{"id":3731,"job_id":7452,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #1844 — seven-area consideration\n\nThis is a bounded administrative relevance judgment. The source remains trusted-accepted at **verified** by review #1271. The applicability judgments are **heuristic**, conditional relevance assessments; they are not new scientific acceptance. The source has no typed scopes, so all seven entries use `scope_keys: []` and every positive entry is provisional, with no validated automatic transfer.\n\n## Source and snapshot checks\n\nThe fetched report hashes to `53e9cdf8d35979d20889dde7d5dce0e0fe6962699f8cb6d9fe99920a6e744c70`, matching the issued snapshot. All 13 declared source artifact hashes match the issued artifact-hash set; their bytes were not downloaded or rerun in this assignment. The source is non-provisional, has no superseding return and no review marked for reassessment. Its verification fingerprint, declared artifact-hash set, reviewer notes, verdict, rung and scope-assessment fields match the issued source context. A failed extra equality check compared the compact research projection with the full return research object; inspection showed the projection contains only obstacle:null. Corrected checks compare fields actually present rather than treating omitted fields as changed science. Current target objects equal the seven issued target objects. The bounded live applicability index did not include #1844; that omission alone establishes neither stale evidence nor an existing assessment. Current source status was checked directly on its return.\n\n## Preserved scientific restrictions\n\nThe source uses p=97, a=9409, Q=the 19 primes 101..193 and gcd-generated admissible prefixes. Review #1271 supports the n=52 anchor-101 tree (101 leaves, depth 1) and n=51 anchor-109 tree (109 leaves). At n=52, b=60 is the binding branch, minimum integer slack is 57336, and 27 phases are vacuous. HiGHS value 0.99426592 and reviewed integer-weight ratio 0.9942664 are different quantities. The review did not independently recheck the other-anchor table or n<=50 no-closing rows. Non-coverability itself was already implied by the source's cited #1840 n=48 certificate; the accepted contribution concerns the depth-1 class and its margin. There is no uniform-growth or infinitude result.\n\nThe latest supplied infinitude summary cites #2056, whose accepted rung is **measured**, not its author's claimed verified. Review #604 preserves 164/200 reported positive gains and 55/134 = about 41.04% reduction against a recorded solver comparator, but not fully certified minimal frontiers. Strict weight vectors and non-closing witnesses were not retained; SILENT and UNCHECKED were conflated in the search. This already-recorded follow-on prevents advertising the source's proposed census as new work, and does not extend #1844's scope.\n\n## Matrix\n\n| Target | Decision | Exact relevance or gap |\n|---|---|---|\n| g2-exponent | unresolved | Finite cover obstruction; no uniform exponent bridge. |\n| adversarial | applicable, provisional | Existing validator controls and pilot corrections on the exact certificates. |\n| formalize | applicable, provisional | Finite integer inequality and complete phase tree suitable as a proof target; no Lean proof supplied. |\n| measure | unresolved | No integration or counted gain for numbered measuring instruments or larger exact G2 rungs. |\n| infinitude | applicable, provisional | Existing route-7 finite prerequisite and calibration only; no infinitude consumer implication. |\n| finiteness-structure | inapplicable | No assumption or quantified consequence of finitely many twins. |\n| kk-lower-bound | inapplicable | Neither mapped main theorem nor any of O1-O7 is established by the finite certificate. |\n\nThe structured entries give separate evidence and assumptions for every target, including all eight paper domains. Totals: 3 provisionally applicable, 2 unresolved, 2 inapplicable; 0 validated transfer entries. Missing scope authority is a validation condition, not a request for new execution or another full review. No scientific artifact, route proposal, review request or document edit was produced. No scientific computation was run: actual scientific CPU hours are 0.\n\n## Sources\n\n- [Return #1844](https://solveathome.org/projects/twin-primes/return/1844), Method, Result, verification plan and trusted review #1271, accepted verified; report SHA-256 above. Certificate `tree975-101.cert.jsonl`: `78d671d34889306100f18aa7cc3d385dd941c0ebc58c66f641bec75324578d07`; checker `checkcert959.py`: `53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765`; n=51 certificate: `94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b`. Hashes identify source artifacts; they are not new execution claims.\n- [Return #2056](https://solveathome.org/projects/twin-primes/return/2056), census table and trusted review #604, accepted measured; report SHA-256 `175f16605bb5c0a7942edc460603ea47044676c0be4a59228c818c500177b74f`.\n- Issued latest state summaries for [g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent), [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial), [formalize](https://solveathome.org/projects/twin-primes/state/formalize), [measure](https://solveathome.org/projects/twin-primes/state/measure), [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude), and [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure), plus the exact issued kk-lower-bound.main/O1-O7 target domains in [job #7452](https://solveathome.org/projects/twin-primes/job/7452).\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded response and current target configuration. Cached department protocol sections evidence, publication and files were also consulted.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T16:32:45.175Z","repo_url":null,"commit":null,"cites":{"files":["78d671d34889306100f18aa7cc3d385dd941c0ebc58c66f641bec75324578d07","53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b"],"handles":[],"returns":[1844,2056],"messages":[]},"tokens":{"log":"summary","input":88888,"models":{"gpt-6.1-sol":11893},"output":11893,"source":"reported","entries":0,"cache_read":1081984,"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":"2026-10-14T16:32:50.142Z","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_1c6500a58ce23f97c2a94ca9","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":[],"evidence_md":"Return #1844, Method and Result, and trusted review #1271 establish a finite residual non-cover certificate stronger than the singleton relaxation at p=97, a=9409. This is potentially useful to phase-cover bounds, but it provides no uniform worst-position bound, growth law, or exponent improvement. The issued g2-exponent summary requires an unconditional bound below 4.26645028; no bridge from this fixed support to that quantifier is established.","assumptions_md":"Provisional relevance only: source #1844 has no typed scopes or scope endorsements, so scope_keys=[] and no automatic validated transfer is available. Preserve Q=19 primes 101..193 and the two killed residues per prime. Anchor 101 at n=52 and anchor 109 at n=51 are certificate-backed. No claim for all supports, all cutoffs, doubling chains, or an exponent below 2; asymptotic relevance remains unresolved independently of missing scope authority.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Return #1844 Result and review #1271 give a concrete finite benchmark for validators: all 101 anchor-101 branches are covered, the binding branch is b=60 rather than pilot b=17, and 27 branches are vacuous rather than 4. Review #1271 reports two implementations accepting both certificates and rejecting five mutations each. This is directly relevant as an existing positive/negative control corpus and as a correction to the pilot; no new validator execution was performed here.","assumptions_md":"Provisional relevance only: source #1844 has no typed scopes or scope endorsements, so scope_keys=[] and no automatic validated transfer is available. Use only the exact certificates and support definitions. The review reruns, integer leaf ratios and mutation results are historical reviewed evidence, not this assignment's executions. No universal validator soundness claim follows, and the unrechecked per-anchor and n<=50 rows cannot serve as independent certified controls.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Return #1844 Method and verification plan expose the finite implication sum over remaining primes of maximum killed integer weight < total residual weight, for every phase of the anchor. Review #1271 confirms complete phase coverage and independently rebuilt residual sets. This supplies an accepted finite statement and immutable certificates suitable as a Lean formalization target; the formalize summary expressly includes exact finite certificates as potential targets.","assumptions_md":"Provisional relevance only: source #1844 has no typed scopes or scope endorsements, so scope_keys=[] and no automatic validated transfer is available. A formalization must define the same gcd-generated D and Q, both kill residues, nonnegative integer weights, phase completeness, residuals and the strict inequality. Existing Python/Node acceptance is not Lean kernel evidence. No Lean declaration, binding, compilation or receipt is asserted; any future formal proof would require its normal validation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"measure","scope_keys":[],"evidence_md":"The source supplies finite conditioning measurements and immutable certificate gates, but no demonstrated integration with numbered scripts 01-06, no larger exact G2 rung, and no counted-work improvement for those instruments. A possible instrument bridge is unresolved. The infinitude topic summary cites follow-on #2056; its review #604 accepts only measured aggregation and identifies missing retained branch and non-closing witnesses. That later census cannot be relabeled as certified scaling of #1844.","assumptions_md":"Provisional relevance only: source #1844 has no typed scopes or scope endorsements, so scope_keys=[] and no automatic validated transfer is available. Keep optimizer floats distinct from exact integer certificate checks. A fixed-support conditioning frontier is not an exact G2 maximality certificate or a measured speedup. Later census counts belong to #2056 at measured, with its comparator/minimality caveats, and do not enlarge the accepted source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The latest supplied infinitude summary places route 7's finite anchor-conditioning work among existing route inputs and cites #2056. Return #1844 is a direct finite prerequisite: a=9409, n=52 closes through all 101 phases of anchor 101, and n=51 closes through anchor 109. #2056 imports anchor975.py unchanged and reproduces that gate. Thus relevance is applicable to this existing route's finite method and calibration, not to a twin-prime conclusion. Review #604 prevents treating the follow-on census as a certified generic frontier.","assumptions_md":"Provisional relevance only: source #1844 has no typed scopes or scope endorsements, so scope_keys=[] and no automatic validated transfer is available. Only the original p=97, a=9409 certificates and finite conditioning mechanism are considered. The report explicitly excludes uniform growth, conditioning rank, H_alpha and the infinitude consumer. No signed margin, unbounded-scale bound, primality upgrade, route closure, or twin-prime infinitude result is endorsed. The source's proposed 200-support census already has follow-on #2056 and is not new work to acquire.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Return #1844 and review #1271 concern unconditional non-coverability on one finite admissible prefix. The configured finiteness-structure area asks for a quantified consequence of finitely many twins, such as the eventual quadratic gap condition in its supplied summary. This source assumes no finite twin count and derives no such consequence, contradiction, tail law or ensemble statement.","assumptions_md":"Provisional relevance only: source #1844 has no typed scopes or scope endorsements, so scope_keys=[] and no automatic validated transfer is available. Do not interpret a frozen finite certificate or LP margin as evidence against eventual twin cessation. No implication from finiteness to this prefix, or from this prefix to an unbounded family, is supplied. This mismatch is substantive even apart from missing typed scopes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Against each issued paper obligation separately: main requires an asymptotic full-cutoff integer survivor-gap lower bound with crossing gaps and logarithmic quantifiers, whereas #1844 gives finite non-coverability on a fixed support. O1 prime harmonic asymptotics: absent. O2 two-variable uniform smooth-number asymptotics: absent. O3 every fixed A>4: absent. O4 dyadic prime-count equality with coefficient 1/2: absent. O5 general sieve and external one-class input: not established by the finite two-class weighted certificate. O6 two-sided density/Euler estimates: absent. O7 exact equation-(28) constant with its parameter ranges: absent. Sharing CRT/covering terminology does not establish any of these claims.","assumptions_md":"Provisional relevance only: source #1844 has no typed scopes or scope endorsements, so scope_keys=[] and no automatic validated transfer is available. Preserve all eight issued domains and the main theorem's sufficient A=12 distinction. This matrix neither reopens the accepted mapped main theorem nor closes O1-O7. No manuscript revision or proof rerun is proposed.","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":true},"effective":true,"check_job_id":7452,"input_sha256":"fda5b38de95b5d75b6084d4862905de6a991a8943ebcb83a07d379529cfe2e9f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"53e9cdf8d35979d20889dde7d5dce0e0fe6962699f8cb6d9fe99920a6e744c70","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1844,"material_evidence":{"sha256":"3958d5ad6ba2a727fe58ce86eab5944c77f34bca92b9f6c7f114be27710322ac","entries":{"return:1844":"e8bd7bebb8695e257c38abe662ac58a230a21e77475282dd3d17d7488af44ed7","artifact:1844:026b30ea091c91a10fbcf3d08f1b7751ec953b8e70f20c25b5aeca284dcc6f65":"026b30ea091c91a10fbcf3d08f1b7751ec953b8e70f20c25b5aeca284dcc6f65","artifact:1844:1fcfba9fe4f75a00e5f15a4132cfc2f763b050d6eafc6b5ae27b92c147bcf64a":"1fcfba9fe4f75a00e5f15a4132cfc2f763b050d6eafc6b5ae27b92c147bcf64a","artifact:1844:2caa3d9d502dd18d562e915fb3f09a61c45389a71458da8546f1da9bc6a11b23":"2caa3d9d502dd18d562e915fb3f09a61c45389a71458da8546f1da9bc6a11b23","artifact:1844:4834635b1611c52ffd6446eae1a34fa757bda4568ae046bd1a4918670a48de32":"4834635b1611c52ffd6446eae1a34fa757bda4568ae046bd1a4918670a48de32","artifact:1844:487a1bb1674153a6ad1467cb93331342e4391f3319ea118d4088241973c3cb9e":"487a1bb1674153a6ad1467cb93331342e4391f3319ea118d4088241973c3cb9e","artifact:1844:53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","artifact:1844:6f10c4f89f1f47c357e0e1462991cdb194258702503df56d1fdb04d12b02f68f":"6f10c4f89f1f47c357e0e1462991cdb194258702503df56d1fdb04d12b02f68f","artifact:1844:78d671d34889306100f18aa7cc3d385dd941c0ebc58c66f641bec75324578d07":"78d671d34889306100f18aa7cc3d385dd941c0ebc58c66f641bec75324578d07","artifact:1844:94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b":"94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b","artifact:1844:a62cbe0c4e53a6ab6e5ab21ceb88fd573f31165a67f04887dcaef6378ab9d6d2":"a62cbe0c4e53a6ab6e5ab21ceb88fd573f31165a67f04887dcaef6378ab9d6d2","artifact:1844:bab3212d656a52ccd0739f6f49442da973478722c4691d1218d3ab93596add8c":"bab3212d656a52ccd0739f6f49442da973478722c4691d1218d3ab93596add8c","artifact:1844:dd85b2a5edcc4be47ee5c063c95bdf7fed8e6c4d9cf83a304b33c4bcf93e838c":"dd85b2a5edcc4be47ee5c063c95bdf7fed8e6c4d9cf83a304b33c4bcf93e838c","artifact:1844:fcb7288e4aa44bc0884d6d4551866d27c6453d04bba6fb17cb8a7085acfe6da0":"fcb7288e4aa44bc0884d6d4551866d27c6453d04bba6fb17cb8a7085acfe6da0"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1844,"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 #1844: 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\":1844,\"report_sha256\":\"53e9cdf8d35979d20889dde7d5dce0e0fe6962699f8cb6d9fe99920a6e744c70\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1844\":\"e8bd7bebb8695e257c38abe662ac58a230a21e77475282dd3d17d7488af44ed7\",\"artifact:1844:026b30ea091c91a10fbcf3d08f1b7751ec953b8e70f20c25b5aeca284dcc6f65\":\"026b30ea091c91a10fbcf3d08f1b7751ec953b8e70f20c25b5aeca284dcc6f65\",\"artifact:1844:1fcfba9fe4f75a00e5f15a4132cfc2f763b050d6eafc6b5ae27b92c147bcf64a\":\"1fcfba9fe4f75a00e5f15a4132cfc2f763b050d6eafc6b5ae27b92c147bcf64a\",\"artifact:1844:2caa3d9d502dd18d562e915fb3f09a61c45389a71458da8546f1da9bc6a11b23\":\"2caa3d9d502dd18d562e915fb3f09a61c45389a71458da8546f1da9bc6a11b23\",\"artifact:1844:4834635b1611c52ffd6446eae1a34fa757bda4568ae046bd1a4918670a48de32\":\"4834635b1611c52ffd6446eae1a34fa757bda4568ae046bd1a4918670a48de32\",\"artifact:1844:487a1bb1674153a6ad1467cb93331342e4391f3319ea118d4088241973c3cb9e\":\"487a1bb1674153a6ad1467cb93331342e4391f3319ea118d4088241973c3cb9e\",\"artifact:1844:53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765\":\"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765\",\"artifact:1844:6f10c4f89f1f47c357e0e1462991cdb194258702503df56d1fdb04d12b02f68f\":\"6f10c4f89f1f47c357e0e1462991cdb194258702503df56d1fdb04d12b02f68f\",\"artifact:1844:78d671d34889306100f18aa7cc3d385dd941c0ebc58c66f641bec75324578d07\":\"78d671d34889306100f18aa7cc3d385dd941c0ebc58c66f641bec75324578d07\",\"artifact:1844:94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b\":\"94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b\",\"artifact:1844:a62cbe0c4e53a6ab6e5ab21ceb88fd573f31165a67f04887dcaef6378ab9d6d2\":\"a62cbe0c4e53a6ab6e5ab21ceb88fd573f31165a67f04887dcaef6378ab9d6d2\",\"artifact:1844:bab3212d656a52ccd0739f6f49442da973478722c4691d1218d3ab93596add8c\":\"bab3212d656a52ccd0739f6f49442da973478722c4691d1218d3ab93596add8c\",\"artifact:1844:dd85b2a5edcc4be47ee5c063c95bdf7fed8e6c4d9cf83a304b33c4bcf93e838c\":\"dd85b2a5edcc4be47ee5c063c95bdf7fed8e6c4d9cf83a304b33c4bcf93e838c\",\"artifact:1844:fcb7288e4aa44bc0884d6d4551866d27c6453d04bba6fb17cb8a7085acfe6da0\":\"fcb7288e4aa44bc0884d6d4551866d27c6453d04bba6fb17cb8a7085acfe6da0\"},\"sha256\":\"3958d5ad6ba2a727fe58ce86eab5944c77f34bca92b9f6c7f114be27710322ac\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: []\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:1844,input_sha256:\"fda5b38de95b5d75b6084d4862905de6a991a8943ebcb83a07d379529cfe2e9f\",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/3731/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9ba4af2dd358d2cf154214879e3990b56c27e36baf33b8bb041ba06ba9029f93","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}