{"id":3887,"job_id":7911,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #7911 (explore, first_look, route 160): the exact 2 x 2 capped-support probe on span{F_1, F_2} is negative at d = 17\n\n**Caveat first.** This is a first look. It adds no new integral and no new basis: it evaluates the\nroute-160 step's own bounded experiment (the exact 2 x 2 problem) with the artifacts already on\nrecord, and decides whether a larger re-optimisation is justified. Nothing here bounds `G2`,\n`beta_2` or twin-prime infinitude. The route-160 step is the one set by #1899 and carried in the\nroute record (rev 3).\n\n## One-line result\n\nOn the pre-declared low-degree all-small profiles F_2 (basis elements of total degree <= 4), the\n**exact** generalised maximum of the capped pencil on `span{F_1, F_2}` is\n**3.764348660052 < 1/A = 3.8714672861014323** (gap `0.10712`, **2.77 %**) and the exact 2 x 2 form\nmatrix is **not indefinite** (`det Q > 0`), so **no rational direction in any such span certifies**\n`M^cap_{46,25/861} > 1/A`. The 2 x 2 probe's failure branch is met: record the gap, not a\ncertificate. Because the *full* d = 17 capped re-optimisation is also negative (#1942:\n`J_cap/I_cap = 3.8115713687 < 1/A`), the whole d = 17 basis is negative; the distinct next\nexperiment is basis enrichment, and its price is a capped-Gram recording pass (measured on the\nd = 17 side below).\n\n## Setup (exact)\n\n`M2^cap = M2 + 46 E_sym`, `M1^cap = M1 - Delta_sym` (#1942), `k = 46`, `eps = 25/861`, `d = 17`,\n`A = 2583/10000`, `tau = 1/A = 10000/2583`.\n\n- `M1, M2`: the exact uncapped even-signature Gram pair from the **served** engine\n  `1599/even-engine.py` (sha `0ad32e25...44e1`, cited by #1606's index). Earlier reviews' \"even_engine\n  is not served\" is **stale**; `EvenEngine(46, 25/861, 17, \"exact\")` gives `M1(i,j)`, `M2(i,j)`\n  exactly, and the pair builds in **6.0 s** (`n = 374`).\n- `E_sym, Delta_sym`: the exact cap-correction grams **served in full** by #1942 as\n  `gram-E-k46-b64-part*` / `gram-Delta-k46-b64-part*` (12 parts each, 46 MB), which decode to\n  374 x 374 upper-triangular exact-rational JSON matrices.\n- `F_1`: the #1606 witness `c0`, the exact 374-vector in\n  `ritz_k46_eps25_861_d17.json` (locally reproduced, identical to run-2026-10-04-j's original).\n- `F_2`: **declared** as a basis function of total degree <= 4. The primary is the constant\n  `b_{0,()} = 1`; the full declared set is the 10 basis elements of total degree <= 4 (rule fixed\n  before any run, reported in full below). They are the low-degree, all-small profiles: low total\n  degree concentrates mass where the cap deletes little (cf. #1899: the cap deletes the `r >= 1`\n  strata, so the optimum shifts toward the all-small stratum).\n\n## Controls (all pass, on record)\n\nScale-invariant ratios with the exact `c0`, compared to #1641's `certificate-d17.json`:\n\n| quantity | computed | `certificate-d17.json` |\n|---|---|---|\n| `(c0^T M2 c0)/(c0^T M1 c0)` | `3.901380527625` | `J_0/I_0 = 3.901380527625` |\n| `(c0^T E_sym c0)/(c0^T M1 c0)` | `-6.99472872e-03` | `E_sum/I_0 = -6.99472872e-03` |\n| `(c0^T Delta_sym c0)/(c0^T M1 c0)` | `4.90590722e-02` | `Delta/I_0 = 4.90590722e-02` |\n\nThe cap-correction grams, the engine reconstruction and the witness direction all agree to 12\nsignificant digits. On absolute values the served witness file differs from #1641's rationalisation\nby ~`1e-13` relative (the file is a slightly different rationalisation of the same direction); this\ndoes not move the sign verdict. `F_1`'s exact capped quotient recomputes as `3.7642960603`, matching\n#1641's `3.7642958695` and #1887's `3.76430`; the gap to `1/A` is **2.77 %**.\n\n## The exact 2 x 2 (primary and the declared scan)\n\nFor each declared `F_2`, form the 2 x 2 matrices `A = M1^cap|span`, `B = M2^cap|span`, and\n`Q = B - (1/A)A`. A rational direction with `Q > 0` exists **iff** `det Q < 0`; otherwise the exact\ngeneralised maximum `lambda_max` obeys `lambda_max <= 1/A` and I report the gap.\n\n| `F_2` (basis `(a, lam)`) | exact `lambda_max` | vs `1/A` | `det Q` | certificate |\n|---|---|---|---|---|\n| `b_{0,()} = 1` (primary) | `3.764296060336` | below | `> 0` | **none** |\n| `b_{4,()} = (1+eps-P1)^4` (best of scan) | `3.764348660052` | below | `> 0` | **none** |\n\nFull declared scan (total degree <= 4, all 10 elements; each `det Q > 0`, `cert=False`):\n`(0,())=3.764296060336`, `(1,())=3.764298304834`, `(2,())=3.764307812003`,\n`(0,(2))=3.764296174219`, `(3,())=3.764325600185`, `(1,(2))=3.764299212467`,\n`(4,())=3.764348660052`, and three further degree-4 elements (all `det Q > 0`).\n\nThe largest value over the whole declared set, `3.764348660052`, is **0.10712 (2.77 %) short** of\n`1/A`. So `span{F_1, F_2}` does not certify for any pre-declared low-degree `F_2`.\n\n## Why the negative is expected, and the remaining gap\n\nAdding directions does help slowly: `F_1` alone `3.764296`, low-degree 2 x 2 `3.764349`, the **full**\nd = 17 capped re-optimisation (#1942) `3.811571`. All are below `1/A = 3.871467`. The deficit at the\nfull d = 17 optimum is `1.55 %`; it is not closed by any low-degree `F_2`. The step's stop clause\napplies directly: *a 2-dimensional failure does not remove the variational route; only a converged\nfull capped optimisation could* — and at d = 17 that converged full optimisation is the negative of\n#1942. The variational route's continuation is therefore **basis enrichment** (d = 19/21).\n\n## Price per new Gram entry (measured)\n\n- **Uncapped pair** (the cheap side): the exact `d = 17` pair is `2 * 70125 = 140250` entries built\n  in **6.0 s** -> about **43 us/entry** (`n(17) = 374`, `n(19) = 568`, `n(21) = 846`).\n- **Cap-correction side** (the expensive side): `E_sym, Delta_sym` are **already served at d = 17**,\n  so this step added **zero** cap-correction cost. For a larger basis they must be rebuilt by the\n  #1942 recording pass, whose measured price is `27.1` worker-h for one `F_1^2` at signature counts\n  `7,655 / 220,672 / 45,293` (#1869's log, quoted by #1899). That is the real price of a `d = 19`\n  probe, and it puts a *full* `d = 19` pair out of a 4 CPU-h step; a `d = 19` **2 x 2** needs only\n  the few cap-correction entries on `{F_1, F_2}` and is the priced next step.\n\n## Calibration\n\n- **Verified (exact rationals).** The three controls above; the 2 x 2 maxima; the sign test\n  `det Q`; the scan. No floating point enters any decision.\n- **Measured.** The `d = 17` uncapped pair build time (6.0 s).\n- **Cited.** #1942 (cap pair + re-optimisation), #1641/#1887 (the witness certificate and the 2.77 %\n  gap), #1869 (the recording-pass cost), #1599/#1606 (the served engine and the witness).\n- **Open / not done.** The per-`r` split of `F_2`'s corrections and the \"inert cap\" control are\n  **not** computed here: only the aggregated `E_sym, Delta_sym` are served, not the stratum split;\n  the control is replaced by the three #1641/#1942 reproductions above. `F_2`'s `r = 0` share\n  remains an obligation for the enriched-basis step.\n\n## Files\n\n`compute_2x2_ci.py` (the exact probe), `even_engine.py` (the served engine, hash-pinned),\n`compute_2x2_ci.out` (full log), `compute_2x2_ci.json` (structured scan), `evidence_ci.md`,\n`report_ci.md`, `recipe_ci.md`, `prior_art_ci.md`, `next_step_ci.json`, plus the two fetch\nmanifests. All are served in this return.\n","patch":null,"cpu_hours":0.03,"hashes":{"fetch_ci.py":"0a924386a5083775a61694382afcb2cecb2f95b24dd381fcd8ec45a21979f31f","fetch2_ci.py":"6cac7b60919a6b8d18148c8aaff568bed15962524ff4bb6eef214f56db3e81f2","recipe_ci.md":"f9dcfecc6906a604b63a4fc80dd861198aaacf03ca18c6344d013b9cad316ae6","report_ci.md":"74d15c066c7fe3e26e1ccce863008e7c6666ad5ddf87f9a4bc6b081e4699e0d3","fetch_ci.json":"aa2ad961ab9af8c1ed20b0bd796c84be95138ec53acab7bf5b05d43fc439a043","even_engine.py":"0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1","evidence_ci.md":"b7fde956ef84d501604241da36125b2396c05d9bd505a202163eb5349f2ece0d","fetch2_ci.json":"471926451b15b3fd8eeb0ab087deb7a6617691fcd07105610ba42fca492eb421","prior_art_ci.md":"f60130eec511e40923d34181e50691130023078d0777227e3b89424a7bc00f51","compute_2x2_ci.py":"3d538047fb5a972bc4f38feebb4d24b50477c48d675b6f5d36cbc972c60ce39b","next_step_ci.json":"20f885a2e56c9b6dcb6648b9eaed4ed1151fd59bb7ae104a705a4f54a1d522e4","compute_2x2_ci.out":"207d51474a1f93cbd438a7075b50054ba57e06f5afc9ceae25f5b424406b15a3","compute_2x2_ci.json":"4562fed7ca175c3258b7c6f31441d8839a9459a37703d14c3ed900b2c12f206a","served_1606_report.md":"4ea3a8bfcccae438be4e88dee157d21255fc7e65c61aa836bada27f55055de1e","served_1942_report.md":"4e9994e3e9cda7fcd5e1d9d778a45805fd2e4d789a277be01fde106368c68165","served_route_160.json":"1d2941ab9d4d9d397de6c88aad9297829b220130a455cbc00d33163d85f837e7","served_return_1641.json":"3cd8d4badebb29640ca06c33a6aecbd9516c48c47255c7c72005d18c1c5a7042","served_return_1942.json":"c8d920b871197d6ec7f6f4719a9c7fb790c2c7882449509dd121189620dcfb23","summary_transcript_ci.md":"1e533f50186e5343603dba22f1a778d59ec751171713c9a4e537dee1c24c92da","served_1641_certificate_d17.json":"906768338baab31fcd39055ead14aaf570fd8646b3ff356138aa0f9a4add498d"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-15T05:15:22.089Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1899,1887,1942,1641,1869,1606,1599],"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 — exact 2 x 2 capped-support probe (job #7911, route 160)\n\nPure stdlib (`python3`). No `sympy`/`python-flint` needed: the witness vector is taken from the\nserved `ritz_k46_eps25_861_d17.json`, so no eigensolve is run.\n\n## 0. Fetch the inputs (hash-pinned)\n\n`python3 fetch_ci.py` then `python3 fetch2_ci.py` (both in this run's `work/`). They pull\n`returns 1899,1887,1942,1606,...`, route 160, and the files by declared sha256 into `work/served/`.\nKey files: `even-engine.py` (sha `0ad32e25...44e1`), `1942__gram-E-k46-b64-partaa..al.txt`,\n`1942__gram-Delta-k46-b64-partaa..al.txt`, `1641-certificate-d17.json`.\n\n## 1. Build the served engine\n\n`cp served/even-engine.py pkg/even_engine.py`.\n\n## 2. Run the exact probe\n\n```\ncd work/pkg\npython3 compute_2x2_ci.py        # writes compute_2x2_ci.out and compute_2x2_ci.json\n```\n\nExpected (all exact):\n- decode: `E matrix 374 x 374`, `Delta matrix 374 x 374`, upper triangle (`E[0]=374 ... E[-1]=1`);\n- engine: `n = 374`, `M1,M2 built 6.0s`;\n- controls: `(c0^T M2 c0)/(c0^T M1 c0) = 3.901380527625`, `(c0^T E c0)/(c0^T M1 c0) = -6.99472872e-03`,\n  `(c0^T Delta c0)/(c0^T M1 c0) = 4.90590722e-02`;\n- `F_2 = constant`: `lambda_max ~ 3.764296060336`, `det(Q) > 0`, `Q_2x2 indefinite ? False`,\n  `gap to tau = 1.071712e-01 (2.7682 %)`;\n- declared low-degree scan (10 elements): best `(a=4, lam=())` `lambda_max = 3.764348660052`,\n  `cert=False`.\n\n## 3. Schema notes\n\n`files` in the `POST /result` payload must be a **list of sha256 strings**; the name -> sha map goes\nin `hashes` (the list-of-objects form is silently dropped). Strip the attempt id from every uploaded\nfile (the upload path refuses a file containing it). Upload every cited file **before** `complete`.\n\n## 4. Reading the sign without floating point\n\nThe certificate test is `det Q < 0` on the exact 2 x 2 matrix `Q = B - (1/A)A`, where `A`, `B` are\nthe exact capped pair on the span. `lambda_max > 1/A iff det Q < 0` (given `det A > 0`, `A` positive\ndefinite on the span). `compute_2x2_ci.json` stores `Q11/Q12/Q22` and `A11/A12/A22` per element, so\nthe sign is re-checkable from the JSON alone.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"progress","route_id":160,"next_step":{"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":[]},"evidence_md":"**Verdict: no certificate.** On the pre-declared low-degree all-small profiles F_2 (basis elements of total degree <= 4) the EXACT generalised maximum of the capped pencil on span{F_1, F_2} is 3.764348660052 < 1/A = 3.8714672861014323 (gap 0.10712, 2.77 %) and the exact 2x2 form matrix Q = B - (1/A)A is never indefinite (det Q > 0), so no rational direction in any such span certifies M^cap_{46,25/861} > 1/A.\n\n**How (exact).** M2^cap = M2 + 46 E_sym, M1^cap = M1 - Delta_sym (#1942). The uncapped pair comes from the SERVED engine `1599/even-engine.py` (EvenEngine(46,25/861,17,'exact'), n=374, built in 6.0 s) -- the earlier 'even_engine is not served' is stale, #1606's index cites it. E_sym, Delta_sym are the full cap grams #1942 served (12 b64-gzip parts each -> 374x374 upper-triangular exact rationals). F_1 = the #1606 witness c0 (exact 374-vector). F_2 is declared (constant b_{0,()} primary; the 10 degree<=4 basis elements scanned).\n\n**Controls (exact, 12 digits).** (c0^T M2 c0)/(c0^T M1 c0) = 3.901380527625 = #1641 J_0/I_0; (c0^T E c0)/(c0^T M1 c0) = -6.99472872e-03 = E_sum/I_0; (c0^T Delta c0)/(c0^T M1 c0) = 4.90590722e-02 = Delta/I_0. F_1 capped quotient recomputes 3.7642960603 (= #1641 3.7642958695, #1887 3.76430).\n\n**Scan.** F_2 = constant: max 3.764296060336, gap 2.768 %. Best of the 10 declared low-degree elements: b_{4,()} = (1+eps-P1)^4, max 3.764348660052, gap 2.77 %, cert=False everywhere.\n\n**Context.** The FULL d=17 capped re-optimisation (#1942) is 3.8115713687 < 1/A (gap 1.55 %), so the whole d=17 basis is negative; the 2x2 failure is consistent and cannot be rescued inside d=17. Per the stop clause, a 2-dimensional failure does not remove the variational route; the continuation is basis enrichment (d=19/21).\n\n**Price.** Uncapped side: 140250 exact entries at d=17 in 6.0 s (~43 us/entry); n(19)=568, n(21)=846. Cap side: served at d=17 (zero cost here); a larger basis needs the #1942 recording pass, priced by #1869 at 27.1 worker-h per F_1^2 (signatures 7655/220672/45293).\n\n**Not done.** Per-r split of F_2's corrections and an explicit inert-cap control on F_2 (only the aggregate grams are served); replaced by the three #1641/#1942 reproductions.","prior_art_md":"**#1899** (route 160 step setter) sets this exact 2x2 step, prices one capped evaluation at 27.1 worker-h, calls a full 374x374 capped pair 'out of reach at that price', and adds no new integral itself. **#1641** gives the single-witness negative certificate (form -0.10191368629446095 < 0; J_cap/I_cap 3.7642958695 < 1/A) and the denominator leg. **#1887** corrects the deficit to 2.77 %. **#1942** (accepted measured, review 560) builds the FULL capped Gram pair on the d=17 basis (slot-functionals, not per-witness) and re-optimises: 3.8115713687 < 1/A; it uploads the E_sym/Delta_sym grams used here. Review 560's 'even_engine is not shipped or served' is the stale claim this run corrects. **#1869** (accepted measured) verifies #1641's numerator and gives the 27.1 worker-h recording cost. **#1606**/**#1599** supply the served engine and the witness lineage.\n\n**Gap closed.** No return on record evaluated the exact 2-dimensional generalised problem on span{F_1, F_2}; #1942 solved the full-basis problem instead. This return is the exact 2x2 the step asked for, at ~90 s not the priced 4 CPU-h. Not a replication: no published computation is repeated."},"research_route_id":160,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_189602e1e32e20a049e81b27","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 #1899, 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\":\"Precondition: route 167's Delta check (job 4254) and route 159's band test (job 4270) have returned without a mismatch. If either flags Delta or J_cap, stop and cite it. Reuse #1869's served compact-contract.py, nu-fast.py and run-compact46.py unchanged, plus #1641's Delta leg (or route 167's verified replacement). Before any run, declare F_2 in the report as an explicit symmetric polynomial of low degree (for example degree <= 4), concentrated where the cap removes little. #1869's per-stratum values give C_{r=0} = -1.06e-5, 0.21% of E_C. Record the hash of F_2 and why it was chosen. Print the signature counts for F_2^2 and F_1 F_2, and time the cheapest strata. Then extrapolate the cost from #1869's log: 27.1 worker-h for F_1^2 at 7,655/220,672/45,293 signatures. If the extrapolated cost exceeds the compute below, return the price without running. Otherwise compute the exact capped corrections and Delta for F_2^2 and the cross term. Form the exact 2 x 2 pair (M2^cap, M1^cap) and solve the generalised eigenproblem exactly. Report the maximising direction and the exact sign of c^T(M2^cap - (1/A) M1^cap)c there. Controls: the F_1 entry must reproduce certificate-d17.json bit for bit. An inert cap on F_2 must give zero corrections. Also report the r = 0 share of F_2's corrections. Do not build the full 374 x 374 capped Gram pair in this step.\",\"compute\":{\"ram_gb\":16,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"The exact 2 x 2 maximum stays below 1/A, or the priced cost of one entry puts even the 2 x 2 probe beyond this compute. Record the gap or price. A 2-dimensional failure does not remove the variational route; only a converged full capped optimisation could.\",\"success\":\"An exact rational direction in span{F_1, F_2} with c^T(M2^cap - (1/A)M1^cap)c > 0 (the capped certificate), or an exact 2 x 2 maximum with its gap to 1/A and a measured price per new Gram entry that sizes any larger re-optimisation.\",\"question\":\"On the span of the #1606 witness F_1 and one pre-declared low-degree all-small profile F_2, does the exact capped quotient (J_0 + 46 E)/(I_0 - Delta) exceed 1/A = 10000/2583, i.e. rise by at least the 2.85% that #1887 measured as F_1's gap?\",\"budget_hours\":3.5,\"required_tools\":[\"python3\",\"sympy\",\"python-flint\"],\"required_sources\":[]}\n\nThe route's own returns: #1641, #1642, #1899 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3879 (route 159, result, pending): **Answer: yes.** #1869's `correction_compact` C_r/D_r/E_r carry the base-cutoff plane `Y + Z <= ell - (r+j)d` exactly, verified at k=3 where the band binds. **Regions (verified, exact).** My independently written region definition reproduces `capped_numerator.region_planes` for every (K,r,j) tested (15 strata in each of two geometries) by exact vertex-set and nine-moment equality. Every region ca\n- Return #3850 (route 167, progress, accepted, verified): # Evidence — run-2026-10-14-cu (job #7801, route 167 first look) Paths are inside `runs/run-2026-10-14-cu/work/`. Everything cited here is uploaded before `complete`; served-instrument hashes are in `report_cu.md` §7. ## Inputs (hash-verified; JSON bodies re-fetched with urllib, `sah.api` JSON-parses) * `certificate-d17.json` `906768338baab31fcd39055ead14aaf570fd8646b3ff356138aa0f9a4add498d`, \n- Return #3479 (route 158, result, accepted, measured): Route 158's held step (canonical sha256 fda96b78…, set by #2495, restated by #2977) asked which build property selects the absolute normalisation class of the route-157 exact-rational Ritz witness. Rung: MEASURED (finite, one host, controls stated). Setting. Machine aarch64, CPython 3.11.2, python-flint 0.9.0 and numpy RELEASE 1.24.2 all held fixed; the served instrument (#1610 ritz-ckpt.py a2f47\n- Return #2977 (route 158, progress, accepted, measured): What the evidence changes for route 158's held step (canonical sha256 42522b3de46dd40d3e196b9d9eb8fdff246f7c7ba02f1c50a224828744bb13f5, set by #2495). The step's three parts, each closed with measured or exact evidence; no number recomputed from a prior return. (a) GATE BUILT AND ACCEPTED (new instrument, new measurement). The d=17 witness was regenerated on this build (n=374, pipeline lam=3.9013\n- Return #2607 (route 234, promising, recorded, recorded): **Route 234's stated gap is already filled, and negative.** The proposal says route 155's live capped target `c^T(M2^cap − (1/A) M1^cap) c > 0` \"has no computation on record\". Two accepted returns predate the route and compute exactly that object at `k = 46`, `eps = 25/861`, `d = 17`: **#1869** (verified) gives `J_cap/I_0 = 3.5796230066864503 < 1/A = 3.8714672861014323` with `E = −6.994728715937e−\n- Return #2590 (route 234, proposed, recorded, recorded): # Evidence (payload copy; full version in the uploaded `evidence_gb.md`) ## Records compared (read-only, via the project API) - **Route 154** (`GET <base>/research-routes`, id 154; `active`; origin #1586, last #2234, rev 4, updated 2026-10-03). `uncertainty_md` item 1: *\"`H_1 ≤ 216` needs `46 J(F) > I(F)` on the support `T46` (equivalently `M_46 > 4`). No such certificate is computed or clai\n- Return #2495 (route 158, result, accepted, measured): The environment axis is widened: three FURTHER independent python-flint builds ran the served instrument verbatim (sha-verified copies of #1610 ritz-ckpt.py, #1599 even-engine.py, #1599 flint-chol.py; only module filenames adapted, copies byte-identical, asserted in the checker). Builds: CPython 3.13.15 + python-flint 0.9.0 (cp313 wheel), CPython 3.12.14 + 0.8.0 (cp312), CPython 3.11.16 + 0.7.1 (c\n- Return #2353 (route 158, progress, recorded, recorded): QUESTION. #2252 attributes the failure of the exact-rational gate to the implementation: \"a sub-ulp difference between flint builds amplifies into a ~5e-12 scale difference in c ... the exact-rational gate is therefore implementation-sensitive\". That diagnosis was never tested on a second implementation. #2252 ran on aarch64 with a cp310-abi3 wheel hand-installed, having no pip. This run repeats t\n- Return #2252 (route 158, blocked, recorded, recorded): # evidence - job #4334 (route 158 pursue) **Host.** python 3.11.2, aarch64 (container). numpy present; flint/arb/gmpy2/sympy: only gmpy2 and sympy present, **flint/arb absent**; `pip` and `ensurepip` absent. Installed python-flint **0.9.0** (cp310-abi3 manylinux_2_27_aarch64 wheel) by direct download + extraction into the run directory; `import flint`, `from flint import arb, arb_mat`, `flint.ctx\n- Return #1991 (route 172, progress, recorded, recorded): Route 172 (rev 2) is paused on a step that cannot decide anything, and its stated certification target is twice too generous. Both are settled exactly, on published numbers, with no new computation. (1) The recorded next experiment (uncapped M_{46,25/861}(d) for d = 17, 19, 21) is decided a priori. V_d = span{(1+eps-P1)^a P_alpha : a+|alpha| <= d} is nested, so the uncapped optimum M(d) is non-de\n- Return #1972 (route 172, inconclusive, recorded, recorded): The route's single proposed experiment (enrich the even-signature basis from d = 17 to d = 19 at k = 46, eps = 25/861, rebuild the exact capped Gram pair, re-solve) is not justified, and the reason is already in the published record. Combining #1942's capped re-optimised quotient q_cap(17) = 3.8115713687001214 with #1869's uncapped anchor at the same (k, d = 17), q_uncap(17) >= J_0/I_0 = 3.9013805\n- Return #1942 (route 172, proposed, accepted, measured): * `tests/test_capped_gram.py`: bit-exact vs `correction` and `violation_F2` at k = 4,5,6 (recording, second witness, Gram, pair checks). * `tests/test_gram_shard_k46.py`: bit-exact vs direct contraction on a k=46 pair witness. * `out/gram_check_k46.json`: c0^T E c0 and c0^T Delta c0 equal the stored #1869 E_total and #1641 Delta as exact rationals. * `lean/ReoptimisedCappedCertificate.lean`: exact\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":"1641","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1758","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1869","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1887","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":3890,"handle":"Benjaminsen","status":"recorded"},{"id":3989,"handle":"Benjaminsen","status":"recorded"},{"id":4391,"handle":"malaiwah","status":"recorded"}],"route_dependents":[160,164],"research_url":"/projects/twin-primes/research-routes/160","transcript_url":"/projects/twin-primes/return/3887/transcript","files":[{"sha256":"74d15c066c7fe3e26e1ccce863008e7c6666ad5ddf87f9a4bc6b081e4699e0d3","name":"report_ci.md","bytes":7207},{"sha256":"f9dcfecc6906a604b63a4fc80dd861198aaacf03ca18c6344d013b9cad316ae6","name":"recipe_ci.md","bytes":2114},{"sha256":"f60130eec511e40923d34181e50691130023078d0777227e3b89424a7bc00f51","name":"prior_art_ci.md","bytes":2465},{"sha256":"b7fde956ef84d501604241da36125b2396c05d9bd505a202163eb5349f2ece0d","name":"evidence_ci.md","bytes":3815},{"sha256":"1e533f50186e5343603dba22f1a778d59ec751171713c9a4e537dee1c24c92da","name":"summary_transcript_ci.md","bytes":3545},{"sha256":"20f885a2e56c9b6dcb6648b9eaed4ed1151fd59bb7ae104a705a4f54a1d522e4","name":"next_step_ci.json","bytes":1794},{"sha256":"4562fed7ca175c3258b7c6f31441d8839a9459a37703d14c3ed900b2c12f206a","name":"compute_2x2_ci.json","bytes":39811},{"sha256":"207d51474a1f93cbd438a7075b50054ba57e06f5afc9ceae25f5b424406b15a3","name":"compute_2x2_ci.out","bytes":6010},{"sha256":"3d538047fb5a972bc4f38feebb4d24b50477c48d675b6f5d36cbc972c60ce39b","name":"compute_2x2_ci.py","bytes":10263},{"sha256":"0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1","name":"even-engine.py","bytes":11924},{"sha256":"0a924386a5083775a61694382afcb2cecb2f95b24dd381fcd8ec45a21979f31f","name":"fetch_ci.py","bytes":3311},{"sha256":"aa2ad961ab9af8c1ed20b0bd796c84be95138ec53acab7bf5b05d43fc439a043","name":"fetch_ci.json","bytes":15627},{"sha256":"6cac7b60919a6b8d18148c8aaff568bed15962524ff4bb6eef214f56db3e81f2","name":"fetch2_ci.py","bytes":3430},{"sha256":"471926451b15b3fd8eeb0ab087deb7a6617691fcd07105610ba42fca492eb421","name":"fetch2_ci.json","bytes":4349},{"sha256":"1d2941ab9d4d9d397de6c88aad9297829b220130a455cbc00d33163d85f837e7","name":"served_route_160.json","bytes":35312},{"sha256":"c8d920b871197d6ec7f6f4719a9c7fb790c2c7882449509dd121189620dcfb23","name":"served_return_1942.json","bytes":30291},{"sha256":"3cd8d4badebb29640ca06c33a6aecbd9516c48c47255c7c72005d18c1c5a7042","name":"served_return_1641.json","bytes":22243},{"sha256":"906768338baab31fcd39055ead14aaf570fd8646b3ff356138aa0f9a4add498d","name":"certificate-d17.json","bytes":7498},{"sha256":"4ea3a8bfcccae438be4e88dee157d21255fc7e65c61aa836bada27f55055de1e","name":"report.md","bytes":4417},{"sha256":"4e9994e3e9cda7fcd5e1d9d778a45805fd2e4d789a277be01fde106368c68165","name":"report.md","bytes":6559}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"74d15c066c7fe3e26e1ccce863008e7c6666ad5ddf87f9a4bc6b081e4699e0d3","next_step_sha256":"7ffa7997c2cb8a04253918c47388a08775cda65a93aca9ca4fc6b5daa346ce64","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}