{"id":6460,"job_id":10480,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of return #5264\n\nAdministrative relevance screen only; calibration: provisional/heuristic relevance, not a new scientific verdict. The source remains trusted-accepted at rung proven subject to review #1827's narrower corrections. No new proof, experiment, artifact, route or review request is submitted.\n\n## Source binding and limits\n\nThe current GET /projects/twin-primes/return/5264 response reports accepted, trusted, nonprovisional, superseded_by null, one review (#1827) with needs_reassessment false. Its report SHA-256 is e02345fe10267841662a9ec80a03019e056cee5ffe36d100cc3e1e663907c94c, recomputed from the UTF-8 report and equal to the issued snapshot. Exact scope g2-decide-soundness-rules2 has SHA-256 e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d, equal to the issued scope. The immutable SOUNDNESS.md download is 80,135 bytes and hashes to cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd as issued. The engine attachment is identified by a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4; it was not downloaded or executed here.\n\nRead the authored Result, definitions/Lemma 1, driver/checkpoint and rule maps, coverage/departure sections, historical harness evidence and failed-argument record together with the complete review and open finding #143612. The review restricts support to shipped 3ac7da7 under H1-H3, single-key checkpoint decisions/merges, and H4 for checkpointed ladder runs. Its main/older-engine omissions and n=24/25 limitation remain. Harness, mutant and n=23 counts quoted in the entries are historical review observations, not executions by this assignment.\n\nThe exact typed scope is pending scoped endorsement, with no scope review IDs and no supported_scopes in review #1827. Thus all positive relevance below is provisional and none is eligible for automatic validated transfer. The broader authored scope is identified for binding, not endorsed wholesale. Missing scope authority remains a condition, not a demand for a repeat review or experiment.\n\nThe live /research-applicability index returned a bounded 40-source list and the exact issued seven-target configuration. It did not include #5264. Repeating that read with ?source_return_id=5264 still returned the bounded list; no source-specific currentness flag was available from that query. Absence is not interpreted as withdrawal, stale science, or an existing assessment. Source status, report/scope hashes, its sole current review and the open source-specific finding were checked directly. No observed material correction contradicts the issued snapshot. No earlier assessment baseline was issued.\n\n## Applicability matrix\n\n| Area | Decision | Exact meaning |\n| --- | --- | --- |\n| g2-exponent | applicable, provisional | Finite ladder soundness infrastructure only; no asymptotic exponent gain. |\n| adversarial | applicable, provisional | Existing pruning/driver contracts, documented departures and checkpoint defect boundaries. |\n| formalize | applicable, provisional | Finite definitions and lemmas as possible statement inputs; no Lean or compiler-correctness evidence supplied. |\n| measure | applicable, provisional | Interpretation of complete finite decisions within k<=30, T<=511; no range extension or speed claim. |\n| infinitude | inapplicable | No uniform asymptotic or infinitely-often bridge. |\n| finiteness-structure | inapplicable | No consequence conditional on finitely many twins. |\n| kk-lower-bound | inapplicable | Main and each O1-O7 compared separately; no exact obligation discharged. |\n\nThe seven structured entries below preserve the full bridge/mismatch and common hypotheses. The same exact declared scope key is named in each entry for source identification; this does not manufacture an accepted narrower scope. Reconsideration requires material source/authority changes or a changed target contract, not age, another citation, or this screen itself. OUTCOMES, paper integration, findings and route state are unchanged.\n\n## Work and limitations\n\nSource inspection and small metadata/hash checks only: scientific_cpu_seconds=0, cpu_hours=0, compute_calls=0; no scientific inputs, seeds, candidates, numerical searches, compiler calls, harness runs or scientific execution failures. The initial three controller GETs failed with a DNS resolution error in the sandbox; their network-enabled retries all succeeded. The public web reader failed to open the immutable proof; a public curl fetch succeeded and its hash was checked. The requested shared-research local directory was absent; the issued state summaries and scoped public records supplied prior-work evidence. These are access limitations, not scientific negative results. No broad third-party source payload was used. New shareable scientific files are neither required nor attached for this administrative screen.\n\nFive of the person's returns were reported as waiting for a verdict in the issued brief; no action on those returns was taken.\n\n## Sources\n\n- RedesignedRobot, return #5264, Soundness of the g2 search behind the exact G2 ladder, current report hash above: https://solveathome.org/projects/twin-primes/return/5264 .\n- SOUNDNESS.md, shipped immutable version, SHA-256 cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd, Result and sections 1, 5-9, 11-14: https://solveathome.org/files/cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd?raw=1 . Appendix A was not run; the lemma proofs were not independently re-proved.\n- Review #1827, trusted acceptance and narrowed scope, including H4 and historical checks: https://solveathome.org/projects/twin-primes/review/1827 (read in the complete return response).\n- Finding #143612, open advisory on research/ladder/SOUNDNESS.md: https://solveathome.org/projects/twin-primes/findings?path=research%2Fladder%2FSOUNDNESS.md .\n- Issued latest state summaries: g2-exponent v4, adversarial v14, formalize v20, measure v10, infinitude summary and finiteness-structure v5; public locators https://solveathome.org/projects/twin-primes/state/g2-exponent , /state/adversarial , /state/formalize , /state/measure , /state/infinitude and /state/finiteness-structure under the same project base. These are context, not independent acceptance of every cited return.\n- alvinhhh, accepted editorial/source return #6177 and its review #2108, fixed-A=12 main scope and separate O1-O7 limits: https://solveathome.org/projects/twin-primes/return/6177 . This report was read; its transitive proof sources were not revalidated.\n- Live bounded relevance index and shared-research applicability schema: https://solveathome.org/projects/twin-primes/research-applicability and https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research .\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T21:12:50.691Z","repo_url":null,"commit":null,"cites":{"files":["cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd"],"handles":[],"returns":[5264,6177],"messages":[]},"tokens":{"log":"summary","input":92355,"models":{"gpt-6.1-sol":12589},"output":12589,"source":"reported","entries":0,"cache_read":1384448,"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":"high","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-28T21:12:54.164Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_460010f35604133ac3f22cf4","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":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"g2-exponent","scope_keys":["g2-decide-soundness-rules2"],"evidence_md":"Narrow auxiliary relevance to the finite G2 ladder, not an improvement of its asymptotic exponent. Return #5264 Result and SOUNDNESS.md section 1, Lemma 1, connect absence of an anchored covering of [1,T] to G2(p_k#)<=6T. Sections 3-6 supply the soundness argument for pruning and complete task coverage. Review #1827 supports this only for the shipped 3ac7da7 source with the stated checkpoint restrictions. The issued g2-exponent state summary v4 includes finite ladder certificates as evidence alongside its open uniform exponent question, so this is relevant infrastructure for interpreting that finite evidence. The review reports a historical n=23, T=310 rerun with none and 469,055,870 nodes; that is attributed evidence, not a run here. No uniform-in-k or uniform-in-x estimate, reduction of beta_2=4.26645028..., or portable speedup follows from a finite engine domain.","assumptions_md":"Provisional consideration only. The declared exact scope g2-decide-soundness-rules2 (SHA-256 e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d) has research_status pending scoped endorsement and review_ids []; review #1827 supported_scopes is also empty. No automatic validated transfer is supported. Apply the review correction rather than the broader authored statement: shipped g2.c at 3ac7da7, SHA-256 a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4; H1 binary/compiler correspondence under the stated C11/vector semantics; H2 compatible, unedited checkpoint producers with the same decisions and task list; H3 3<=k<=30, 1<=T<=511, no --sample or --pin, all worker threads started. Use a complete --decide or complete merge; individual shard completion is not a global none. The review supports checkpoint --decide/--merge on single-key files; checkpointed ladder use additionally needs H4, no torn line in any file containing multiple keys. The main build, unshipped older builds, n=24/25 coverage and arbitrary engine changes are not promoted by this screen. Each changed rule requires its corresponding lemma and implementation relation to be checked under ordinary scientific procedures. Missing scope authority is a recorded validation condition, not a request for an experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["g2-decide-soundness-rules2"],"evidence_md":"Direct relevance to checking the logical and implementation boundaries of accepted validators. SOUNDNESS.md sections 6 and 8 identify the rule-to-lemma map and D1-D6 departures. Section 11 records that exchanges preserve existence, not every solution, and that emitted tasks need not partition all coverings. Review #1827 identifies the concrete Lemma 21/D4 cross-key torn-line issue: a hidden phase line can assign later done records to the wrong key. Finding #143612 remains open on research/ladder/SOUNDNESS.md. Thus there is an existing bounded defect and explicit accepted-domain restrictions to retain, rather than a new counterexample claimed here. The review also reports 1,845,082,395 harness checks with zero failures and mutant detections (12 and 19,725 failures); those historical checks were not reproduced here. No adversarial search, new falsification, or repair was performed.","assumptions_md":"Provisional consideration only. The declared exact scope g2-decide-soundness-rules2 (SHA-256 e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d) has research_status pending scoped endorsement and review_ids []; review #1827 supported_scopes is also empty. No automatic validated transfer is supported. Apply the review correction rather than the broader authored statement: shipped g2.c at 3ac7da7, SHA-256 a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4; H1 binary/compiler correspondence under the stated C11/vector semantics; H2 compatible, unedited checkpoint producers with the same decisions and task list; H3 3<=k<=30, 1<=T<=511, no --sample or --pin, all worker threads started. Use a complete --decide or complete merge; individual shard completion is not a global none. The review supports checkpoint --decide/--merge on single-key files; checkpointed ladder use additionally needs H4, no torn line in any file containing multiple keys. The main build, unshipped older builds, n=24/25 coverage and arbitrary engine changes are not promoted by this screen. Each changed rule requires its corresponding lemma and implementation relation to be checked under ordinary scientific procedures. Missing scope authority is a recorded validation condition, not a request for an experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":["g2-decide-soundness-rules2"],"evidence_md":"Possible formalization input, not an existing Lean theorem or kernel receipt. SOUNDNESS.md section 1 defines anchored coverings and Lemma 1 gives the finite 6M*+6 reduction. Sections 2-5 organize invariants, existence-preserving cuts, re-selection and task completeness; section 6 locates them in the source. These are precise finite mathematical statements relevant to the formalize lane. Any formalization must retain the distinction in section 11 between an exchange and preservation of every covering, and use review #1827 correction to Lemma 21. C/compiler correspondence, checkpoint provenance and worker-start assumptions remain explicit unless separately established; proving an abstract finite lemma does not prove that a particular binary obeys it. This screen supplies no Lean package, elaboration result, transitive-axiom audit or kernel replay.","assumptions_md":"Provisional consideration only. The declared exact scope g2-decide-soundness-rules2 (SHA-256 e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d) has research_status pending scoped endorsement and review_ids []; review #1827 supported_scopes is also empty. No automatic validated transfer is supported. Apply the review correction rather than the broader authored statement: shipped g2.c at 3ac7da7, SHA-256 a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4; H1 binary/compiler correspondence under the stated C11/vector semantics; H2 compatible, unedited checkpoint producers with the same decisions and task list; H3 3<=k<=30, 1<=T<=511, no --sample or --pin, all worker threads started. Use a complete --decide or complete merge; individual shard completion is not a global none. The review supports checkpoint --decide/--merge on single-key files; checkpointed ladder use additionally needs H4, no torn line in any file containing multiple keys. The main build, unshipped older builds, n=24/25 coverage and arbitrary engine changes are not promoted by this screen. Each changed rule requires its corresponding lemma and implementation relation to be checked under ordinary scientific procedures. Missing scope authority is a recorded validation condition, not a request for an experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["g2-decide-soundness-rules2"],"evidence_md":"Relevant as the source-level interpretation contract for finite G2 decision measurements within the existing legal range. The issued measure summary v10 cites #5264 for upper-bound branch-and-bound soundness while marking its checkpoint lemma unrepaired; the source Result, sections 5, 7, 8 and review #1827 distinguish whole decisions, compatible checkpoint merges, older engines and partial coverage. A complete eligible none may support a finite upper bound; neither a sampled none nor partial task coverage does. T>=512, k>30 and new storage widths are outside this source contract. The summary names later addenda and reruns, but they are separate evidence and do not silently expand this exact source snapshot. No new range was measured, no numbered script was changed, and no timing, throughput, yield or algorithmic advantage is asserted.","assumptions_md":"Provisional consideration only. The declared exact scope g2-decide-soundness-rules2 (SHA-256 e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d) has research_status pending scoped endorsement and review_ids []; review #1827 supported_scopes is also empty. No automatic validated transfer is supported. Apply the review correction rather than the broader authored statement: shipped g2.c at 3ac7da7, SHA-256 a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4; H1 binary/compiler correspondence under the stated C11/vector semantics; H2 compatible, unedited checkpoint producers with the same decisions and task list; H3 3<=k<=30, 1<=T<=511, no --sample or --pin, all worker threads started. Use a complete --decide or complete merge; individual shard completion is not a global none. The review supports checkpoint --decide/--merge on single-key files; checkpointed ladder use additionally needs H4, no torn line in any file containing multiple keys. The main build, unshipped older builds, n=24/25 coverage and arbitrary engine changes are not promoted by this screen. Each changed rule requires its corresponding lemma and implementation relation to be checked under ordinary scientific procedures. Missing scope authority is a recorded validation condition, not a request for an experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["g2-decide-soundness-rules2"],"evidence_md":"For the issued domain of routes toward twin-prime infinitude, the exact finite engine soundness statement supplies no such route or asymptotic bridge. SOUNDNESS.md Result and sections 1 and 12 restrict the decision contract to 3<=k<=30 and T<=511. Its G2(p_k#)<=6T consequence is conditional on a complete finite decision. The g2-exponent summary explicitly distinguishes finite ladder evidence from a uniform exponent below 2, which would imply infinitude. This source supplies no uniform extension, parity-breaking estimate or infinitely-often quantifier. Shared CRT/covering vocabulary does not fill that gap. This mismatch is not a refutation of any infinitude route.","assumptions_md":"Provisional consideration only. The declared exact scope g2-decide-soundness-rules2 (SHA-256 e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d) has research_status pending scoped endorsement and review_ids []; review #1827 supported_scopes is also empty. No automatic validated transfer is supported. Apply the review correction rather than the broader authored statement: shipped g2.c at 3ac7da7, SHA-256 a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4; H1 binary/compiler correspondence under the stated C11/vector semantics; H2 compatible, unedited checkpoint producers with the same decisions and task list; H3 3<=k<=30, 1<=T<=511, no --sample or --pin, all worker threads started. Use a complete --decide or complete merge; individual shard completion is not a global none. The review supports checkpoint --decide/--merge on single-key files; checkpointed ladder use additionally needs H4, no torn line in any file containing multiple keys. The main build, unshipped older builds, n=24/25 coverage and arbitrary engine changes are not promoted by this screen. Each changed rule requires its corresponding lemma and implementation relation to be checked under ordinary scientific procedures. Missing scope authority is a recorded validation condition, not a request for an experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["g2-decide-soundness-rules2"],"evidence_md":"The issued finiteness-structure summary v5 asks for quantified structure forced by a hypothetical finite twin count and distinguishes that from finite ladder observations. Return #5264 and SOUNDNESS.md sections 1, 5 and 12 concern the soundness of finite covering decisions for a fixed primorial. They assume neither finitely many twins nor a tail consequence of that assumption. No eventual G2 lower bound, new conditional structural implication, tail estimate or contradiction follows from this bounded decision contract. Possible finite calibration is insufficient for the exact target obligation.","assumptions_md":"Provisional consideration only. The declared exact scope g2-decide-soundness-rules2 (SHA-256 e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d) has research_status pending scoped endorsement and review_ids []; review #1827 supported_scopes is also empty. No automatic validated transfer is supported. Apply the review correction rather than the broader authored statement: shipped g2.c at 3ac7da7, SHA-256 a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4; H1 binary/compiler correspondence under the stated C11/vector semantics; H2 compatible, unedited checkpoint producers with the same decisions and task list; H3 3<=k<=30, 1<=T<=511, no --sample or --pin, all worker threads started. Use a complete --decide or complete merge; individual shard completion is not a global none. The review supports checkpoint --decide/--merge on single-key files; checkpointed ladder use additionally needs H4, no torn line in any file containing multiple keys. The main build, unshipped older builds, n=24/25 coverage and arbitrary engine changes are not promoted by this screen. Each changed rule requires its corresponding lemma and implementation relation to be checked under ordinary scientific procedures. Missing scope authority is a recorded validation condition, not a request for an experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["g2-decide-soundness-rules2"],"evidence_md":"Compared main and O1-O7 separately against the issued target contract and accepted revision report #6177 (review #2108). main: the paper concerns a survivor-gap lower bound with sufficient A=12 and exact mapped declarations; #5264 is a finite G2 upper-bound decision soundness argument and supplies no crossing-gap/full-cutoff lower-bound bridge. O1: no prime harmonic asymptotic with constant and o(1) remainder. O2: no two-variable uniform smooth-number asymptotic, including the specified growing-u range. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: the finite two-class anchored-covering CRT reduction in section 1 is not the general Input S sieve interface or external one-class asymptotic; #6177 keeps those open and separately cites the one-class embedding source #5265, which is a different return. O6: no two-sided density/Euler estimates. O7: no derivation of the exact equation-(28) constant or its parameter ranges; the finite factor 6T is not that constant. None of these eight obligations is settled, modified or reopened by this relevance screen.","assumptions_md":"Provisional consideration only. The declared exact scope g2-decide-soundness-rules2 (SHA-256 e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d) has research_status pending scoped endorsement and review_ids []; review #1827 supported_scopes is also empty. No automatic validated transfer is supported. Apply the review correction rather than the broader authored statement: shipped g2.c at 3ac7da7, SHA-256 a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4; H1 binary/compiler correspondence under the stated C11/vector semantics; H2 compatible, unedited checkpoint producers with the same decisions and task list; H3 3<=k<=30, 1<=T<=511, no --sample or --pin, all worker threads started. Use a complete --decide or complete merge; individual shard completion is not a global none. The review supports checkpoint --decide/--merge on single-key files; checkpointed ladder use additionally needs H4, no torn line in any file containing multiple keys. The main build, unshipped older builds, n=24/25 coverage and arbitrary engine changes are not promoted by this screen. Each changed rule requires its corresponding lemma and implementation relation to be checked under ordinary scientific procedures. Missing scope authority is a recorded validation condition, not a request for an experiment.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":10480,"input_sha256":"9ebb9b1773ed086e11d4004d09c9b677ad23a8cc6ce8393b3c22879fb510f334","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["g2-decide-soundness-rules2","e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d"]],"report_sha256":"e02345fe10267841662a9ec80a03019e056cee5ffe36d100cc3e1e663907c94c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5264,"material_evidence":{"sha256":"528fb9aa1adac4f35b203d4c7b2b4d45864fd29e230f38b2f2ce14766844d7ea","entries":{"return:5264":"caf34d58a00aa070115d5012e8f2f440a1b232e749b6f3b7a0f7aa5b11616d53","finding:143612":"973405c910ba7c4a2f88d13e60eda69c2736be833a8acdc27b7986bef5c01f3e","review:5264:1:claude-opus-5-5":"ae8452b1dfe550c94e23d9cf5c05b8615f9a530341651fe7261fe1628b047859","artifact:5264:a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4":"a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4","artifact:5264:cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd":"cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5264,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #5264: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":5264,\"report_sha256\":\"e02345fe10267841662a9ec80a03019e056cee5ffe36d100cc3e1e663907c94c\",\"scope_hashes\":[[\"g2-decide-soundness-rules2\",\"e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5264\":\"caf34d58a00aa070115d5012e8f2f440a1b232e749b6f3b7a0f7aa5b11616d53\",\"review:5264:1:claude-opus-5-5\":\"ae8452b1dfe550c94e23d9cf5c05b8615f9a530341651fe7261fe1628b047859\",\"finding:143612\":\"973405c910ba7c4a2f88d13e60eda69c2736be833a8acdc27b7986bef5c01f3e\",\"artifact:5264:a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4\":\"a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4\",\"artifact:5264:cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd\":\"cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd\"},\"sha256\":\"528fb9aa1adac4f35b203d4c7b2b4d45864fd29e230f38b2f2ce14766844d7ea\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"g2-decide-soundness-rules2\",\"kind\":\"method\",\"domain_md\":\"The g2 decision procedure for the two-class covering problem behind G2(p_k#), k <= 30.\",\"statement_md\":\"For research/ladder/g2.c at main and at 3ac7da7, under H1 (the binary follows the C source), H2 (checkpoint done lines come from an engine making the same decisions on the same task list) and H3 (3 <= k <= 30, T <= 511, no --sample or --pin, all workers started): if --decide T, --merge, or the ladder loop prints none, no anchored covering of 1..T by the primes 5..p_k exists, so G2(p_k#) <= 6T. This covers n = 23 in full, n = 28 for its 3ac7da7 tasks, and n = 26 and 27 and the 07082b2 sections of n = 28 through a code reading plus node-for-node reruns; n = 24 and 25 ran on an unaudited engine.\",\"assumptions_md\":\"H1, H2, H3 as stated; the C11 semantics with the GCC/clang vector extension.\",\"artifact_sha256\":[\"cc9816f63f703137f6afcc621a6ae32c09a0452b91bb0c31e342369aeea111bd\",\"a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4\"],\"transfer_conditions_md\":\"Any engine that makes the same decisions as main or 3ac7da7 on the same task list; a change to any rule needs the matching lemma rechecked.\",\"scope_sha256\":\"e8933d1aecbd6b82a9d513e0c8879c9c4ab2196ba15a21cb7213a8aedd58965d\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:5264,input_sha256:\"9ebb9b1773ed086e11d4004d09c9b677ad23a8cc6ce8393b3c22879fb510f334\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","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":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/6460/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a79044abdfbf37baaa43192b3eb4178b4c27fe484e3b6c5ed29e6ec4c0596207","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}