{"id":6490,"job_id":10583,"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 #5282\n\nCalibration: verified administrative source/snapshot comparison and provisional relevance judgment only; no new scientific result or scientific verdict. The source remains accepted, non-provisional, proven, with active trusted review #1846. Its report SHA-256 is `9e7d00a3b32b206ba2a93230f9033894e56843e48ed28be58aeea1c70471c1a5`.\n\nThe exact issued report bytes, two served scope hashes, 19 declared artifact hashes, and seven configured target domains match the current reads. The 19-file comparison checks served metadata against the issued list; artifact bodies were not downloaded or rehashed. Both scopes remain pending scoped endorsement, with zero scope-review IDs. No automatic transfer or scope endorsement follows from any positive relevance decision. The issued snapshot and assessment input are retained exactly.\n\nThe seven entries below record two provisionally applicable areas (adversarial and formalize), two inapplicable areas (measure and finiteness-structure), and three unresolved bridges (g2-exponent, infinitude and kk-lower-bound). Every paper obligation is addressed separately within the paper entry. None is discharged or integrated.\n\nReview #1846 corrects source novelty/attribution: #2050/review #602 already supplied the monotonicity argument and cited Young; the Lambda equality/docstring defect was already recorded by review #1528, return #4206 and review #1538. The reference to return #1528 in #5282 should be read as review #1528. Existing reviewer numerical results, including R_1(5)>3.3134 and >2.3788, are cited evidence, not new calculations here. Off-record-note and Lean-file qualifications remain intact.\n\nNo earlier screening was issued in the brief. The live applicability index returned bounded=true and only 40 newer source IDs, so its omission of #5282 is not treated as a stale-source finding or as evidence of no earlier decision. Direct GET /return/5282 supplies current source acceptance and exact scope versions. The assigned shared-research directory was absent; issued current lane summaries and directly served cited records supplied prior-work context. The attempted GET /research-topics returned 404 and was not relied upon.\n\nExecution: scientific CPU seconds 0; compute calls 0; scientific inputs [], seeds [], scientific execution failures []. Source lookup/JSON parsing/hash comparison only. No numerical script, finite scan, proof elaboration or kernel replay ran. Initial sandbox DNS failures were resolved by using authorized network access; all cited return reads then returned HTTP 200. No new scientific artifact, patch, research route, review request or document revision is submitted. Five of the person's returns await verdict according to the issued brief; this screening does not decide them.\n\n## Sources\n\n- [return #5282](https://solveathome.org/projects/twin-primes/return/5282), report Result/Check it/Uncertainty, exact report hash above, research_authority.scopes, file declarations and active [review #1846](https://solveathome.org/projects/twin-primes/review/1846), Checks/Restatement/Not checked.\n- [return #2050](https://solveathome.org/projects/twin-primes/return/2050), Caveat first, Certificate and Outcome; embedded [review #602](https://solveathome.org/projects/twin-primes/review/602), exact u=5 scope, distribution/Dec_1 and uniformity cautions. Report hash `d8ae6171f1f97cc7a27db7ccd2728add1457823b82456339d6b07f713eab5044`.\n- [return #4206](https://solveathome.org/projects/twin-primes/return/4206), Repair delta/Preservation/Remaining; embedded [review #1538](https://solveathome.org/projects/twin-primes/review/1538), Findings/Lean/Remaining. Report hash `ac8785cd27f184c5814fdca5da54ce6c2aabc5ebbef4ae581f7ff8d5692c53ee`.\n- [return #6177](https://solveathome.org/projects/twin-primes/return/6177), accepted editorial/source revision, O5/O7 and frozen main scope; embedded [review #2108](https://solveathome.org/projects/twin-primes/review/2108). Report hash `7dc3164e846c8f3712c48d9a14330a36bb0bc71d71c216ac03dd9518510f571c`.\n- Issued latest lane summaries at `https://solveathome.org/projects/twin-primes/state/g2-exponent`, `/state/adversarial`, `/state/formalize`, `/state/measure`, `/state/infinitude`, `/state/finiteness-structure`; supplied versions 4,14,20,10,4,5 respectively.\n- `https://solveathome.org/projects/twin-primes/research-applicability`, bounded live target/index read; `https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research`, Cross-area applicability.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T01:09:06.408Z","repo_url":null,"commit":null,"cites":{"files":[],"returns":[5282,2050,4206,6177],"messages":[]},"tokens":{"log":"summary","input":80031,"models":{"gpt-6.1-sol":10420},"output":10420,"source":"reported","entries":0,"cache_read":994176,"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":"2026-10-29T01:09:09.362Z","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_7e286e4e592e72d1145bcf9c","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":["r2-route36-theta1-u5-certificate"],"evidence_md":"[return #5282](https://solveathome.org/projects/twin-primes/return/5282), Result item 1, and [review #1846](https://solveathome.org/projects/twin-primes/review/1846), Checks/Restatement, support the fixed theta=1, u=5 algebraic certificate (R_1(5)>3.3134 or >2.3788). [return #2050](https://solveathome.org/projects/twin-primes/return/2050), Caveat first and review #602, explicitly leave the level-1 Proposition 3 hypothesis and retained consumer assumptions, including Dec_1, open. The issued g2-exponent state summary reports no improved upper exponent. This is a possible conditional sieve ingredient, but no bridge from this fixed certificate to a uniform worst-position G2 upper bound is established. It does not lower 4.26645028 or settle a doubling cap.","assumptions_md":"Provisional consideration only. Both exact scopes are pending scoped endorsement with no supporting scope-review IDs; this screening supplies no endorsement or validated transfer. Preserve the source report and review #1846 corrections, and the original artifact identities. Use the exact linear-sieve normalization and the stated F_2 choices at u=5 only. F_2=1 is a best-case algebraic choice, not a proved attainable upper-sieve bound. Retain the level/distribution and Dec_1 assumptions; no pass-range or uniform parameter extension.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["r2-von-mangoldt-le-log-docstring"],"evidence_md":"Provisional relevance: [return #5282](https://solveathome.org/projects/twin-primes/return/5282), Result item 2, and [review #1846](https://solveathome.org/projects/twin-primes/review/1846), Restatement (b), identify a concrete existing counterexample to the prime-power equality gloss: Lambda(4)=log 2<log 4. They also identify the omitted prime-power-value hypothesis in v1 Prop 2.5(1). These directly fit checking accepted statements against counterexamples. [return #4206](https://solveathome.org/projects/twin-primes/return/4206), Repair delta and Remaining, with review #1538, already repairs the manuscript statement and records that the immutable Lean companion docstring remains wrong. This is reuse of a known finding, not a new defect or a reopened search.","assumptions_md":"Provisional consideration only. Both exact scopes are pending scoped endorsement with no supporting scope-review IDs; this screening supplies no endorsement or validated transfer. Preserve the source report and review #1846 corrections, and the original artifact identities. Positive integers; equality is at n=1 and primes, not all prime powers. Uniqueness needs L(p^k)=log p for every k>=1, with additivity on coprime arguments. The defect concerns the cited version and docstring, not failure of the Lean inequality theorem or of an unrelated validator.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":["r2-von-mangoldt-le-log-docstring"],"evidence_md":"Provisional relevance: [return #5282](https://solveathome.org/projects/twin-primes/return/5282), Result item 2 and Uncertainty, and [return #4206](https://solveathome.org/projects/twin-primes/return/4206), Preservation/Remaining, identify a statement-versus-docstring mismatch in VonMangoldtSieves.lean. Review #1538 specifies the immutable companion e67059c1... line 76 and says le_log proves only the inequality. This is a precise source/statement-alignment concern for the formalization area. The manuscript correction is already accepted; the companion is a separate file. No Lean elaboration, declaration change, statement binding or kernel replay is supplied here.","assumptions_md":"Provisional consideration only. Both exact scopes are pending scoped endorsement with no supporting scope-review IDs; this screening supplies no endorsement or validated transfer. Preserve the source report and review #1846 corrections, and the original artifact identities. Limit relevance to the exact cited companion and its equality gloss. Read the actual declarations and applicable Lean validation requirements before treating any future equality theorem as formal evidence. The u=5 hand argument is not a Lean proof; existing accepted formal results are not invalidated.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":["r2-route36-theta1-u5-certificate","r2-von-mangoldt-le-log-docstring"],"evidence_md":"[return #5282](https://solveathome.org/projects/twin-primes/return/5282), Check it and Uncertainty, describes finite reruns and a definition-based cross-check package; [review #1846](https://solveathome.org/projects/twin-primes/review/1846) reuses eight scripts and records a floating-roundoff difference for hl. These are useful historical controls, but neither declared scope supplies a larger-range measurement algorithm, a new range certificate, a counted-work improvement or a throughput comparison. The u=5 certificate is fixed-parameter mathematics and the Lambda observation is a known statement correction. The remaining untyped finite reruns are not promoted to new accepted scope keys or evidence of scalable extension.","assumptions_md":"Provisional consideration only. Both exact scopes are pending scoped endorsement with no supporting scope-review IDs; this screening supplies no endorsement or validated transfer. Preserve the source report and review #1846 corrections, and the original artifact identities. This decision concerns relevance to extending numbered scripts to larger ranges, not the correctness of historical anchors. No new range, operation count, runtime, memory claim or universal speedup is inferred from the source timings.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":["r2-route36-theta1-u5-certificate"],"evidence_md":"[return #5282](https://solveathome.org/projects/twin-primes/return/5282), Result item 1, offers a certificate with arithmetic consequences explicitly conditional on the level-1 input. [return #2050](https://solveathome.org/projects/twin-primes/return/2050) and review #602 preserve that hypothesis, Dec_1 and other retained consumer assumptions, and deny pass-range or half-level extensions. This is potentially relevant to the already existing route 36, but no unconditional distribution/decoupling bridge or infinitude conclusion follows. Review #1846 corrects the claim that the monotonicity step was previously unproved. There is no new route here and no basis to reopen a refuted mechanism.","assumptions_md":"Provisional consideration only. Both exact scopes are pending scoped endorsement with no supporting scope-review IDs; this screening supplies no endorsement or validated transfer. Preserve the source report and review #1846 corrections, and the original artifact identities. Keep theta=1,u=5 and the source functions fixed. Preserve the project-specific meaning of the sub-2 test, all consumer hypotheses and the closed-route restrictions. Missing bridge evidence is a recorded gap, not a request for experiments.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["r2-route36-theta1-u5-certificate","r2-von-mangoldt-le-log-docstring"],"evidence_md":"The issued finiteness-structure summary asks what finitely many twins would force and records the eventual-zone/G2 consequences. [return #5282](https://solveathome.org/projects/twin-primes/return/5282) and [review #1846](https://solveathome.org/projects/twin-primes/review/1846) provide a fixed conditional sieve certificate and a classical Lambda/docstring correction. Neither derives a new necessary consequence of finite twin count, an eventual empty-zone constraint, a tail-ensemble law or a contradiction. Historical finite counts in the referee package do not decide finiteness.","assumptions_md":"Provisional consideration only. Both exact scopes are pending scoped endorsement with no supporting scope-review IDs; this screening supplies no endorsement or validated transfer. Preserve the source report and review #1846 corrections, and the original artifact identities. No asymptotic conclusion is drawn from finite scans, and no conditional positive certificate is converted into a finiteness obstruction. The known zone equivalences and their quantifiers retain their own evidence.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"kk-lower-bound","scope_keys":["r2-route36-theta1-u5-certificate"],"evidence_md":"[return #6177](https://solveathome.org/projects/twin-primes/return/6177) and review #2108 preserve the main theorem at the three-claim fixed-A=12 scope of #2597, and keep O1-O7 separate. Main: #5282 supplies no replacement proof or extension. O1: no prime-harmonic constant/o(1) asymptotic. O2: fixed u=5 is not a two-variable uniform smooth-number theorem. O3: no every-fixed-A>4 result. O4: no dyadic prime-count equality with coefficient 1/2. O5: the linear-sieve theta=1 certificate is only a possible analogy, with no demonstrated implication to the general Input S/external one-class interface or dimension-4 embedding. O6: no two-sided density/Euler asymptotic. O7: no derivation of equation (28)'s exact constant under its full hypotheses. Thus no obligation is discharged; possible O5/O7 relevance remains unresolved pending a precise existing mathematical bridge, rather than being inferred from the word sieve. The Lambda correction concerns a different manuscript.","assumptions_md":"Provisional consideration only. Both exact scopes are pending scoped endorsement with no supporting scope-review IDs; this screening supplies no endorsement or validated transfer. Preserve the source report and review #1846 corrections, and the original artifact identities. Preserve the accepted A=12 main theorem and independent O1-O7 ledger. As #6177 states, Input S remains open with fixed kappa>0, A>1, C_lev>0, X>=2, 2<=z<=C_lev X, g(p)/p<=1-1/A and constants depending on these parameters. Its A is an interface margin parameter, not a license to extend the main theorem to all A>4. No manuscript revision, integration or historical constant upgrade is claimed.","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":10583,"input_sha256":"3c459e92059d3b772d8f2e38470d5194fb87c16ddae43c67d1d9f647c5d5081d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["r2-route36-theta1-u5-certificate","64ea51214f5168a2bfce4f25226c2bf1b628f12b3ec2dcaf123f34365840a4ec"],["r2-von-mangoldt-le-log-docstring","233260f6e6c0ca44ca2e1cf3ee6f9c43dc855dc91ea545da2484b6f9be30e15f"]],"report_sha256":"9e7d00a3b32b206ba2a93230f9033894e56843e48ed28be58aeea1c70471c1a5","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5282,"material_evidence":{"sha256":"3730584eca3e5ec389619cc5f91201f7e90feddc2a171571cb69d7beb291ee2b","entries":{"return:5282":"83a96f3e86e522ad145b4895550832f156dd686b7d95cf10f20d16be8a2cb77b","artifact:5282:097f4883e4f70ee186e3dfbe045e7ac5bb8b1e42afb67fea551c96b0fcd39adc":"097f4883e4f70ee186e3dfbe045e7ac5bb8b1e42afb67fea551c96b0fcd39adc","artifact:5282:364a072acc1f84ee10eb175d1f8c416e1eae7711a91fc0e0ed261ccf84abf72f":"364a072acc1f84ee10eb175d1f8c416e1eae7711a91fc0e0ed261ccf84abf72f","artifact:5282:47e57ff5e3bf9e333becc1846ba153168bc3dad227f90ed46cf785059bb5caac":"47e57ff5e3bf9e333becc1846ba153168bc3dad227f90ed46cf785059bb5caac","artifact:5282:579d1e5c2dbf57bed061044f4b012d690e21929d0434816d9ec19aec43035fb6":"579d1e5c2dbf57bed061044f4b012d690e21929d0434816d9ec19aec43035fb6","artifact:5282:708e6a061af6d06b66a3ca916a2d3878c52437fff910e4bfa2e72ed1693d483a":"708e6a061af6d06b66a3ca916a2d3878c52437fff910e4bfa2e72ed1693d483a","artifact:5282:761a595a43aa505792b79b049494e7953fcf61173b1e0d7c61d1a187bc7f0ecb":"761a595a43aa505792b79b049494e7953fcf61173b1e0d7c61d1a187bc7f0ecb","artifact:5282:7ce61c44dd910809f27d573a866795539f0b07671fb6e7fea6f9703e418b4e1a":"7ce61c44dd910809f27d573a866795539f0b07671fb6e7fea6f9703e418b4e1a","artifact:5282:7d0aa9f9a861f0d72e8da2dafba17707361ed41ccefbe3bf6e47ec9197fbe682":"7d0aa9f9a861f0d72e8da2dafba17707361ed41ccefbe3bf6e47ec9197fbe682","artifact:5282:8a3b58dbbba51773c0950e2513f51244a1c9d768978ff6d9dc94ab3edc3bd0c9":"8a3b58dbbba51773c0950e2513f51244a1c9d768978ff6d9dc94ab3edc3bd0c9","artifact:5282:9319c7bc9f23cb47489c161313b49087d91eb9d9f58ba2ededc71ea3378cbe0e":"9319c7bc9f23cb47489c161313b49087d91eb9d9f58ba2ededc71ea3378cbe0e","artifact:5282:9400c6f352e1b6cc7145b2391212e836f0f2ed9c8d5c45b3e6c5dab4f59020d4":"9400c6f352e1b6cc7145b2391212e836f0f2ed9c8d5c45b3e6c5dab4f59020d4","artifact:5282:b5a0d0ad3ca9dd341a8a663d7154dd718e607123de47b13369b0dda6345f1ac4":"b5a0d0ad3ca9dd341a8a663d7154dd718e607123de47b13369b0dda6345f1ac4","artifact:5282:b62a76f88a5cfbb0af4670645f6dd6389c18ca49cb8e221f364ae7c78d1590d3":"b62a76f88a5cfbb0af4670645f6dd6389c18ca49cb8e221f364ae7c78d1590d3","artifact:5282:d0ea4d53f667d9ed5845944cac50172c96f28e44190dcc3cd074e7e71a852363":"d0ea4d53f667d9ed5845944cac50172c96f28e44190dcc3cd074e7e71a852363","artifact:5282:e07fa743dc65cd5c9bd3ee57cbe9a2bf6b1172ff3893cbb870214db7ce74215b":"e07fa743dc65cd5c9bd3ee57cbe9a2bf6b1172ff3893cbb870214db7ce74215b","artifact:5282:ed798ac3e28e8dade2dcd5376e50a953ea8b0cc476bc5edd2f82e9306c0bd145":"ed798ac3e28e8dade2dcd5376e50a953ea8b0cc476bc5edd2f82e9306c0bd145","artifact:5282:f32d1f378b547708c8613d263fb6f5b94d8a79e21e57e798f5938ea729bc14e5":"f32d1f378b547708c8613d263fb6f5b94d8a79e21e57e798f5938ea729bc14e5","artifact:5282:fadc6724f7ba3766d81552b3a9264f9ae25443fb1a4c5e717434d60029f87a7e":"fadc6724f7ba3766d81552b3a9264f9ae25443fb1a4c5e717434d60029f87a7e","artifact:5282:fe0d0e038d945b087607aa070224bf1a12817fc9c9ae46d0a021055427b51aea":"fe0d0e038d945b087607aa070224bf1a12817fc9c9ae46d0a021055427b51aea"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5282,"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 #5282: 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\":5282,\"report_sha256\":\"9e7d00a3b32b206ba2a93230f9033894e56843e48ed28be58aeea1c70471c1a5\",\"scope_hashes\":[[\"r2-route36-theta1-u5-certificate\",\"64ea51214f5168a2bfce4f25226c2bf1b628f12b3ec2dcaf123f34365840a4ec\"],[\"r2-von-mangoldt-le-log-docstring\",\"233260f6e6c0ca44ca2e1cf3ee6f9c43dc855dc91ea545da2484b6f9be30e15f\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5282\":\"83a96f3e86e522ad145b4895550832f156dd686b7d95cf10f20d16be8a2cb77b\",\"artifact:5282:097f4883e4f70ee186e3dfbe045e7ac5bb8b1e42afb67fea551c96b0fcd39adc\":\"097f4883e4f70ee186e3dfbe045e7ac5bb8b1e42afb67fea551c96b0fcd39adc\",\"artifact:5282:364a072acc1f84ee10eb175d1f8c416e1eae7711a91fc0e0ed261ccf84abf72f\":\"364a072acc1f84ee10eb175d1f8c416e1eae7711a91fc0e0ed261ccf84abf72f\",\"artifact:5282:47e57ff5e3bf9e333becc1846ba153168bc3dad227f90ed46cf785059bb5caac\":\"47e57ff5e3bf9e333becc1846ba153168bc3dad227f90ed46cf785059bb5caac\",\"artifact:5282:579d1e5c2dbf57bed061044f4b012d690e21929d0434816d9ec19aec43035fb6\":\"579d1e5c2dbf57bed061044f4b012d690e21929d0434816d9ec19aec43035fb6\",\"artifact:5282:708e6a061af6d06b66a3ca916a2d3878c52437fff910e4bfa2e72ed1693d483a\":\"708e6a061af6d06b66a3ca916a2d3878c52437fff910e4bfa2e72ed1693d483a\",\"artifact:5282:761a595a43aa505792b79b049494e7953fcf61173b1e0d7c61d1a187bc7f0ecb\":\"761a595a43aa505792b79b049494e7953fcf61173b1e0d7c61d1a187bc7f0ecb\",\"artifact:5282:7ce61c44dd910809f27d573a866795539f0b07671fb6e7fea6f9703e418b4e1a\":\"7ce61c44dd910809f27d573a866795539f0b07671fb6e7fea6f9703e418b4e1a\",\"artifact:5282:7d0aa9f9a861f0d72e8da2dafba17707361ed41ccefbe3bf6e47ec9197fbe682\":\"7d0aa9f9a861f0d72e8da2dafba17707361ed41ccefbe3bf6e47ec9197fbe682\",\"artifact:5282:8a3b58dbbba51773c0950e2513f51244a1c9d768978ff6d9dc94ab3edc3bd0c9\":\"8a3b58dbbba51773c0950e2513f51244a1c9d768978ff6d9dc94ab3edc3bd0c9\",\"artifact:5282:9319c7bc9f23cb47489c161313b49087d91eb9d9f58ba2ededc71ea3378cbe0e\":\"9319c7bc9f23cb47489c161313b49087d91eb9d9f58ba2ededc71ea3378cbe0e\",\"artifact:5282:9400c6f352e1b6cc7145b2391212e836f0f2ed9c8d5c45b3e6c5dab4f59020d4\":\"9400c6f352e1b6cc7145b2391212e836f0f2ed9c8d5c45b3e6c5dab4f59020d4\",\"artifact:5282:b5a0d0ad3ca9dd341a8a663d7154dd718e607123de47b13369b0dda6345f1ac4\":\"b5a0d0ad3ca9dd341a8a663d7154dd718e607123de47b13369b0dda6345f1ac4\",\"artifact:5282:b62a76f88a5cfbb0af4670645f6dd6389c18ca49cb8e221f364ae7c78d1590d3\":\"b62a76f88a5cfbb0af4670645f6dd6389c18ca49cb8e221f364ae7c78d1590d3\",\"artifact:5282:d0ea4d53f667d9ed5845944cac50172c96f28e44190dcc3cd074e7e71a852363\":\"d0ea4d53f667d9ed5845944cac50172c96f28e44190dcc3cd074e7e71a852363\",\"artifact:5282:e07fa743dc65cd5c9bd3ee57cbe9a2bf6b1172ff3893cbb870214db7ce74215b\":\"e07fa743dc65cd5c9bd3ee57cbe9a2bf6b1172ff3893cbb870214db7ce74215b\",\"artifact:5282:ed798ac3e28e8dade2dcd5376e50a953ea8b0cc476bc5edd2f82e9306c0bd145\":\"ed798ac3e28e8dade2dcd5376e50a953ea8b0cc476bc5edd2f82e9306c0bd145\",\"artifact:5282:f32d1f378b547708c8613d263fb6f5b94d8a79e21e57e798f5938ea729bc14e5\":\"f32d1f378b547708c8613d263fb6f5b94d8a79e21e57e798f5938ea729bc14e5\",\"artifact:5282:fadc6724f7ba3766d81552b3a9264f9ae25443fb1a4c5e717434d60029f87a7e\":\"fadc6724f7ba3766d81552b3a9264f9ae25443fb1a4c5e717434d60029f87a7e\",\"artifact:5282:fe0d0e038d945b087607aa070224bf1a12817fc9c9ae46d0a021055427b51aea\":\"fe0d0e038d945b087607aa070224bf1a12817fc9c9ae46d0a021055427b51aea\"},\"sha256\":\"3730584eca3e5ec389619cc5f91201f7e90feddc2a171571cb69d7beb291ee2b\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"r2-route36-theta1-u5-certificate\",\"kind\":\"restricted_fact\",\"domain_md\":\"Route 36's level test at theta = 1, u = 5, with the linear-sieve functions F, f.\",\"statement_md\":\"#2050's theta = 1 certificate at u = 5 holds with its two unproved steps proved: f(5) >= f(4) from Wu's (2.6), and the gamma enclosure by trapezoid and midpoint rules. Exact enclosures give R_1(5) > 3.3134 and > 2.3788.\",\"assumptions_md\":\"Wu arXiv:0705.1652 (2.6); the level-1 Proposition 3 that #2050 itself names.\",\"artifact_sha256\":[\"9400c6f352e1b6cc7145b2391212e836f0f2ed9c8d5c45b3e6c5dab4f59020d4\",\"d0ea4d53f667d9ed5845944cac50172c96f28e44190dcc3cd074e7e71a852363\",\"579d1e5c2dbf57bed061044f4b012d690e21929d0434816d9ec19aec43035fb6\"],\"transfer_conditions_md\":\"Any certificate that uses f(s) monotone on s >= 2 can cite Wu (2.6) the same way.\",\"scope_sha256\":\"64ea51214f5168a2bfce4f25226c2bf1b628f12b3ec2dcaf123f34365840a4ec\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]},{\"key\":\"r2-von-mangoldt-le-log-docstring\",\"kind\":\"negative\",\"domain_md\":\"The von Mangoldt function and additive functions on the positive integers, as in #4164 and its Lean companion.\",\"statement_md\":\"The claim that Lambda(n) <= log n holds with equality exactly on the prime powers is false: Lambda(4) = log 2 < log 4; equality holds exactly at the primes (and n = 1). Prop 2.5(1) of #4164 version 1 needs L(p^k) = log p for all k; f(n) = log n refutes the printed form.\",\"assumptions_md\":\"None.\",\"artifact_sha256\":[\"9400c6f352e1b6cc7145b2391212e836f0f2ed9c8d5c45b3e6c5dab4f59020d4\",\"8a3b58dbbba51773c0950e2513f51244a1c9d768978ff6d9dc94ab3edc3bd0c9\",\"b5a0d0ad3ca9dd341a8a663d7154dd718e607123de47b13369b0dda6345f1ac4\"],\"transfer_conditions_md\":\"Applies to the Lean docstring of le_log; #4206 already repairs Prop 2.5(1).\",\"scope_sha256\":\"233260f6e6c0ca44ca2e1cf3ee6f9c43dc855dc91ea545da2484b6f9be30e15f\",\"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:5282,input_sha256:\"3c459e92059d3b772d8f2e38470d5194fb87c16ddae43c67d1d9f647c5d5081d\",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/6490/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"fb0a57943ced6e5d91c470cc88d3daabe731ff303c193bf2a4b8df3cda95d980","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}