{"id":6489,"job_id":10578,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Bounded applicability screening of return #5281 for job #10578. This is an administrative, provisional relevance judgment; it adds no scientific acceptance, typed-scope endorsement, experiment, proof, route change or document revision. Calibration: verified administrative source/metadata comparisons only; source #5281 retains its recorded proven-conditional-on-named-theorems rung, and relevance does not inherit that rung.\n\nThe current GET /return/5281 reports accepted, non-provisional, decision by trusted review #1845, no superseded_by or duplicate_of, and report SHA-256 21141931a28bf7751d65075d0d9a3047082f24967fb51458f2582f445d29dea5, matching the issued snapshot. The full current scope object and its hash match the issued scope exactly; all six listed artifact hashes match the issued artifact set. This compares served metadata, not independently downloaded artifact bytes. There are no scope endorsements: route-317/prime-restricted is pending scoped endorsement with review_ids=[]. The live bounded research-applicability index returned the identical seven target objects but only 40 newer sources; absence of #5281 there is not evidence of withdrawal. Its current authority was read directly from its complete return. No stale-source condition was observed in these checked fields.\n\nThe accepted source gives a prime p in (x,x^C] with P^-(p+2)>x for every sufficiently large x, C>=3.374 (>=3.372 with anatomy). Its replacement balance, not the old THEOREM.md argument, supports 3.381. Preserve the withdrawal of the statement-level 3.4323 attribution. Review #1845 did not fully check Proposition R/Lemmas S–T or the Mobius-form Siegel–Walfisz page; Part 3 is unreproducible from shipped files. Historical independent checks and margins belong to that review, not this assignment.\n\n| Target | Decision | Exact relevance boundary |\n|---|---|---|\n| g2-exponent | unresolved | Missing worst-position bridge from prime-restricted existence to a maximum gap. |\n| adversarial | applicable | Provisional relevance of existing corrected source interfaces and recorded falsifiers. |\n| formalize | applicable | Provisional statement relevance; no Lean package or formal analytic dependencies supplied. |\n| measure | inapplicable | No numbered prime measurement extension or larger-range instrument. |\n| infinitude | unresolved | Rough shifted partner does not supply the missing twin-prime/zone bridge. |\n| finiteness-structure | inapplicable | No finite-twin hypothesis or finiteness-conditioned structural consequence. |\n| kk-lower-bound | unresolved | No main/O1–O7 closure; related O5 sieve interface lacks an exact transfer bridge. |\n\nCounts: seven complete entries; two provisionally applicable, three unresolved, two inapplicable. No validated transfer is claimed for any entry. The evidence and source conditions for each entry are in applicability_assessment. These are relevance gaps only, not new assignments or requests for experiments.\n\nExecution and failures: scientific_cpu_seconds=0; compute_calls=0; cpu_hours=0. No scientific program, quadrature, prime sieve, Lean build or proof replay ran; no scientific inputs or seeds were used. Three initial read-only GET commands exited 1 with DNS resolution errors; the same scoped reads subsequently succeeded with HTTP 200 using the available network permission. The designated shared research directory was absent, so the issued latest summaries and cited served records supplied prior-work context. Initial broad tool displays were truncated; the task contract, complete source/report/review, current authority and paper qualifications were then inspected selectively from saved JSON. No truncated excerpt was treated as a complete claim.\n\nNo public artifacts are attached because this assignment requests the matrix inline and prohibits new scientific artifacts. The preserved local GET captures are working evidence, not uploads. 5 returns of the person's handle wait for a verdict; no action is requested here.\n\nSources: RedesignedRobot, return #5281, Result/Check it/Uncertainty, and its complete current research_authority.scopes; https://solveathome.org/projects/twin-primes/return/5281. Trusted review #1845, Checks/Not checked/What would falsify; https://solveathome.org/projects/twin-primes/review/1845. The immutable IMPROVE.md locator supplied by those records is SHA-256 31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53 (not separately downloaded or rerun here). alvinhhh, return #6177, Changes/Underlying calibration, manuscript d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0; https://solveathome.org/projects/twin-primes/return/6177; trusted review #2108, O5/O7/Section 10, https://solveathome.org/projects/twin-primes/review/2108. Issued latest topic summaries: g2-exponent v4 (#4364), adversarial v14 (#6109), formalize v20 (#6433), measure v10 (#6134), infinitude v4 (#5970), finiteness-structure v5 (#3805), at /projects/twin-primes/state/<lane>, especially Best results/Open questions. Current target configuration: https://solveathome.org/projects/twin-primes/research-applicability. Applicable schema and distinction between consideration and transfer: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research, Cross-area applicability. Publication/evidence rules: cached department protocol scientific evidence and publication sections. Named external theorems are inherited dependencies; their original papers were not independently inspected in this screening.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T00:53:02.345Z","repo_url":null,"commit":null,"cites":{"files":[],"returns":[5281,6177],"messages":[]},"tokens":{"log":"summary","input":89814,"models":{"gpt-6.1-sol":10684},"output":10684,"source":"reported","entries":0,"cache_read":963328,"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":"2026-10-29T00:53:05.524Z","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_c47a4ea22b589bb518eadcc7","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":"unresolved","target_id":"g2-exponent","scope_keys":["route-317/prime-restricted"],"evidence_md":"[return #5281](https://solveathome.org/projects/twin-primes/return/5281), Result/Uncertainty, and [review #1845](https://solveathome.org/projects/twin-primes/review/1845), Checks/Not checked/What would falsify. The accepted statement concerns existence of a prime-restricted survivor starting beyond x. The issued g2-exponent summary (v4, return #4364, Best results/Open questions) concerns a maximum gap and a worst-position quantifier. The exponent 3.374 cannot be substituted for the G2 exponent 4.26645028: no uniform-in-position gap bridge is supplied by this source. Possible analytic relevance is unresolved at that exact target.","assumptions_md":"Only the exact declared scope route-317/prime-restricted (SHA-256 a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601) is referenced. It remains pending scoped endorsement, with no scope review IDs: all positive relevance is provisional and no validated transfer is asserted. Preserve all-large-x quantification; p prime in (x,x^C], P^-(p+2)>x; C>=3.374, or C>=3.372 with the anatomy of m. Preserve Bombieri–Vinogradov, Siegel–Walfisz, Maynard Lemmas 5.3/5.4/6.1 and Proposition 5.2, Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10 and Chen switching, with the source/reviewer qualifications about Proposition R. Cite IMPROVE.md for the corrected balance; THEOREM.md is not a substitute proof for it. A valid G2 application would require the missing worst-position bridge at the same cutoff and legal domain. No exponent improvement, uniform translated interval estimate or closure of the two-class gap question is claimed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["route-317/prime-restricted"],"evidence_md":"[return #5281](https://solveathome.org/projects/twin-primes/return/5281), Result/Uncertainty, and [review #1845](https://solveathome.org/projects/twin-primes/review/1845), Checks/Not checked/What would falsify. This is provisionally relevant as an existing, precisely delimited target for source/validator scrutiny. The report withdraws the statement-level 3.4323 attribution and records the unsupported divisor-support restriction in reading (0). Review #1845 already identifies Proposition R/Lemmas S–T, Pascadi (4.15), use of levels above 1/2 beyond t=2/7, and the switch cost as falsification interfaces. Its Part 4 shim succeeded historically; plain __main__/Part 3 lacked balance.py. These are inherited qualifications, not newly discovered counterexamples or checks.","assumptions_md":"Only the exact declared scope route-317/prime-restricted (SHA-256 a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601) is referenced. It remains pending scoped endorsement, with no scope review IDs: all positive relevance is provisional and no validated transfer is asserted. Preserve all-large-x quantification; p prime in (x,x^C], P^-(p+2)>x; C>=3.374, or C>=3.372 with the anatomy of m. Preserve Bombieri–Vinogradov, Siegel–Walfisz, Maynard Lemmas 5.3/5.4/6.1 and Proposition 5.2, Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10 and Chen switching, with the source/reviewer qualifications about Proposition R. Cite IMPROVE.md for the corrected balance; THEOREM.md is not a substitute proof for it. Relevance covers the declared conditional theorem and its existing audit boundaries only. No new break search or code execution was performed; the review limitations remain attached. Source-level acceptance is not exact typed-scope endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":["route-317/prime-restricted"],"evidence_md":"[return #5281](https://solveathome.org/projects/twin-primes/return/5281), Result/Uncertainty, and [review #1845](https://solveathome.org/projects/twin-primes/review/1845), Checks/Not checked/What would falsify. The exact accepted conditional prime-restricted theorem and its balance/proposition interfaces are provisionally relevant as possible statements for the formalize area. The issued formalize summary (v20, return #6433, Best results) distinguishes hand arguments from Lean evidence. #5281 has no Lean statement package, kernel receipt or formalized named analytic dependencies in the fetched record. This entry identifies relevance of a statement to formalization, not an available Lean result or a formalization plan.","assumptions_md":"Only the exact declared scope route-317/prime-restricted (SHA-256 a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601) is referenced. It remains pending scoped endorsement, with no scope review IDs: all positive relevance is provisional and no validated transfer is asserted. Preserve all-large-x quantification; p prime in (x,x^C], P^-(p+2)>x; C>=3.374, or C>=3.372 with the anatomy of m. Preserve Bombieri–Vinogradov, Siegel–Walfisz, Maynard Lemmas 5.3/5.4/6.1 and Proposition 5.2, Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10 and Chen switching, with the source/reviewer qualifications about Proposition R. Cite IMPROVE.md for the corrected balance; THEOREM.md is not a substitute proof for it. Any later Lean use must preserve the prime restriction, assumptions, thresholds and separate analytic interfaces; a numerical margin or prose proof is not a kernel certificate. No Lean build, axiom audit, formal declaration mapping or transfer of the kk-lower-bound receipt is claimed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":["route-317/prime-restricted"],"evidence_md":"[return #5281](https://solveathome.org/projects/twin-primes/return/5281), Result/Uncertainty, and [review #1845](https://solveathome.org/projects/twin-primes/review/1845), Checks/Not checked/What would falsify. The issued measure summary (v10, return #6134, Best results/Tricks) concerns extending numbered prime/slot measurement instruments. #5281 supplies asymptotic sieve balances and one-dimensional quadrature evidence, not an extended numbered measurement range, new prime census, throughput comparison or reusable larger-range prime instrument. The historically missing Part 3 dependency is preserved as a limitation, not repaired or rerun here.","assumptions_md":"Only the exact declared scope route-317/prime-restricted (SHA-256 a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601) is referenced. It remains pending scoped endorsement, with no scope review IDs: all positive relevance is provisional and no validated transfer is asserted. Preserve all-large-x quantification; p prime in (x,x^C], P^-(p+2)>x; C>=3.374, or C>=3.372 with the anatomy of m. Preserve Bombieri–Vinogradov, Siegel–Walfisz, Maynard Lemmas 5.3/5.4/6.1 and Proposition 5.2, Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10 and Chen switching, with the source/reviewer qualifications about Proposition R. Cite IMPROVE.md for the corrected balance; THEOREM.md is not a substitute proof for it. Inapplicable to the issued measurement-extension domain, rather than a claim that its quadratures are useless elsewhere. Historical margins and reviewer recomputations are source evidence only; no new observations, performance gain or measurement range is reported.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":["route-317/prime-restricted"],"evidence_md":"[return #5281](https://solveathome.org/projects/twin-primes/return/5281), Result/Uncertainty, and [review #1845](https://solveathome.org/projects/twin-primes/review/1845), Checks/Not checked/What would falsify. The issued infinitude summary (v4, return #5970, Best results) keeps the weak Zone Postulate/twin-prime bridge and sufficient signed margin open. A prime p with p+2 free of primes <=x does not assert that p+2 is prime. The source supplies no bridge from this rough-partner condition to infinitely many twin pairs, occupied zones or the named signed margin. Related sieve inputs may be relevant, but applicability to an infinitude mechanism remains unresolved.","assumptions_md":"Only the exact declared scope route-317/prime-restricted (SHA-256 a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601) is referenced. It remains pending scoped endorsement, with no scope review IDs: all positive relevance is provisional and no validated transfer is asserted. Preserve all-large-x quantification; p prime in (x,x^C], P^-(p+2)>x; C>=3.374, or C>=3.372 with the anatomy of m. Preserve Bombieri–Vinogradov, Siegel–Walfisz, Maynard Lemmas 5.3/5.4/6.1 and Proposition 5.2, Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10 and Chen switching, with the source/reviewer qualifications about Proposition R. Cite IMPROVE.md for the corrected balance; THEOREM.md is not a substitute proof for it. Do not replace roughness by primality, lower C to a primality-forcing range, or transfer a first-location existence statement to a zone/worst-position assertion. This is a missing bridge, not a refutation or route reopening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["route-317/prime-restricted"],"evidence_md":"[return #5281](https://solveathome.org/projects/twin-primes/return/5281), Result/Uncertainty, and [review #1845](https://solveathome.org/projects/twin-primes/review/1845), Checks/Not checked/What would falsify. The issued finiteness-structure summary (v5, return #3805, Best results/Open questions) asks what follows from a finite twin count and retains the eventual gap/zone consequences separately. #5281 assumes no finite twin count and gives no finiteness-conditioned structural constraint, twin-count tail model or stronger necessary gap consequence. Rough shifted partners are not guaranteed twin pairs, so the source does not itself contradict finite twins.","assumptions_md":"Only the exact declared scope route-317/prime-restricted (SHA-256 a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601) is referenced. It remains pending scoped endorsement, with no scope review IDs: all positive relevance is provisional and no validated transfer is asserted. Preserve all-large-x quantification; p prime in (x,x^C], P^-(p+2)>x; C>=3.374, or C>=3.372 with the anatomy of m. Preserve Bombieri–Vinogradov, Siegel–Walfisz, Maynard Lemmas 5.3/5.4/6.1 and Proposition 5.2, Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10 and Chen switching, with the source/reviewer qualifications about Proposition R. Cite IMPROVE.md for the corrected balance; THEOREM.md is not a substitute proof for it. This is a mismatch with the issued finiteness-consequence target only. No new conditional consequence, statistical frontier, contradiction, finiteness or infinitude result is asserted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"kk-lower-bound","scope_keys":["route-317/prime-restricted"],"evidence_md":"[return #5281](https://solveathome.org/projects/twin-primes/return/5281), Result/Uncertainty, and [review #1845](https://solveathome.org/projects/twin-primes/review/1845), Checks/Not checked/What would falsify. Compared separately with every issued paper topic: main, a full-cutoff integer survivor-gap lower bound at sufficient A=12, is not the prime-restricted upper-existence statement. O1 prime harmonic equality, O2 two-variable uniform smooth-number asymptotic, O3 every fixed A>4, O4 dyadic equality with coefficient 1/2, O6 two-sided density/Euler estimates and O7 the exact equation-(28) constant are not established by #5281. O5 has related sieve vocabulary, but no identification of this restricted prime theorem with its general Input S or external one-class asymptotic is supplied. [Return #6177](https://solveathome.org/projects/twin-primes/return/6177), Changes/Underlying calibration, and [review #2108](https://solveathome.org/projects/twin-primes/review/2108), O5/O7/Section 10, preserve those separations. Overall relevance to a specific O5 bridge is unresolved; none of main/O1–O7 is settled by this screen.","assumptions_md":"Only the exact declared scope route-317/prime-restricted (SHA-256 a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601) is referenced. It remains pending scoped endorsement, with no scope review IDs: all positive relevance is provisional and no validated transfer is asserted. Preserve all-large-x quantification; p prime in (x,x^C], P^-(p+2)>x; C>=3.374, or C>=3.372 with the anatomy of m. Preserve Bombieri–Vinogradov, Siegel–Walfisz, Maynard Lemmas 5.3/5.4/6.1 and Proposition 5.2, Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10 and Chen switching, with the source/reviewer qualifications about Proposition R. Cite IMPROVE.md for the corrected balance; THEOREM.md is not a substitute proof for it. Keep the accepted three-claim main scope separate. O5 retains fixed kappa,A,C_lev, the uniform margin, level/range and constant dependencies; its accepted embedding is separate from the external asymptotic. #5281 supplies no general-parameter equivalence or constants for O7. No manuscript revision or document integration is attempted.","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":10578,"input_sha256":"986dd9511220ac1edb39945c0825e9b01fa55746865e2f452ec4e704eb36f09f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["route-317/prime-restricted","a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601"]],"report_sha256":"21141931a28bf7751d65075d0d9a3047082f24967fb51458f2582f445d29dea5","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5281,"material_evidence":{"sha256":"573327296f7c9d2cb716a9453200b51c20c406199aaaf85c5ffd62bfd5e1ffa5","entries":{"return:5281":"a9b6a7fc34c0017ae9fe7478880ff42c59d7ea78e21e4a0f8fd134052332fb9e","artifact:5281:31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53":"31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53","artifact:5281:5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c":"5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c","artifact:5281:8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71":"8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71","artifact:5281:8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09":"8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09","artifact:5281:92718f4c45f0b570247a6ef7ed5c553fd5af76ed710d1eeabd4e41bc4eca9577":"92718f4c45f0b570247a6ef7ed5c553fd5af76ed710d1eeabd4e41bc4eca9577","artifact:5281:c6703ca799ae04729de79c79ee7a0852b39366caf71b5a1f74cdcce327493772":"c6703ca799ae04729de79c79ee7a0852b39366caf71b5a1f74cdcce327493772"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5281,"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 #5281: 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\":5281,\"report_sha256\":\"21141931a28bf7751d65075d0d9a3047082f24967fb51458f2582f445d29dea5\",\"scope_hashes\":[[\"route-317/prime-restricted\",\"a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5281\":\"a9b6a7fc34c0017ae9fe7478880ff42c59d7ea78e21e4a0f8fd134052332fb9e\",\"artifact:5281:31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53\":\"31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53\",\"artifact:5281:5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c\":\"5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c\",\"artifact:5281:8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71\":\"8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71\",\"artifact:5281:8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09\":\"8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09\",\"artifact:5281:92718f4c45f0b570247a6ef7ed5c553fd5af76ed710d1eeabd4e41bc4eca9577\":\"92718f4c45f0b570247a6ef7ed5c553fd5af76ed710d1eeabd4e41bc4eca9577\",\"artifact:5281:c6703ca799ae04729de79c79ee7a0852b39366caf71b5a1f74cdcce327493772\":\"c6703ca799ae04729de79c79ee7a0852b39366caf71b5a1f74cdcce327493772\"},\"sha256\":\"573327296f7c9d2cb716a9453200b51c20c406199aaaf85c5ffd62bfd5e1ffa5\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"route-317/prime-restricted\",\"kind\":\"restricted_fact\",\"domain_md\":\"Primes p in (x, x^C] with P-(p+2) > x.\",\"statement_md\":\"For every C >= 3.374 and all large x there is a prime p in (x, x^C] with p + 2 free of the primes <= x (C >= 3.372 with the anatomy of m). In particular #4482's 3.381 holds without any step read from a proof.\",\"assumptions_md\":\"Bombieri-Vinogradov; Maynard (triply well factorable) Lemmas 5.3, 5.4, 6.1 and Proposition 5.2; Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint); Lichtman arXiv:2109.02851v2 Theorem 2.10; Chen's switching; Siegel-Walfisz.\",\"artifact_sha256\":[\"31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53\",\"8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71\",\"5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c\",\"8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09\",\"c6703ca799ae04729de79c79ee7a0852b39366caf71b5a1f74cdcce327493772\",\"92718f4c45f0b570247a6ef7ed5c553fd5af76ed710d1eeabd4e41bc4eca9577\"],\"transfer_conditions_md\":\"Readers of #4482 should cite this balance, not THEOREM.md's proof, for 3.381 at statement level; THEOREM.md's proof needs reading (0) and step (2).\",\"scope_sha256\":\"a7b2ab1f94de3df012603ff058a60d2963c8969149326a17df1248dbfd4ff601\",\"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:5281,input_sha256:\"986dd9511220ac1edb39945c0825e9b01fa55746865e2f452ec4e704eb36f09f\",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/6489/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"851c5e59573408cdf4a61f1c7bd616f41aa1724d19bd34162e13cea785da427c","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}