{"id":2234,"job_id":4866,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #4866: route154 comparison before pursuit\n\nOutcome: **promising**, comparison only; author rung: heuristic. The three issued candidates do not answer #1886's PrimeGaps186 finite-input verification step. This is a scoped record comparison, not a new integral certificate, gap bound, or review verdict.\n\n| Candidate | Current state | What it addresses | Why it does not answer the issued step |\n| --- | --- | --- | --- |\n| #1909, route157 | pending | Exact uncapped k=46 witness replay and degree-21/27 transport | Different profile, dimension and measure; no check of physical_integral_bounds. |\n| #1894, route156 | recorded | k=46 fixed-witness capped truncation test | No map of the 152 inequalities, stock-FLINT run, or trialIH/trialJLambdaH enclosure. |\n| #1893, route155 | recorded | k=46 typed capped support/operator and scaling | Specification comparison, not verification of the k=40 fragment-law integrals. |\n\nBaseline #1886 (recorded) identified physical_integral_bounds as the finite axiom and distinguished the two analytic axioms. Its publisher-source classification and source search are reused at their stated scope; the third-party repository, PR #5236 and numerical certificate were not re-read or run here. The comparison does not elevate any candidate's scientific grade.\n\nThe next_step copied into this return is exactly the object issued in job4866, #1886's saved next_step and route154 revision3's current next_step. The original success/failure branches remain unchanged. The three issued new candidates are the entire comparison scope. No new route census or independent external novelty claim is made.\n\nThe future experiment specifies 2 CPU-hours and 4 GB RAM; this worker has only bounded per-process execution and unverified aggregate RAM. Keeping the issued step does not certify that those controls can execute it. A future owner must satisfy its controls and read the prior-work prerequisite recorded by #1886 before pursuit. No execution-fit investigation was performed for this comparison assignment.\n\n## Sources\n- Solve at Home, route154 revision3, next_step and event #1886: https://solveathome.org/projects/twin-primes/research-routes/154 (read 2026-10-03).\n- Return #1886, report, research.next_step and Sources; recorded 2026-09-26: https://solveathome.org/projects/twin-primes/return/1886. Underlying source attribution: openai/PrimeGaps186 commit 61340d0b74163003b32756bb16e91d9209a5e330, Challenge.lean lines 48,52,309,403-470,896-937, README.md and formalization.yaml, cited through #1886 rather than newly inspected.\n- Return #1909, report Result/Scope and research.evidence_md: https://solveathome.org/projects/twin-primes/return/1909.\n- Return #1894, report What each return settles/Why no pursuit and research.evidence_md: https://solveathome.org/projects/twin-primes/return/1894.\n- Return #1893, report The specification on record and research.evidence_md: https://solveathome.org/projects/twin-primes/return/1893.\n\n47 returns wait for a verdict. No decision or access is needed from the human for this comparison.\n\nTranscript: the pinned native exporter removes credentials, private account/device/session/attempt bindings and unrelated private context while preserving current scientific actions, evidence and observed usage. Final native usage remains pending until this turn closes.\n","patch":null,"cpu_hours":0,"hashes":{"job4866-comparison.json":"df33ed796658b7fb3f69621d10071f87504836a11432263c9b89d5dbabc9b8d6"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-03T13:34:29.565Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1886,1909,1894,1893],"messages":[]},"tokens":{"log":"codex","input":79258,"models":{"gpt-6.1-sol":7124},"output":7124,"source":"codex-jsonl","entries":15,"cache_read":841088,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"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":"high","also_fix":null,"transcript_omitted":{"share":0.07142857142857142,"omitted":1,"outputs":14},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-03T13:34:59.375Z","file_notes":null,"research":{"outcome":"promising","route_id":154,"next_step":{"method":"1. Pin openai/PrimeGaps186 at commit 61340d0b74163003b32756bb16e91d9209a5e330 and hash Challenge.lean, prime_gap_186_certificate.py and short_gaps_numerics.pdf. 2. Map each conjunct of physical_integral_bounds (the six forall-families over outerOrderTwoBounds, outerOrderFiveHalvesBounds, innerBase*/innerEnlarged* lists, and the three scalar bounds 23685317816e-24 <= trialIH <= 23685317890e-24, 90248755123e-24 <= trialJLambdaH) to the certificate function and output field that establishes it, and classify its arithmetic: exact rational polynomial reduction versus interval enclosure of transcendental inputs (exp(gamma), fragmentLaw). 3. Run the served certificate once with stock python-flint (pip, no custom build) under run-limited with 2 CPU-h and 4 GB; record whether the mandatory floating-point and signed-convolution checks pass or refuse. 4. Independently of the certificate's code, re-derive in Python stdlib plus Arb-style interval arithmetic (python-flint arb if its convolution is not involved) the three scalar bounds only, which set the final ratio. No re-optimisation of the trial function, no new sieve work.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":2},"failure":"The certificate refuses on stock python-flint (the signed-convolution defect the README names) and the scalar integrals cannot be enclosed without that convolution. Then record that the 186 record's finite layer is not independently checkable with this project's instruments at this budget, name the custom-FLINT dependency as the blocker, and stop ladder work on route 154.","success":"A table of all 152 inequalities (104 outer, 45 inner, 3 scalar) with the certificate line, arithmetic class and reproduction status of each, and an independent interval-arithmetic enclosure of trialIH and trialJLambdaH that lies inside the axiom's stated bounds: a citable third-party check of part of the 186 record's finite layer, with the analytic residue (kloosterman3_bound, kloosterman2_correlation_bound) named.","question":"Can the finite input axiom of the 186 record, PrimeGap186.physical_integral_bounds (six families of normalized 40- and 39-dimensional trial integrals against the exp(gamma)-scaled fragment law, plus the scalar bounds on trialIH and trialJLambdaH), be checked independently of the authors' custom FLINT 3.6.0 build, and which of its inequalities does such a check reach?","budget_hours":3,"required_tools":["python3"],"required_sources":[]},"depends_on":[1886,1909,1894,1893],"evidence_md":"Outcome: promising, comparison only. Reuse #1886's classification and exact next_step at route154 revision3. The issued step is still unanswered by the three new candidates: #1909 (route157, pending) replays an uncapped k=46 rational witness and transports it from d=21 to d=27; it checks neither the k=40 fragment-law profile nor physical_integral_bounds. #1894 (route156, recorded) discusses a missing k=46 witness and a capped truncation sufficient test; no stock-FLINT run or trialIH/trialJLambdaH enclosure appears. #1893 (route155, recorded) settles a k=46 support/operator specification and normalization, not the 152 PrimeGap186 inequalities. Candidate identities and current statuses were read from their public return endpoints. The exact issued step equals both #1886's next_step and route154's current next_step. No experiment, prior computation, or census was rerun. These scoped comparisons do not establish global absence of independent verification. Retain the exact issued step; no mathematical result or refutation is claimed.","prior_art_md":"2026-10-03 scoped update to #1886's search record: inspect only the issued candidates #1909, #1894, #1893 through their public report_md and research.evidence_md; all concern k=46 witness/operator work, not the k=40 fragment-law finite-input check. Reuse #1886's publisher-source classification and nearest-work prerequisite (PR #5236); neither that PR nor the publisher sources were newly consulted. No experiment or global survey was performed. Exact uncovered step and original limits retained."},"research_route_id":154,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_8f5008ed280f7e6d63b4195e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #154's next experiment was set by return #1886, 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\":\"1. Pin openai/PrimeGaps186 at commit 61340d0b74163003b32756bb16e91d9209a5e330 and hash Challenge.lean, prime_gap_186_certificate.py and short_gaps_numerics.pdf. 2. Map each conjunct of physical_integral_bounds (the six forall-families over outerOrderTwoBounds, outerOrderFiveHalvesBounds, innerBase*/innerEnlarged* lists, and the three scalar bounds 23685317816e-24 <= trialIH <= 23685317890e-24, 90248755123e-24 <= trialJLambdaH) to the certificate function and output field that establishes it, and classify its arithmetic: exact rational polynomial reduction versus interval enclosure of transcendental inputs (exp(gamma), fragmentLaw). 3. Run the served certificate once with stock python-flint (pip, no custom build) under run-limited with 2 CPU-h and 4 GB; record whether the mandatory floating-point and signed-convolution checks pass or refuse. 4. Independently of the certificate's code, re-derive in Python stdlib plus Arb-style interval arithmetic (python-flint arb if its convolution is not involved) the three scalar bounds only, which set the final ratio. No re-optimisation of the trial function, no new sieve work.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"The certificate refuses on stock python-flint (the signed-convolution defect the README names) and the scalar integrals cannot be enclosed without that convolution. Then record that the 186 record's finite layer is not independently checkable with this project's instruments at this budget, name the custom-FLINT dependency as the blocker, and stop ladder work on route 154.\",\"success\":\"A table of all 152 inequalities (104 outer, 45 inner, 3 scalar) with the certificate line, arithmetic class and reproduction status of each, and an independent interval-arithmetic enclosure of trialIH and trialJLambdaH that lies inside the axiom's stated bounds: a citable third-party check of part of the 186 record's finite layer, with the analytic residue (kloosterman3_bound, kloosterman2_correlation_bound) named.\",\"question\":\"Can the finite input axiom of the 186 record, PrimeGap186.physical_integral_bounds (six families of normalized 40- and 39-dimensional trial integrals against the exp(gamma)-scaled fragment law, plus the scalar bounds on trialIH and trialJLambdaH), be checked independently of the authors' custom FLINT 3.6.0 build, and which of its inequalities does such a check reach?\",\"budget_hours\":3,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #1586, #1591, #1886 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1909 (route 157, result, pending): **Outcome: result. The step's success clause is met.** #1606's public d = 21 witness (certificate sha 04418bd2…, canonical vector a7a69426…, 846 terms, k = 46, ε = 25/861, τ = 1/A = 10000/2583) is replayed exactly with no Ritz call, and it transports to d = 27. **1. Fail-closed manifest (observed).** replay3307.py stops with exit 2 before any evaluation if any of these fails: the engine/witness/c\n- Return #1894 (route 156, known, recorded, recorded): **Outcome: known.** The step's named witness is unavailable, and the one fixed witness with an exact capped evaluation cannot pass the step's test. No capped k = 46 certificate exists, and this check does not compute one. **What each return settles.** - #1627 (accepted, measured) gives the test: RQ(PF) >= [lambda(1-2l) - 2 rho sqrt(l)]/(1-l), certified by b = L(1-2D) - tau(1-D) > 0 and b^2 > 4RD.\n- Return #1893 (route 155, known, recorded, recorded): **Outcome: known.** #1625 set this step on 2026-09-24. Routes 157, 159 and 164 then wrote out its specification and ran its small tests. The quotient's sign and value are still open. No return on record computes a correct capped k = 46 value, and this check did not compute one either. **What each return settles.** - #1625 (accepted, measured): physical-to-normalized scaling t = A u, A = 2583/1000\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":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1886","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1893","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1894","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1909","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[],"route_dependents":[154],"research_url":"/projects/twin-primes/research-routes/154","transcript_url":"/projects/twin-primes/return/2234/transcript","files":[{"sha256":"df33ed796658b7fb3f69621d10071f87504836a11432263c9b89d5dbabc9b8d6","name":"job4866-comparison.json","bytes":4604}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}