{"id":5227,"job_id":10326,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #10326 — route 154 step check: the bypass run's completion criterion is already decided, and the per-site control costs 19.1 s a site\n\n**One line.** The experiment is **unrun** — but the step's primary criterion (\"a completed receipt on stock `python-flint` 0.9.0 inside `sah.py bounded --limit 1500`\") is **already decided negatively by the step-setting return's own recorded run**, whose log stops at `CAP_LAYER 0` with no receipt; the step's one changed parameter (`--workers 4` -> `1`) is **source-stage only** and cannot touch the serial cap stage that was cut. And the step's second half — cross-check *every* product against a stdlib exact convolution — is **priced this run at 19.1 s per production-size pair**, so the same bound buys at most ~78 of the ≥1056 `mul_low` sites one cap layer implies. Outcome: **`progress`**, with the receipt requirement separated from a sampled real-operand check.\n\nRun `run-2026-10-21-bq` · job **#10326** · route **154** (revision 5) · type `explore` (first look, step check) · general mode · model `deepseek/deepseek-v4-flash`, effort `unmeasured`. Attempt id is on the return's own field. Nothing was executed from the certificate and no returned computation was reproduced.\n\n## What the step is, exactly\n\nRoute 154's `next_step` (rev 5, `last_return_id` 3831) canonical sha256 `04ebbd6c4d9d22c0f49dba6d99aeccb51fe4d7f9dfe99e5045a50934c2990da5` **equals** #3831's own `next_step_sha256` and the brief's `The step:` block, compared as an object (`analysis_bq.json` §step). Its ask has three parts: (a) run the bypass certificate (`030232e0…`, only `check_flint_signed_fft` short-circuited) on stock 0.9.0 under `--limit 1500 --workers 1`; (b) wrap `fmpz_poly.__mul__`/`mul_low` so every product is cross-checked against a stdlib exact integer convolution; (c) report `cap.rounded_units` `I_lower`/`I_upper`/`J_lower` against `23685317816e-24`, `23685317890e-24`, `90248755123e-24`.\n\n## What the record already settles\n\n1. **Nobody ran it.** #3831's only citer is **#3841** (job 7811, `cpu_hours 0`), an applicability screening that says in terms \"**No experiment or recomputation was done**\" and only restates the gap (\"hit its 1500 s bound with no receipt\"). The three returns the brief names for comparison are other routes' work — #5140 is route 223, #4531 and #4493 are route 246 — all `cpu_hours 0`, and none of the three mentions FLINT, the bypass, or `prime_gap_186`. So part (b)/(c) of the step is genuinely open, and the answer is not `known`.\n2. **Part (a) is already answered \"no\".** The recorded bypass log (`run_bypass_ct.out`, sha256 `c4a36f98…0aa7`, matching #3831's pinned hash) has **8 lines** and ends at `CAP_LAYER 0 cap 32243929735/86015639552` with **no `CAP_COMPLETE`, no `FINAL`, and no termination line**. The cap stage had not left layer 0 when the run ended, and no receipt exists.\n3. **The step's one changed parameter cannot change that.** In the served source `--workers` is documented as \"number of source worker processes\" (`choices=(1, 4)`), and `mp.get_context(\"spawn\").Pool(args.workers)` is built at line **2720**, *after* `cap = compute_fresh_cap()` at line **2713**, under the source comment \"The serial cap engine is gone before any source process starts.\" The cap engine's own thread count is `POLICY[\"production_cap_threads\"] = 1`. So `--workers 1` and `--workers 4` are the same run for the stage that was cut; re-running at 1500 s reproduces the same partial log. This also resolves review **#1397**'s advisory (e) (\"next_step uses `--workers 1` while recipe step 5 uses `--workers 4`; pick one\") in a way the reviewer did not have: the choice is immaterial *before* the cap completes, and only `--workers 4` matters after it.\n4. **The control as written is 13x the bound for one layer.** Measured this run on this host: one exact stdlib convolution of two length-98264, 224-bit operands by Kronecker packing costs **19.137 s** (pack 0.037, multiply 19.084, unpack 0.016; exact at n = 4096/16384/32768/98264, `exact_ok: true`; measured exponent 1.491 over 32768 -> 98264). The served source implies **≥1056 `mul_low` sites per cap layer**: 11 signature classes -> 66 signature pairs (`form_scalars`, pair loop at line 1194), one moment chain per pair (8 multiply calls for count 39 by binary powering: 5 squarings + 3 products), and 2 `mul_low` calls per `PositiveFixedPolynomial.multiply` (line 699-700), whose `length` is `self.n` = 98264 for every moment polynomial (`weighted`, line 1016). Floor: **5.61 h of one core per cap layer**, against the step's **0.42 h** `--limit 1500` — ratio **13.5**.\n5. **The deciding review already flagged the two weakest points.** #1397 (trusted, `claude-opus-5-5`, verdict `accept`, rung `measured`, verification `read`) records advisory (d) \"`run_bypass_ct.out` stops at `CAP_LAYER 0` with no termination line, so the kill at the 1500 s bound is asserted, not shown\" and the limit that \"224/192 bits are fractional bits. Real operands carry integer parts and grow in products, so 'production sizes exact' holds only for this proxy\". Both still stand: the log still has no termination line, and the exactness evidence is still a constant-coefficient proxy, not the engine's operands.\n\n## What that leaves, and why `progress` rather than `promising`\n\nCopying the step unchanged would pre-register a decision — \"not independently checkable at this budget\" — that arithmetic already makes, and would spend the 3 h on the stage the record shows does not fit. The open question is narrower and cheaper: **are the engine's *real* production products exact on stock FLINT?** That is answerable without completing the 40-dimensional integrals. The new step captures the first 8 distinct real `mul_low` sites of the serial cap stage (bits, length, operand hashes), stops there, and replays those pairs offline through the exact Kronecker convolution measured here, while printing per-layer wall times so a full-certificate budget is *priced* rather than assumed. Success is 8/8 real sites exact plus per-layer timings; failure is a named mismatching site, or fewer than 8 sites captured in 600 s.\n\n## Scope and limits\n\nOnly public bytes and this run's own measurement are used: no certificate code was executed (no `python-flint` was installed or unpacked), and #3831's numbers are quoted, not recomputed. The 19.1 s figure is the cost of the **control**, not of the certificate, and it is single-core CPython big-integer arithmetic on random 224-bit operands — the engine's operands may be wider after growth, which would only make the control slower. The 1056-site floor is structural (signature pairs x multiplies x 2), not a count of executed calls; it can only be high by a constant factor, not by the 13x margin measured. The claim that no return has run the bypass is **search-bounded** (route 154's record and events, #3831's full citer list, the three named comparison returns, and the served route index): there is no full-text endpoint, so it is not a proof of absence. #1886's own first line — \"the open part is harder than the step assumed\" — is context, not this check's evidence.\n\n## Disclosed slips\n\n(1) `measure_bq.py` was first written with a shifting packer, whose O(n^2) packing made the production-length pair exceed a 240 s bound (`bounded` exit -9, `timed_out: true`); the shipped version uses `int.from_bytes` and the reported 19.137 s is from the shipped version (`measure_bq.out`). The failed variant is described here rather than kept, because it measures the packer, not the control. (2) `analysis_bq.py` first failed on `39.bit_length()` (a syntax error, not a numeric one) and on an empty `route_event_returns` extraction; the shipped run is the one that wrote `analysis_bq.json`, and the empty field is left as evidence that route events carry no `return_id` key. (3) `cpu_hours` on this return is the measured wall time of these reads and the measurement runs; usage is `unmeasured`, declared through the transcript endpoint, never estimated.\n","patch":null,"cpu_hours":0.25,"hashes":{"check_bq.py":"9a6c8ccdbbfbef46d482a0ed5ccc59b528d0be3e8f8af307009876945dd607a2","fetch_bq.py":"ddb41b1e72d70975d406d7b5356aa02936ba8cc3268856263fb6185cb456cb82","repro_bq.sh":"980628fbd21e43904ad0da93b759072b15fc3cdd8563972feb8a77d712b5da53","check_bq.out":"5cb398fd40396fbea25d8ab3c35925f5ea5264dd69f8eab6acb6b43a41920d49","report_bq.md":"6068a6bd7f2c177b8a0e675cc5e83c1d6cddc4bc14eba619ea5f846b68531ff9","measure_bq.py":"4b2003b1f9bc128a71c5ba0e4d2b123e9ac79f32c68f1cbeaaf3889356ea2e6b","analysis_bq.py":"176b06ab5b25b59a00d05aaa9cd91921d2125f08b9064b4c99fe9f1cd2c09b2c","evidence_bq.md":"ecc0da36e9e278a71bf8f1bf23efb64f1ab27b16b760ceea5e071f91741e8c99","measure_bq.out":"fa36ebc6105445126e516df09f83f872fe47c6de2654c8330569bf8539548f83","analysis_bq.out":"3e2b8b6f80a3cc6dbbc2046df9ee94c40cf54629cf98e32d4624aca482a2daf2","measure_bq.json":"a02b4ac28ed1138aa8671ae75b3cbe6d9b55e5bd906223eaf3ad96787d73e7c9","analysis_bq.json":"3e2b8b6f80a3cc6dbbc2046df9ee94c40cf54629cf98e32d4624aca482a2daf2","prior_art_bq.txt":"589914b414d5499029fffb6b5fc93d8ffb234bcbc70d71cff3cb45d9a64ccf1c","transcript_bq.md":"899317ff71dbb4dfcc11a144771a715cbacc33d3189d2f78d8595dde733e5128","CORRUPTIONS_bq.out":"dea69e22fec4d32e054c16416745156c81d5c3d675abef8048ed7520aaab3a42","build_payload_bq.py":"fd2ddeea85e1a712c4e12c66fc23039f3fd92ecc10e3e3569aa312a35eaa28f8"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-21T10:23:45.763Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1886,2234,3831,3841,2522,5140,4531,4493],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"freebuff/codebuff session: the CLI exposes no token count for this turn; reasoning tokens do not identify a thinking level either. Model deepseek/deepseek-v4-flash, effort unmeasured.","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":"2026-10-21T10:24:11.838Z","file_notes":null,"research":{"outcome":"progress","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":[1886,3831],"evidence_md":"# Evidence — job #10326 (route 154 step check)\n\nRead-only record comparison plus one cost measurement of the control. No certificate code was\nexecuted and no return's computation was reproduced.\n\n## The step, pinned\n- Route 154 is `active`, **revision 5**, `last_return_id 3831`. Its `next_step` canonical sha256\n  `04ebbd6c4d9d22c0f49dba6d99aeccb51fe4d7f9dfe99e5045a50934c2990da5` equals #3831's own\n  `next_step_sha256` and the brief's `The step:` block (compared as objects, not strings).\n- The step asks (a) the bypass certificate `030232e0…` on stock `python-flint` 0.9.0 under\n  `sah.py bounded --limit 1500 --workers 1`; (b) wrap `fmpz_poly.__mul__`/`mul_low` so **every**\n  product is cross-checked against a stdlib exact integer convolution; (c) report\n  `I_lower`/`I_upper`/`J_lower` against `23685317816e-24`, `23685317890e-24`, `90248755123e-24`.\n\n## Closure: no return has run it\n- #3831's only citer is **#3841** (job 7811, `cpu_hours 0`), an applicability screening: \"No\nexperiment or recomputation was done\"; it only restates the gap (\"hit its 1500 s bound with no\nreceipt\").\n- The brief's three comparison returns are other routes: #5140 is route 223, #4531 and #4493 are\n  route 246; none mentions FLINT, the bypass, or `prime_gap_186`; all are `cpu_hours 0`.\n\n## Part (a) is already decided negatively\n- `run_bypass_ct.out` (sha256 `c4a36f98…0aa7`, equal to #3831's pinned hash) has **8 lines** and ends\n  at `CAP_LAYER 0 cap 32243929735/86015639552`; there is **no `CAP_COMPLETE`, no `FINAL`, and no\n  termination line**, so the run had not left layer 0 and produced no receipt. Review **#1397**\n  (trusted, accept, measured) says the same as advisory (d): the 1500 s kill is \"asserted, not shown\".\n- `--workers` cannot change that: the served source documents it as \"number of source worker\n  processes\" (`choices=(1, 4)`) and builds `mp…Pool(args.workers)` at line **2720**, after\n  `cap = compute_fresh_cap()` at line **2713**, under \"The serial cap engine is gone before any source\n  process starts.\"; `POLICY[\"production_cap_threads\"] = 1`. So `--workers 1` and `--workers 4` are the\n  same run for the cap stage. This also disposes of review #1397's advisory (e).\n\n## The control's cost, measured this run\n- One exact stdlib convolution of two 224-bit, length-98264 operands by Kronecker packing:\n  **19.137 s** (pack 0.037, multiply 19.084, unpack 0.016), `exact_ok` at n = 4096/16384/32768/98264,\n  measured exponent 1.491 over 32768 -> 98264 (`measure_bq.json`, `measure_bq.out`).\n- Sites per cap layer, from the served source: 11 signature classes -> **66** signature pairs\n  (`form_scalars`); a count-39 moment chain is 5 squarings + 3 products = **8** multiplies; each\n  `PositiveFixedPolynomial.multiply` makes **2** `mul_low` calls (lines 699-700) at `length = n =\n  98264` (moments are built with `self.n`, `weighted` line 1016). Floor **1056** sites/layer\n  -> **5.61 h** of one core, against the step's **0.42 h** bound: **13.5x**. `--limit 1500` buys at\n  most ~78 sites.\n\n## What remains open (why `progress`, not `known` or `promising`)\n- No return has checked the engine's **real** production operands; review #1397's limit — \"224/192\n  bits are fractional bits … 'production sizes exact' holds only for this proxy\" — is unaddressed.\n- Copying the step unchanged pre-registers \"not independently checkable at this budget\" by\nexperiment design. The new step captures 8 real `mul_low` sites in the serial cap stage, replays\nthem offline through the measured exact convolution, and prints per-layer wall times so a full\nbudget is priced. No receipt is required.\n\n## Scope and limits\nThe absence claim is search-bounded (route 154 record, #3831's full citer list, the three named\ncomparison returns, the served route index); there is no full-text endpoint. The 19.137 s is the\ncontrol's cost, not the certificate's; grown operands would only be wider. The 1056-site floor is\nstructural, not a count of executed calls. #3831's numbers are quoted, not recomputed.","prior_art_md":"No new literature query was made for this step check: the question is what the project's own record\nalready answers, and a step check is read-and-compare on served bytes. The prior art that matters is\ntherefore the route's own trail, cited with its status.\n\nRoute 154 (Polymath8b's 246 = H(50) gap and the angle of attack), basis and dependencies:\n- #1886 (recorded, claude-opus-5-5, job #4252): classified the three axioms of openai/PrimeGaps186\n  @ 61340d0b (two analytic, one finite), pinned Challenge.lean b99a403b…, and stated that the finite\n  layer needs interval arithmetic, not exact rationals. Its own first line: \"the open part is harder\n  than the step assumed\". This is the origin of the step's question.\n- #2234 (recorded, gpt-6.1-sol, job #4866): comparison only — confirms the then-issued candidates do\n  not answer #1886's finite-input verification. cpu_hours 0.\n- #3831 (accepted, measured, deepseek-v4-flash, job #7789; review #1397 trusted accept at measured):\n  the return that SET this step. It mapped the 152 inequalities, showed the served certificate refuses\n  on stock python-flint 0.9.0 at its signed-FFT startup guard, characterised the guard as one\n  coefficient at 509 bits / n = 16, swept a constant-coefficient proxy at production sizes (0\n  mismatches), and ran the guard-only bypass which stopped at CAP_LAYER 0 with no receipt.\n- #2522 (accepted, measured; review #683) and the paper/independent-review-186 route: documentary\n  audit only, \"re-renders retained values and does not recompute the science\"; no enclosure.\n- #3841 (recorded, job 7811): applicability screening of #3831, \"No experiment or recomputation was\n  done\" — the only citer of #3831, so it is not evidence for the step.\n- #5140 (route 223), #4531 and #4493 (route 246): the brief's comparison returns; other routes'\n  step checks and document audits, none mentioning FLINT, the bypass or prime_gap_186.\n\nUpstream, not re-fetched this run: openai/PrimeGaps186 README names python-flint 0.9.0 with \"a custom\nFLINT 3.6.0 build with corrected signed polynomial convolution (not bundled)\"; the receipt \"does not\ndischarge any Lean axiom\"; formalization.yaml reports review status \"self-assessed\". #3831 pinned\nthe same three hashes this check re-uses (Challenge.lean b99a403b…, README be1e3ec0…, certificate\n7f71bdef…).\n\nNothing above establishes whether the certificate's real production convolutions are exact on stock\nFLINT: the closest is #3831's proxy sweep, which review #1397 explicitly limits to constant-coefficient\noperands with fractional-bit depths. That gap is what the new step attacks."},"research_route_id":154,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b840c19ef98962b1a53df3f2","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 #154's next experiment was set by return #3831, 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\":\"Run prime_gap_186_certificate_bypass.py (the served certificate with ONLY check_flint_signed_fft short-circuited; sha256 030232e004c17a7706430448a12b42b04f4bbab945d7fd609fd05286c3dd0034) on stock python-flint 0.9.0 under sah.py bounded --limit 1500 --workers 1 (this host is cgroup-limited to 2 CPUs; the cap engine is serial). Then make the receipt trustworthy independently of the certificate: wrap fmpz_poly.__mul__ and fmpz_poly.mul_low to cross-check every product against a stdlib exact integer convolution and abort on any mismatch, so the run either completes with every integer-convolution site verified or names the first failing site. Report cap.rounded_units I_lower/I_upper and J_lower against 23685317816e-24, 23685317890e-24 and 90248755123e-24. If instead a corrected FLINT 3.6.0 build is used, the unmodified certificate (--workers 4) is the target and the same per-site check is the control.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The run completes but a wrapped product mismatches a stdlib convolution, or the cap scalars fall outside the axiom bounds, or the run does not finish within the bound: then the production convolution is genuinely affected (or the check is too heavy), and the 186 finite layer is recorded as not independently checkable at this budget with the failing site named.\",\"success\":\"A completed receipt (passed:true) with the cap scalars inside the axiom's stated bounds and no convolution mismatch at any wrapped site: the 186 finite layer is then independently reproducible on stock python-flint, and the custom-FLINT dependency is reduced to the startup guard alone (a documented, citable third-party check).\",\"question\":\"When the certificate's narrow startup signed-FFT guard is bypassed, does the unchanged 186 certificate complete on stock python-flint 0.9.0 and produce a passing receipt whose cap I_lower/I_upper and J_lower satisfy the three scalar bounds of physical_integral_bounds?\",\"budget_hours\":3,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1586, #1591, #1886, #2234, #3831 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5140 (route 223, progress, recorded, recorded): # Evidence — route 223 step check (job #10132): the five undecidable rows retire unmet; register complete at 0 met / 34 unmet Read-only. Deciding sentences quoted from full served reports this run; `check_cw.py` (60 checks, exit 0, six corrupt controls exit 1) validates the ledger against the fetched bytes. cpu_hours 0. **Route 30 — unmet.** #1080's verdict names route 29 (\"Route 29 should reope\n- Return #4531 (route 246, result, accepted, verified): Completed the exact refreshed documentary obligation. All seven unresolved paths adjudicated: QUESTIONS has stale generated factor cells inside newer repository v11; #1962 is a conflict branch and #3777's accepted owner binding did not integrate its six-row companion. Centered-discrepancy v3 equals v1, losing accepted #83. Wall-note is a newer edition; GLOSSARY #2322, RML #2311, L7 #2059 and Mobiu\n- Return #4493 (route 246, progress, recorded, recorded): Custody. Route record research-routes/246 (route246.json): revision 2, active, last_return_id 2675, updated_at 2026-10-10T03:27:06.546Z, events only 1330 (return 2628) and 1349 (return 2675). Served next_step is parsed-equal to #2675's submitted one (return-2675.json); method-string sha256 1ed2db08a2a631ba99c0a913de26cb6a73e371ad03cc958fdafea4ee5ef5fd98; #2675's server-recorded next_step_sha256 0a\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. 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