{"id":5984,"job_id":10337,"problem_id":1,"lane_id":null,"type":"explore","user_id":111,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 10337: route 154 pursuit. needs_capability (python3 with python-flint 0.9.0)\n\n**Caveat first.** Nothing was executed. This machine has no Python interpreter (only the Windows Store stub) and no C compiler. The step requires running the served certificate file `prime_gap_186_certificate_bypass.py` on stock python-flint 0.9.0 and capturing its `fmpz_poly.mul_low` sites. That needs python3 with python-flint 0.9.0. The step is returned unchanged with its tool requirement made explicit. This is not a research obstacle, and the route stays active.\n\n## Prior-work update (2026-10-26)\n- **Query:** \"FLINT fmpz_poly mullow signed coefficients bug small prime FFT incorrect result python-flint 0.9.0\".\n- **Inspected results:** python-flint PRs #336 and #180 and issue #109 (not about `fmpz_poly` multiplication), and the FLINT `fmpz_poly` documentation (no multiplication defect stated).\n- **What the search shows:** `mul_low` on `fmpz_poly` was added in python-flint 0.9.0 (gh-322, per the changelog entry surfaced in the search). I found no public report of signed-coefficient errors in `fmpz_poly_mullow` or the FFT path.\n- **Limits:** this is a bounded negative in GitHub and FLINT-doc vocabulary, not proof of absence. The FLINT 3.x changelog and the python-flint issue tracker were not swept item by item. The upstream openai/PrimeGaps186 README's statement about a \"custom FLINT 3.6.0 build with corrected signed polynomial convolution\" stays as quoted in the route record and was not re-fetched.\n- **Effect on the step:** none. The step's real-operand capture-and-replay is still the only way to decide whether the certificate's production products are exact on stock FLINT.\n\n## Step (unchanged)\nAs in the route record (set by #5227; confirmed open by step check #5979). The `required_tools` now names `python3`, and `shortfall` records what this machine lacked.\n\n## Sources\nRoute 154 record; #5227; #5979; python-flint GitHub PR #336 and #180 and issue #109; flintlib.org `fmpz_poly` documentation.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T08:19:55.886Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5227,5979],"messages":[]},"tokens":{"log":"summary","input":4,"models":{"claude-opus-5-5":3182},"output":3182,"source":"reported","entries":0,"cache_read":793000,"cache_write":3631,"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":"medium","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":"needs_capability","route_id":154,"next_step":{"method":"Price the control, then sample real sites. (1) Take the served bypass file prime_gap_186_certificate_bypass.py (sha256 030232e0…; its only hunk is inside check_flint_signed_fft, per review #1397 item 3) and add a capture wrapper that, for the first 8 DISTINCT production fmpz_poly.mul_low sites reached in the SERIAL cap stage, records site index, bits, length, an operand fingerprint (sha256 over the canonical 59-byte little-endian word stream of the scaled integer coefficients) and the FLINT product's fingerprint; stop after the 8th site so the capture itself is cheap, and keep --workers 1 (it selects source worker processes only and cannot speed the cap stage). (2) Offline, with no FLINT code, replay each captured pair exactly: pack the operand words into CPython big integers, multiply, unpack the low `length` coefficients, compare fingerprints and report the first differing coefficient. This run measured one such replay at length 98264 as 19.137 s with exact_ok at n = 4096/16384/32768/98264 (work/measure_bq.py). (3) Redirect the cap stage's progress output so each layer's wall time is recorded, and report the per-site replay seconds so a full-certificate budget is priced from measurement. Do not require a completed receipt.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":2},"failure":"Any captured real site mismatches (name site index, bits, length and the first differing coefficient: the production convolution is affected there and the custom-FLINT dependency is not guard-only), or fewer than 8 distinct sites are captured inside sah.py bounded --limit 600 (the capture is then too heavy and those sites are recorded as not independently checkable at this budget, with the layer reached named). A completed receipt is part of neither branch.","success":"8/8 captured real production sites reproduce exactly under the stdlib Kronecker replay (identical fingerprint, no differing coefficient) and the cap stage's per-layer wall times are recorded: the production convolution is then exact at real operands on stock FLINT, the custom-FLINT dependency is reduced to the startup guard for those sites, and the full certificate's cost is priced from measured layer times rather than from the 1500 s bound.","question":"Are the certificate's real production fmpz_poly.mul_low products (224-bit fixed coefficients, length 98264) exact on stock python-flint 0.9.0 at the first 8 distinct sites of the serial cap stage, and what wall time does one cap layer actually cost on this host?","shortfall":"This machine has no python3 interpreter (Windows Store stub only) and no C compiler; the step runs the served Python certificate on stock python-flint 0.9.0.","budget_hours":3,"strict_tools":["python3"],"required_tools":["python3"],"required_sources":[]},"depends_on":[5227],"evidence_md":"Nothing executed. The step (set by #5227, confirmed open by step check #5979) needs python3 with python-flint 0.9.0 to run the served bypass certificate and capture real mul_low sites; this machine lacks python3. Step returned unchanged with required_tools and shortfall.","prior_art_md":"Search 2026-10-26, query: FLINT fmpz_poly mullow signed coefficients bug small prime FFT incorrect result python-flint 0.9.0. Inspected: python-flint PR #336, PR #180, issue #109 (unrelated); flintlib.org fmpz_poly docs (no defect stated). mul_low was added to fmpz_poly in python-flint 0.9.0 (gh-322). No public report of signed-coefficient mullow errors found; FLINT 3.x changelog and python-flint tracker not swept item by item. Bounded negative, not absence. Remaining gap unchanged: real-operand exactness of the certificate products on stock FLINT."},"research_route_id":154,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_70682f6fbf6580733b92340d","run_id":"run_916812d086720b070e62de98","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":"sarenayu","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/154 and return #5227. Return the ordinary report and transcript plus research: {route_id: 154, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", 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: research findings only>, 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. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\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 #5979 compared this step with the returns on record and found it still open.\n> \n> Step unchanged and unanswered. #5227 set it (route 154 last_return_id 5227, rev 6); no later route-154 return. #3831 swept constant-coefficient proxies only (limited by review #1397); #5227 priced one replay (19.137 s at length 98264) but captured no real site. Comparison returns #5953 (route 223), #5562 (route 128), #5402 (route 97) contain no FLINT/mul_low/bypass/replay content and do not bear on the step.\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":"5227","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[154],"research_url":"/projects/twin-primes/research-routes/154","transcript_url":"/projects/twin-primes/return/5984/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e65cd05a07127a67d602097444ce2eed0b724a7649632354a4779d05acb5d99e","next_step_sha256":"ccbafaedb27a452626de014154a2916198c74c41c9fdf4cd4d2e730361f45f86","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}