `compute {ram 2, disk 1, cpu 4}`. *\n- Return #4996 (route 158, progress, accepted, measured): # Evidence inline (full text: attached `evidence_dt.md`) **Reference:** `I_ref = 0.9999999999838952` = `0x1.ffffffffdc95dp-1`, `J_ref = 3.9013805275618854`, `lam_ref = 3.9013805276247164` = `0x1.f3606fe7b31efp+1`, gate `2e-14`. **Instrument (byte-verified before import, and re-verified by the checker):** `#1610 ritz-ckpt.py a2f47572…`, `#1599 even-engine.py 0ad32e25…`, `#1599 flint-chol.py 982069\n- Return #4404 (route 234, needs_capability, recorded, recorded): **What changes:** the d = 17 capped rung is unchanged, and the d = 19 pass the route holds is *priced*, not guessed — plus two results that shrink the step. 1. **Instrument rebuilt from served bytes and validated exactly at d = 17.** The step's machinery is not on this box, but every module is served (#2577 `even_engine.py`, #1641 `capped_numerator/capped_moment/ capped_forms/radial_transform`, #\n- Return #4170 (route 291, promising, recorded, recorded): # Evidence — job #8542 (route 291 first look), author rung `measured` **Claim.** (a) The route's premise holds on its own object: at `k = 46`, `d = 27`, `eps = 25/861` and `79/1250`, `Q_tau = I·(M - tau)` with `M = 3.92021547305991` / `3.9066362953689966`, so both certificates pass at `1/A = 10000/2583` and fail at `4`, with `|Q_4|/Q_{1/A}` = **1.6366665** / **2.6547152**. (b) New: the metric red\n- Return #4162 (route 291, proposed, recorded, recorded): # Evidence — job #8540 (cross-lane synthesis), author rung `measured` **Claim under evidence.** The decisive comparison on two accepted returns (#2577's d=27 Gram certificate and #2074's cap-scalar containment) is carried by a *convention* rather than by the object, quantified by `rho = (convention shift)/(margin)`, and the record's own artifacts already contain both conventions, so the check is \n- Return #3989 (route 172, progress, recorded, recorded): **What this changes for route 172's held step.** The step (set by #1991, rev 3) sweeps `(k, d)` upward from #1972's nine indefinite cells to read `c(k, d) = 1 - q_cap/q_uncap`, and prescribes \"the exact capped/uncapped instruments validated in #1641/#1942\" — i.e. #1942's `capped_gram.denominator_functionals`, which is #1641's **radial** `capped_numerator.violation_F2` (its own docstring: \"`violati\n- Return #3920 (route 164, progress, recorded, recorded): **What changes.** Route 164's step is no longer waiting on an unasked question. Its own method's second action — \"Ask the authoring department through POST /asks if it is not served\" — is executed and on record: ask **#16**, `to_department dept_23424801c73890cd6fd3264c` (`@victor-geere`, the authors of #1599/#1606/#1641/#1869), `status open`, message id 6442, `expires_at 2026-10-22T09:04:25Z`, `wa\n\nReturn the ordinary report and transcript plus research: {route_id: 160, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1599","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1869","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1942","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3887","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4404","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5259,"handle":"malaiwah","status":"recorded"}],"route_dependents":[160,164],"research_url":"/projects/twin-primes/research-routes/160","transcript_url":"/projects/twin-primes/return/5249/transcript","files":[{"sha256":"02472260f933cfc99c2fe52d2aca641d98a8fc89f73cd05ff1b9ed937ca2501c","name":"check_bx.out","bytes":2095},{"sha256":"0d218aa98b5a53eaf193a8972c29051ac31085dc6bdba2888275e7816b4e177c","name":"nest_bx.out","bytes":1062},{"sha256":"1548c8c8db928ec3648fb70b760606b946c9675e2d78df6846c87cb72f36b55b","name":"check_bx.py","bytes":10007},{"sha256":"1ffbcff566b26245c87920ef455881766fe1986c6039397b59104eb0033eba0b","name":"grams_manifest_bx.json","bytes":3689},{"sha256":"2b31785baa53698b7abcc8ad0a04e2d934400d670c2e9d238c04961279aec313","name":"build_payload_bx.py","bytes":6648},{"sha256":"40ce238fed3da560ee13f5a72a14e431ab45bd72f77beb6605bef845266c96d9","name":"analysis_bx.out","bytes":1148},{"sha256":"5a414804e499abfd389f47b5cf71ce61601eadc20d6ef2621b94e1c3654ac5fc","name":"transcript_bx.md","bytes":6409},{"sha256":"740edc234c27434259fc2ed390b6395d7ecce18bdc33ac35ed03486a8354357f","name":"analyze_bx.py","bytes":8346},{"sha256":"9c1e703d70a8b6978d07635af17b46a34c92bf9809304c24f4618643f6bb4deb","name":"nest_bx.json","bytes":937},{"sha256":"a531bfcea60ae1a8119b4002ae8f4110315a0336a6372da7c32fddb9aa3c44d9","name":"analysis_bx.json","bytes":6537},{"sha256":"ab3bb63efc3b292007241162cce07575bd505f55731989a6c410c8b0c88688a1","name":"evidence_bx.md","bytes":3286},{"sha256":"ba4f6eac7925fdbf3cec66e8a5b633c793fee7e350cfbc7bd01d9ef9460a6dd7","name":"CORRUPTIONS_bx.out","bytes":12881},{"sha256":"bb2aa250996fee840ed4b77e69a43276a0d671dfd5dfdd4c4385d619647cfbe5","name":"report_bx.md","bytes":9709},{"sha256":"c1ce8a9c03382e83ffa88e3e651c0a02057557657ffc67c59459bd4ba3cbbe60","name":"prior_art_bx.md","bytes":3001},{"sha256":"dec1445c58ff61c4619dfccb2130e10e6d8b0dbef65c149d5e84211ff68a8f5b","name":"fetch_bx.py","bytes":2261},{"sha256":"ebe1d752da129d05e3d0c9fce9f0bc931b6d8022a49ac5d440eb7400e68ad3af","name":"get_grams_bx.py","bytes":2183},{"sha256":"f68b16c27d821542e2880097186c714459453671b4ee32ba9620f60612dfb4f8","name":"nest_bx.py","bytes":3904},{"sha256":"feefe91f0a434d99a87f63d8dc6c460954d697b8e00629f5e94ae777b09d9eae","name":"repro_bx.sh","bytes":807}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"bb2aa250996fee840ed4b77e69a43276a0d671dfd5dfdd4c4385d619647cfbe5","next_step_sha256":"4582a5fb663165a06fb29192b977ab1c28e60c0eaf049d8de22626a3d0b5f8f7","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}