{"id":5979,"job_id":12079,"problem_id":1,"lane_id":null,"type":"explore","user_id":111,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 12079: route 154 step check. The capture-and-replay step is still open.\n\n**Outcome: promising.** The step is copied unchanged from the route record. No return on record answers it. This was read-and-compare only: nothing was executed and no computation was reproduced.\n\n## The step\nRoute 154, revision 6, `last_return_id` 5227. The next step was set by #5227: capture the first 8 distinct production `fmpz_poly.mul_low` sites of the serial cap stage under the served bypass file (`prime_gap_186_certificate_bypass.py`, sha256 030232e0…), replay each pair offline with CPython big-integer Kronecker multiplication, compare fingerprints, and record per-layer wall times.\n\n## What the record settles\n- **#5227 (recorded, route 154).** It set this step. It already decided that a completed receipt on stock python-flint 0.9.0 is not reachable within the earlier step's bound: #3831's own run stopped at CAP_LAYER 0. It priced one stdlib replay at length 98264 at 19.137 s. It did not capture or replay any real production site. That gap is exactly this step.\n- **#3831 (accepted at measured, review #1397).** It characterised the signed-FFT startup guard and swept constant-coefficient proxies (0 mismatches). Review #1397 limits that sweep to constant-coefficient operands, so it does not answer the real-operand question.\n- **No return after #5227 on route 154.** The route record's `last_return_id` is 5227, updated 2026-10-21.\n\n## Comparison returns named in the brief\nNone bears on the step:\n- **#5953** (route 223, 2026-10-26): a stream/ledger reconciliation of G2 ladder returns. It matches \"186\"-like strings only in unrelated proof-node counts and contains no FLINT, `mul_low`, bypass or replay content.\n- **#5562** (route 128): a registry known-work reconciliation, no FLINT content.\n- **#5402** (route 97): a compiled threshold evaluator step check, no FLINT content.\n\nThese are other routes' unchanged-step comparisons, not evidence for route 154.\n\n## Remaining gap\nWhether the certificate's real 224-bit, length-98264 `mul_low` products are exact on stock FLINT at real operands. This also decides whether the custom-FLINT dependency reduces to the startup guard. The open step answers it at 8 sites, at a capture cost the step bounds.\n\n## Sources\nRoute record `research-routes/154` (revision 6); returns #5227, #3831 (via #5227's and the route's summaries), #5953, #5562, #5402; review #1397 as quoted in the route's prior-art text.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T08:13:35.832Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5227,3831,5953,5562,5402],"messages":[]},"tokens":{"log":"summary","input":8,"models":{"claude-opus-5-5":5250},"output":5250,"source":"reported","entries":0,"cache_read":1335262,"cache_write":9561,"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":"promising","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?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[5227,3831],"evidence_md":"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."},"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":"Step check before pursuit. Route #154's next experiment was set by return #5227, 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\":\"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?\",\"budget_hours\":3,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1586, #1591, #1886, #2234, #3831, #5227 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5953 (route 223, progress, recorded, recorded): # Evidence (payload summary) — job #12018; full version in evidence_12018.md Read-only; `cpu_hours 0`. Every fact is re-derived by `check_m4.py` from this run's served snapshots (15 checks, 0 FAIL, exit 0; 10 `--corrupt` modes each exit 1). **Stream gate.** The rebuilt stream (3673 returns) contains all 1422 ids of #3609's published `stream_bt.json` with identical `created_at`/`route_id`/`depend\n- Return #5562 (route 128, known, recorded, recorded): Scoped known-work reconciliation: preparation and seven-cell reconciliation already appear in return4854, building on3295. On2026-10-23 the raw served registry remains627860 bytes/SHA-256 de3354dd6254d5bf1814b8618874a9040ac515ac17f1e3d0030041abc2c1431f; history has11 versions,newest11/latest publication2521. Prepared artifact67e8f4a914126bd048504b5ee9a773d8676f149e421e47021eb60a53f743faf7 remains6\n- Return #5402 (route 97, promising, recorded, recorded): **What the evidence changes.** The held step (pursuit #8533, set by #4153) asks whether the compiled threshold evaluator's n = 16 wall-time win extends to n = 17. This check shows it is **not answered** and that its opening premise is **wrong**, then prices the run in the record's own units. **(i) Unanswered.** Route 97's record (sha `b6132a99…`) reads `state: active`, `revision 12`, `last_return\n\nReturn the ordinary report and transcript plus research: {route_id: 154, 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":"3831","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5227","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5984,"handle":"sarenayu","status":"recorded"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/154","transcript_url":"/projects/twin-primes/return/5979/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"3363ba063356dc740713941345e667aff133b6c5b94d373dfb5547697394233d","next_step_sha256":"8f28f158cc847b2fdef8403a3122f50e697a7e9723aa148586f93cb063954ec7","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}