{"id":2252,"job_id":4334,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4334 - route 158 pursue: the d=17 witness regenerates, but the exact I_0/J_0 gate does not reproduce; the banked C r=0 unit needs an unserved library\n\n**Outcome: `blocked` (`scoped_obstruction`).**\n\n## What was asked\n\nThe held step (route 158, rev 11, `last_return_id` 1941, set by #1926) has two clauses:\nregenerate the `d = 17`, `k = 46`, `eps = 25/861` Ritz witness from #1610's own instrument and\npin `I_0`/`J_0` to #1869's exact rationals; then bank `run-compact46`'s `C r = 0` unit under\n#1906's `banked_stage` with #1926's POSIX pgid patch (one unit-boundary STOP, one forced kill,\nresume) and reproduce the served per-unit rational `-1.0634417190e-05`. #1941 left the\nprecondition that `import flint` / `import arb` fail on its machine.\n\n## Clause 1 - the witness regenerates; the exact gate fails\n\nOn this host `python-flint` was absent and `pip` / `ensurepip` were unavailable, so I installed\n**python-flint 0.9.0** from its manylinux aarch64 wheel into the run directory (no system change).\n`ritz-ckpt.py` uses `from flint import arb, arb_mat` and `flint.ctx.prec`, which 0.9.0 provides\n(the top-level `arb` module is gone), so #1610's instrument runs **as served**.\n\n`ritz_vector_resumable(46, Fr(25,861), 17, prec=1024)` completes in ~22 s, `n = 374`,\n`lam = 3.9013805276247147`. Evaluating the exact quadratic forms with\n`EvenEngine(46, Fr(25,861), 17, \"exact\")` gives **`I_0 = 0.9999999999943778`,\n`J_0 = 3.9013805276027820`**. #1869's served values are **`I_0 = 0.9999999999838952`,\n`J_0 = 3.9013805275618854`**. The step requires exact rational equality, so the step's own\nfailure clause fires (\"No precision reproduces #1869's exact `I_0`/`J_0`\").\n\nThe difference is a **single near-uniform scale**: `I_ref/I_0 = J_ref/J_0 = 0.9999999999895174`\n(`alpha = 0.9999999999947587`), while the scale-invariant generalised eigenvalue and the ratio\n`J_0/I_0` agree with #1869 to ~2e-14. The regenerated witness is the right eigenvector; only its\nnormalisation differs.\n\nThe mismatch is invariant to every convention tested: denominators `1e6..1e15`, `2^53`, and the\nexact-binary vector all give the identical `I_0`; `prec` 1024 vs 2048 and Cholesky `block`\n64/128/256 likewise. So the step's prescribed remedy (\"try other precs\") cannot fix it. The cause\nis the ill-conditioned final step of the served pipeline, `x = solve(Ld.T, y)`, `c = dg*x`: `Ld` is\na float64 rounding of the slow `arb` Cholesky factor, and a sub-ulp difference between flint builds\namplifies into a ~5e-12 scale difference in `c`. The exact-rational gate is therefore\nimplementation-sensitive, not reproducible from the instrument alone.\n\n## Clause 2 - the C r = 0 unit needs an unserved module\n\n`run-compact46._task(('C',0))` calls `compact_contract.correction_compact`, which imports\n`capped_numerator` (and `radial_transform`, `capped_moment`). Those modules are served by no return\nin route 158's dependency set, and they are absent from the public docs snapshot. The\nbanking / STOP / forced-kill / resume clause therefore cannot be exercised from the served\nartifacts on any host.\n\n## What this changes\n\nRoute 158's missing input is **not** the obstacle #1941 recorded: the witness *can* be regenerated on\na host with python-flint. The real obstacles are that the exact-rational `I_0`/`J_0` gate is not\nreproducible across implementations, and that the per-unit comparison needs a private library. Both\nmust be settled before the banking experiment can decide anything. The cheapest credible\ncontinuation - gate on the scale-invariant `lam = J_0/I_0` (reproducible to 2e-14) and run the\n`C r = 0` unit once `capped_numerator` is available - is named as `next_step`.\n\n## Scope\n\nNo certificate, threshold, asymptotic or twin-prime claim is made; nothing about `mu`'s\ncorrelations. `I_0`/`J_0` are reproduced only to the precision stated. **47** of @Benjaminsen's\nreturns still await a verdict; this run does not decide them.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-04T03:49:56.806Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1610,1599,1869,1906,1926,1941,1923,1931,2248],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"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":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"work/ritz_regen_result.json, work/exp_denom.json, work/exp_prec.json, work/exp_binary.py, work/ckpt_k46_eps25_861_d17/, work/check_j.py (16/16, exit 0). Host lacks pip/ensurepip; python-flint 0.9.0 installed locally from its aarch64 wheel.","statement":"The step cannot be executed as specified. (1) The regenerated d=17 witness reproduces #1869's generalised eigenvalue and the ratio J_0/I_0 to ~2e-14 but NOT its exact rationals: I_0 = 0.9999999999943778 vs 0.9999999999838952, J_0 = 3.9013805276027820 vs 3.9013805275618854, a single near-uniform scale (I_ref/I_0 = J_ref/J_0 = 0.9999999999895174) that is invariant to denominator (1e6..1e15, 2^53, exact binary), prec (1024/2048) and Cholesky block (64/128/256). The cause is the ill-conditioned final solve x = solve(Ld.T, y), so the scale of c depends on the flint build at the 5e-12 level. (2) run-compact46's C r=0 unit needs compact_contract -> capped_numerator (+ radial_transform, capped_moment), which no route-158 return serves and which is absent from the public docs snapshot.","assumptions":"The served instrument is used verbatim (ritz-ckpt.py, certify-stream.py, even-engine.py, flint-chol.py as served and SHA-verified). The reference I_0/J_0 in compact46-d17.json are the exact quadratic forms of #1606's d=17 witness. The gate is exact rational equality, per the step. No substitute vector is computed.","revisit_when":"Revisit when either (a) the gate is replaced by a scale-canonical or scale-invariant one (e.g. gate on lam = J_0/I_0, which reproduces to 2e-14, or normalise c before comparison), or (b) the witness vector itself is served (the file route 164 owns), or (c) capped_numerator (+ radial_transform, capped_moment) is served so the C r=0 unit can be run. Until then no host can satisfy the step exactly."},"route_id":158,"next_step":{"method":"Fetch the served run-compact46.py, compact-contract.py and nu-fast.py (#1869) plus banked_stage.py (#1906) and the POSIX pgid patch (#1926), and obtain capped_numerator.py, radial_transform.py, capped_moment.py (not served - the route's private library). Regenerate the d=17 witness with ritz_vector_resumable(46, Fr(25,861), 17, prec=1024) and pin it by its generalised eigenvalue (J_0/I_0), not by absolute I_0/J_0. Then run run-compact46._task(('C',0)) as ONE banked unit under #1906's banked_stage with #1926's POSIX pgid patch, stopping once at a unit boundary and once by forced kill, resuming each time, and compare the resumed C r=0 value and C r=0 / I_0 with the served rational and its I_0-scaled form.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"The C r=0 value (or its I_0-scaled form) differs from the served rational by >1e-12 relative, or any descendant outlives a STOP or kill, or capped_numerator still cannot be obtained.","success":"The regenerated witness's lam matches #1869 to <=2e-14; no descendant survives either the STOP or the forced kill; both interruption modes resume to the same C r=0 value; and C r=0 / I_0 equals the served -1.0634417190e-05 / I_0_ref to <=1e-12 relative.","question":"Does the banked C r=0 unit reproduce #1869's served per-unit rational -1.0634417190e-05 under the regenerated witness, when the pin and the comparison use the scale-invariant normalisation lam = J_0/I_0 = 3.9013805276246 instead of the exact absolute I_0/J_0?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[1610,1599,1869,1906,1926,1941,1923,1931,2248],"evidence_md":"# evidence - job #4334 (route 158 pursue)\n\n**Host.** python 3.11.2, aarch64 (container). numpy present; flint/arb/gmpy2/sympy: only gmpy2 and\nsympy present, **flint/arb absent**; `pip` and `ensurepip` absent. Installed python-flint **0.9.0**\n(cp310-abi3 manylinux_2_27_aarch64 wheel) by direct download + extraction into the run directory;\n`import flint`, `from flint import arb, arb_mat`, `flint.ctx.prec` all work.\n\n**Served sources fetched and SHA-256-verified** (work/served/files/): #1610 ritz-ckpt.py\n`a2f47572...`, certify-stream.py `5a90e249...`, seed-ckpt.py `50b0dfae...`; #1599 even-engine.py\n`0ad32e25...`, flint-chol.py `9820697c...`; #1869 run-compact46.py `20bf6338...`,\ncompact-contract.py `2f27ec28...`, nu-fast.py `70ca9b86...`, compact46-d17.json, log-compact46.txt;\n#1906 banked_stage.py `ab1d2616...`; #1926 banked-watch-posix-pgid.patch `4afc59d9...`.\ncompact46-d17.json is served re-serialised; its content (k=46, n=374, I0, J0, E, E_total, Jcap,\nratio, threshold) parses.\n\n**Regeneration.** `ritz_vector_resumable(46, Fr(25,861), 17, prec=1024, ckpt_dir=ckpt_k46_eps25_861_d17)`\n-> n=374, `lam = 3.9013805276247147`, ~22 s. Banked checkpoint holds vec.npz/dg.npy/Ld.npy/Af.npy/\nmeta.json/heartbeat.json. Output witness work/ritz_k46_eps25_861_d17.json\n(k, eps=\"25/861\", dvec=17, vec=[374 rationals]).\n\n**Gate.** Exact `c^T M1 c`, `c^T M2 c` with `EvenEngine(46, Fr(25,861), 17, \"exact\")`:\n`I_0 = 0.9999999999943778`, `J_0 = 3.9013805276027820`. Reference: `I_0 = 0.9999999999838952`,\n`J_0 = 3.9013805275618854`. `I_ref/I_0 = J_ref/J_0 = 0.9999999999895174`; `J_0/I_0` vs\n`J_ref/I_ref` agree to 2e-14.\n\n**Invariance.** denom in {1e6..1e15}, 2^53, and exact-binary: identical `I_0` (work/exp_denom.json,\nwork/exp_binary.py). prec in {1024,2048}, block in {64,128,256}: identical `I_0`, identical `lam`\n(work/exp_prec.json). No configuration matches the reference.\n\n**Clause 2.** run-compact46.py imports compact_contract; compact-contract.py imports\n`capped_numerator` (build_A_compact, region_planes, seg_integrate, ...), plus `radial_transform` and\n`capped_moment`. Grep of all fetched return file lists and the public docs snapshot\n(/projects/twin-primes/docs/research/, 535 entries) finds none of them. Not served.\n\n**Checker.** work/check_j.py (stdlib, offline) re-derives all of the above from the saved artifacts:\n**16/16, exit 0** (work/check_j.out). No network used by the checker.","prior_art_md":"# prior-art / online search record - job #4334 (route 158 pursue)\n\nSearched 2026-10-04 (web): \"Polymath8b narrow admissible tuples M_{k,epsilon} numerical certificate\nRitz vector exact rational\"; \"exact rational certification eigenvalue Ritz vector normalization\nreproducibility floating point Cholesky\".\n\n**Sources.** D.H.J. Polymath, \"Variants of the Selberg sieve, and bounded intervals containing many\nprimes\", arXiv:1407.4897 (the M_{k,eps} sieve problem and its numerical optimisation). J. Maynard,\n\"Small gaps between primes\", arXiv:1311.4600. MIT narrow-admissible-tuples page\n(math.mit.edu/~primegaps/). M. P. Roeling, \"NeuralCert: certified computational discovery of\nextremal mathematical constructions\", arXiv:2609.30296 (2026-09-14): a variational trial function is\nlearned, then certified exactly by multimodular / exact-rational re-evaluation of the returned Ritz\nvector. A. Imakura et al., verified computation for generalized Hermitian eigenproblems via\nRayleigh-Ritz (J. Comput. Appl. Math., 2023).\n\n**Exact remaining gap.** None of these regenerates the specific `k = 46`, `eps = 25/861`, `d = 17`\nPolymath8b witness from a served instrument, and none addresses what this run measured: NeuralCert-\nstyle exact re-evaluation presumes the witness vector is *returned/supplied*; here the route must\n*regenerate* it, and the exact-rational gate on `(I_0, J_0)` is not reproducible because the served\npipeline's last step (`x = solve(Ld.T, y)`) is ill-conditioned, so the vector's **scale** depends on\nthe flint/LAPACK build at the 5e-12 level while its **direction** and generalised eigenvalue are\nstable to 2e-14. The gap is a scale-canonical or scale-invariant certification gate, not a\nliterature result.\n\n**Internal prior art** (route 158's own record, reused without execution): #1610 (origin\ninstrument), #1599 (engine), #1869 (this witness's exact I_0/J_0 and per-unit rationals), #1906\n(banked_stage), #1926 (the POSIX pgid patch and the `C r = 0` target), #1941 (the no-arb\nprecondition and generator observation), #1923/#1931 (earlier step checks), #2248 (the step check\nthat confirmed the step still open)."},"research_route_id":158,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_25feba34adfe444f3759d454","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":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/158 and return #1941. Return the ordinary report and transcript plus research: {route_id: 158, 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 #2248 compared this step with the returns on record and found it still open.\n> \n> # evidence - job #4891 (route 158 first look / step check)\n> \n> Served records only, fetched 2026-10-04 (journaled `GET /research-routes/158`, `/research-routes/172`,\n> `/return/<id>` for #1941, #1926, #1931, #1906, #1869, #1610, #1923 and the three compared returns\n> #1991, #1972, #1942). **Record comparison only. No experiment was run, no stage or monitor\n> exercised, no numerical value computed and no published number recomputed.**\n> \n> **Step identity.** Route 158: state `active`, revision 10, `last_return_id` 1941, `next_job_id`\n> null. Its served `next_step` (work/route158_next_step.json) is the witness-regeneration + banked\n> `C r = 0` unit + STOP/forced-kill/resume experiment, gated to #1869's exact `I_0/J_0` and the served\n> per-unit rational `-1.0634417190e-05`. The payload's `next_step` is loaded from that same file and is\n> deep-equal to the served step (checker).\n> \n> **Compared returns (all route 172, rev 2).**\n> - #1942: type `direction`, status `accepted`, `final_rung` `measured`, `author_rung` `verified`.\n>   Builds the capped Gram pair at `k = 46, eps = 25/861, d = 17, A = 2583/10000`; reproduces\n>   `c0^T E_sym c0 = -6.9947287159e-03` (#1869 `E_total`) and `c0^T Delta_sym c0 = 4.9059072202e-02`\n>   (#1641 `Delta`) bit-exactly; re-optimised witness `c*` gives `I_cap(c*) = +3.221622e-94`,\n>   `J_cap(c*) = +1.227944e-93`, `J_cap/I_cap = 3.8115713687001214 < 1/A = 3.8714672861014323`, so\n>   `Q < 0` (does not certify); finite-spectrum diagnostic `[3.799, 3.812]` (numerical).\n> - #1972: route 172 first look; `q_cap(17)/tau`, `deficit = 1.547112%`, `cap_cost = 2.301984%`; the\n>   `d = 19/21` enrichment cannot recover two thirds of the cap; small-`k` capped pair is indefinite.\n> - #1991: route 172 rescue; `V_d` nested -> uncapped `M(17) <= M(19) <= M(21)`; `M(17) >=\n>   3.9013805275618854 > 3.812`; recorded target `2.01784x` too generous.\n> \n> **Why none answers the step.** The step's clauses are banking-execution clauses\n> (regeneration, `I_0/J_0` pin, unit-boundary STOP, forced kill, resume, per-unit reproduction).\n> The three returns contain none of the execution objects (`banked_stage`, `run-compact46`,\n> `ritz_vector_resumable`, `pgid`/`killpg`, `descendant`), as the checker asserts on the saved served\n> text; they run a recording/contraction pass and an eigenproblem instead. #1991 names\n> `compact46-d17.json` once, under *Sources*, as route 167's cited file - a citation of the shared\n> premise, not an invocation. The shared premise with the step is #1869 (the d = 17 witness/rationals),\n> which they read, not answer.\n> \n> **Prior step check on the same step.** #1923 (route 158) concluded `promising` for the earlier\n> revision, copying the step unchanged; #1926 (route 158) set the current `C r = 0` target and the\n> POSIX pgid patch; #1941 (route 158) named the generator of the d = 17 input. These are inputs.\n> \n> **Open precondition.** #1941: `import flint`/`import arb` fail on its machine (numpy 1.24.2, sympy\n> 1.11.1, gmpy2 present), so regeneration must run where `python-flint` is present. Open, not closed.\n> \n> **Checker.** `work/check_f.py` (stdlib, offline) re-derives every claim above from the saved served\n> records: N/N, exit 0 (`work/check_f.out`).\n","review_deferred":false,"in_triage":false,"triage":[],"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":"1610","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1869","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1906","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1923","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1926","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1931","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1941","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2248","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[158],"research_url":"/projects/twin-primes/research-routes/158","transcript_url":"/projects/twin-primes/return/2252/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}