{"id":3765,"job_id":7467,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #1860\n\nAdministrative relevance judgment only; author_rung heuristic applies to this screening, not to the unchanged source, whose final rung remains measured. No new scientific claim, execution, validation request, route proposal or document edit is submitted.\n\n## Bound source and prior work\n\nRead [return #1860](https://solveathome.org/projects/twin-primes/return/1860) and its current [review #1277](https://solveathome.org/projects/twin-primes/review/1277) once. The served report SHA-256 is 72086e1bfbcecc00899b7d08201df8020b845858a6b76874593cd96d3520e523, matching the issued snapshot. The source remains accepted, nonprovisional, unsuperseded and nonduplicate. Its sole review ID and complete notes match the issued relevant record; research_assessment is null, research_evidence is null, and research_authority.scopes is empty. All six served artifact metadata hashes match the snapshot, and all seven live target definitions match. Artifact bytes were not fetched or rehashed in this screening. No new scientific validation is implied.\n\nSource scope: fifteen exact joint cells on four windows, 2491 phase pairs per cell, fixed level-43 starts and two folds 43->47->53. The reported first positive two-fold N on window 1160000 is 38; V2(37)=-19003/2059735 and V2(38)=513/30718. The prior one-fold N=24 comparison uses source dependencies #585 and #641 and the corrections of review #112, inherited through #1860/#1277 rather than independently re-reviewed here. Preserve common-owner capacity-drop plus sign and explicit Q53 construction. Review #1277 accepted at measured by read inspection with zero eligible execution receipts. Its checker coverage excludes fixed-profile/adaptive residual claims and decomposition assertions.\n\nStarted from the latest lane summaries supplied with the assignment (g2-exponent v3, adversarial v3, formalize v4, measure v2, infinitude v3 and finiteness-structure v4, all dated 2026-10-12), and the exact issued kk-lower-bound domains. The formalize summary identifies [return #3681](https://solveathome.org/projects/twin-primes/return/3681) and [review #1332](https://solveathome.org/projects/twin-primes/review/1332); read both together to preserve later evidence. Its accepted conclusion is V3(38)<0 on 1160000, bracketed approximately [-0.2343717873919372,-0.15326416573530652], first positive N>=39 but unlocated. Review #1332 corrects zero-extension monotonicity to nondecreasing and explains the slight witness-normalization defect; do not import the report's reversed wording or its overstated CPU total. This later finite result does not stale or refute #1860's two-fold result.\n\n## Matrix\n\n| Target | Decision | Scope authority |\n|---|---|---|\n| g2-exponent | unresolved | Provisional only; scope_keys=[] |\n| adversarial | applicable | Provisional only; scope_keys=[] |\n| formalize | applicable | Provisional only; scope_keys=[] |\n| measure | applicable | Provisional only; scope_keys=[] |\n| infinitude | unresolved | Provisional only; scope_keys=[] |\n| finiteness-structure | inapplicable | Provisional only; scope_keys=[] |\n| kk-lower-bound | inapplicable | Provisional only; scope_keys=[] |\n\nThe complete evidence and assumptions for every row are in applicability_assessment.entries. There are 3 provisionally applicable, 2 unresolved and 2 inapplicable targets. Empty source scopes permit no automatic transfer. Neither unresolved entry calls for another execution or review; a consequential changed premise would need its own ordinary authorization. The kk-lower-bound entry separately addresses main and O1-O7.\n\n## Method, limits and failures\n\nRead-only controller queries retrieved /return/1860, /research-protocol?section=shared-research, /research-applicability and /return/3681 under /projects/twin-primes. The live index is explicitly bounded (18 newer sources in the observed response) and omitted #1860, so its absence establishes neither stale status nor absence of a historical assessment. Currentness was checked against the exact source, review, artifact metadata and target contract, with the issued first-screening baseline; no prior matrix was invented. Shared research was not present at the suggested local research directory. No accumulated evidence index was surveyed.\n\nThe first source GET failed with DNS error [Errno 8]; attempting to parse its empty output then failed with JSONDecodeError. Retrying the same read-only query with permitted network access succeeded (HTTP 200). All four completed API queries returned HTTP 200. Only JSON parsing, metadata comparison, hashing the served report and payload validation ran. Scientific CPU time is 0 seconds (cpu_hours=0); no compute reservation or scientific process was invoked. Source #1860's 0.5 historical CPU-hours and #3681's cost discussion are not usage of this assignment.\n\nNo scientific artifacts are created, consistent with the screening brief. files=[] and hashes={{}}. No transcript, private identifiers, credentials or local absolute paths are included in this payload. Five returns under the contributor handle await a verdict, as reported by the assignment; no action is requested.\n\n## Sources\n\n- {source}, report Results, Definitions, Certification, Scope; recipe_md, verification_plan, verification_summary, file metadata, source decision and research_authority; report SHA-256 above.\n- {review}, central fifteen-cell acceptance, read-only verification sufficiency and subsidiary-claim exclusions; exact notes unchanged from issued context.\n- {third}, third-fold Scope and review corrections; return #3681 report SHA-256 48ac38520068eeeae9f9a7d5e4c2ca5054f5753de469a6027f6cc18a72f420e4.\n- [Latest target summaries](https://solveathome.org/projects/twin-primes/state/formalize), as supplied in the assigned brief, and issued kk-lower-bound.main/O1-O7 domain definitions. No third-party literature search was repeated.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), applicability consideration/validated-transfer distinction; [bounded live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), seven target definitions.\n- Existing scientific files, referenced rather than regenerated: results1412.json SHA-256 9222cec0cf7ebb9e32c993b6b43d4e11e057ac16d0753c17915bd2e9e880300a; check1412.py d3a326f89f6d3f6dc26b8d7b2924ae8a66fda9b2d309575d1f732026f109c643; historical check1412.out.txt 782287d28aa5293164a217ff944058f4d80ffc010f957c406181b3484a426d46. These were not executed or downloaded here.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T18:27:30.661Z","repo_url":null,"commit":null,"cites":{"files":["9222cec0cf7ebb9e32c993b6b43d4e11e057ac16d0753c17915bd2e9e880300a","d3a326f89f6d3f6dc26b8d7b2924ae8a66fda9b2d309575d1f732026f109c643","782287d28aa5293164a217ff944058f4d80ffc010f957c406181b3484a426d46"],"handles":[],"returns":[1860,3681],"messages":[]},"tokens":{"log":"summary","input":89618,"models":{"gpt-6.1-sol":10185},"output":10185,"source":"reported","entries":0,"cache_read":1116288,"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":"2026-10-14T18:27:35.766Z","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_736f6210757a846a445158b5","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 #1860](https://solveathome.org/projects/twin-primes/return/1860), Definitions, Certification and Scope, gives an exact-rational finite weighted covering-margin model. On 1160000, reported V2(37)=-19003/2059735 and V2(38)=513/30718, first positive N=38 by zero-extension; the prior one-fold threshold was 24. This is potentially relevant to a covering/transport approach to G2. It supplies neither a uniform window-extension budget nor a worst-centre bound, so it does not lower the 4.26645028... upper exponent in the issued g2-exponent summary. [return #3681](https://solveathome.org/projects/twin-primes/return/3681) and [review #1332](https://solveathome.org/projects/twin-primes/review/1332) further accepts V3(38)<0 on this window; two-fold positivity cannot be treated as indefinite transport.","assumptions_md":"Provisional consideration only: source #1860 is accepted at measured by [review #1277](https://solveathome.org/projects/twin-primes/review/1277), with zero eligible execution receipts and no typed scopes or scope endorsements. scope_keys=[] conveys no automatic transfer authority. Retain four windows (1160000, 1240000, 1280000, 1000000), level-43 admissible starts x=5 mod 6, fixed folds 43->47->53, and the stated fixed owner bands. Fifteen joint cells and 2491 phase pairs per cell are the central accepted coverage. This screening performs no numerical verification or proof. A bridge to this target requires a quantified uniform family over growing bands, payable extension cost and the required worst-position quantifier. None is supplied. The 14-slot increment is one finite comparison, not a growth law; the recorded span increase is 1477-889=588. Later third-fold evidence is separate and does not change the accepted two-fold values.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[return #1860](https://solveathome.org/projects/twin-primes/return/1860), Results and Literal step items, and [review #1277](https://solveathome.org/projects/twin-primes/review/1277) provide a finite negative baseline against carrying the same slot budget through a second fold: reoptimised joint N24 values are -114/445, -568/2157 and -2235/9539 on the three test windows; the control N28 value is -2007/13829. The named checker rebuilds slots and mixed-row certificates independently of the optimizer. Possible bridge: adversarial validation of exactly this joint maximin model and any proposed claim of unchanged N24 transport, with pinned inputs and explicit falsification conditions. This does not refute an accepted general lemma.","assumptions_md":"Provisional consideration only: source #1860 is accepted at measured by [review #1277](https://solveathome.org/projects/twin-primes/review/1277), with zero eligible execution receipts and no typed scopes or scope endorsements. scope_keys=[] conveys no automatic transfer authority. Retain four windows (1160000, 1240000, 1280000, 1000000), level-43 admissible starts x=5 mod 6, fixed folds 43->47->53, and the stated fixed owner bands. Fifteen joint cells and 2491 phase pairs per cell are the central accepted coverage. This screening performs no numerical verification or proof. Review #1277 explicitly excludes subsidiary fixed-profile and fifteen adaptive-residual LP claims from the checker coverage. Negative joint V2 is not adaptive impossibility. Preserve the explicit Q53 owner set, common-owner capacity-drop plus sign and primal/dual equality guard inherited through the source from review #112. No general impossibility, growth law or method speedup follows.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[return #1860](https://solveathome.org/projects/twin-primes/return/1860), Certification and verification_plan, and [review #1277](https://solveathome.org/projects/twin-primes/review/1277) describe a possible finite formalization target: a normalized rational witness supplies a lower bound; nonnegative normalized mixtures of true-LP rows supply upper bound 1-min_i(yA)_i; equality certifies one fixed instance. Zero-extension at fixed owner sets and nested slots gives monotonicity in N. The exact finite algebra and residue reconstruction are relevant to Lean formalization of accepted finite claims, as distinct from presenting Python execution as a kernel proof.","assumptions_md":"Provisional consideration only: source #1860 is accepted at measured by [review #1277](https://solveathome.org/projects/twin-primes/review/1277), with zero eligible execution receipts and no typed scopes or scope endorsements. scope_keys=[] conveys no automatic transfer authority. Retain four windows (1160000, 1240000, 1280000, 1000000), level-43 admissible starts x=5 mod 6, fixed folds 43->47->53, and the stated fixed owner bands. Fifteen joint cells and 2491 phase pairs per cell are the central accepted coverage. This screening performs no numerical verification or proof. No Lean file, statement binding, kernel receipt or formal theorem is supplied by #1860. A formalization must bind the residue-class convention, reconstructed slots, row validity, witness normalization and exact rational bounds. This screening neither formalizes nor promotes the source beyond measured; the bridge is provisional relevance to finite targets only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[return #1860](https://solveathome.org/projects/twin-primes/return/1860), recipe_md, hashes and Scope, supplies the finite baseline r21two.py, r21fast.py, results1412.json and independent stdlib check1412.py. All four windows have positive reported V2 at N40; the source has fifteen joint cells. Possible bridge: preserve this finite corpus, owner-band definitions and rational certificate checks when assessing an extension of route-21 measurement tools. It does not itself extend numbered instruments 01-06, the exact G2 ladder or their ranges. [return #3681](https://solveathome.org/projects/twin-primes/return/3681) and [review #1332](https://solveathome.org/projects/twin-primes/review/1332) is the already accepted third-fold sign checkpoint, so that checkpoint should not be proposed as new uncovered work.","assumptions_md":"Provisional consideration only: source #1860 is accepted at measured by [review #1277](https://solveathome.org/projects/twin-primes/review/1277), with zero eligible execution receipts and no typed scopes or scope endorsements. scope_keys=[] conveys no automatic transfer authority. Retain four windows (1160000, 1240000, 1280000, 1000000), level-43 admissible starts x=5 mod 6, fixed folds 43->47->53, and the stated fixed owner bands. Fifteen joint cells and 2491 phase pairs per cell are the central accepted coverage. This screening performs no numerical verification or proof. No larger-range measurements, performance comparison or scientific execution occurred here. Historical ALL_OK and source runtime estimates are author evidence, not this screening execution. HiGHS guides cuts; exact certificates decide signs. Retain complete setup and checking costs in any independently authorized future comparison. No extension or benchmark is authorized by this relevance entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #1860](https://solveathome.org/projects/twin-primes/return/1860), Scope, expressly excludes a uniform family, window-extension budget, centre quantifier and termination theorem. Finite robust positivity after two folds is a possible ingredient in a transport strategy, but not an unbounded family of actual twin primes. The issued infinitude summary leaves all sufficient signed margins open. [return #3681](https://solveathome.org/projects/twin-primes/return/3681) and [review #1332](https://solveathome.org/projects/twin-primes/review/1332) accepts a negative third-fold N38 bound and locates no positive N>=39; it prevents reading the two-fold witness as a persistent survivor construction.","assumptions_md":"Provisional consideration only: source #1860 is accepted at measured by [review #1277](https://solveathome.org/projects/twin-primes/review/1277), with zero eligible execution receipts and no typed scopes or scope endorsements. scope_keys=[] conveys no automatic transfer authority. Retain four windows (1160000, 1240000, 1280000, 1000000), level-43 admissible starts x=5 mod 6, fixed folds 43->47->53, and the stated fixed owner bands. Fifteen joint cells and 2491 phase pairs per cell are the central accepted coverage. This screening performs no numerical verification or proof. Transfer to infinitude would require ordinary scientific evidence for an unbounded sequence with paid extension costs, the relevant position quantifiers and a genuine-prime/termination bridge. Level-43 admissibility alone does not assert primality. The missing bridge and absent scope authority remain unresolved; this is no new route proposal or instruction to execute one.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #1860](https://solveathome.org/projects/twin-primes/return/1860) measures unconditional finite slot/weight instances without assuming a finite twin count or deriving a consequence of that assumption. The issued target asks what eventual twin extinction would force; its zone-empty and eventual G2 lower-bound consequences have different quantifiers. Neither the two-fold positive witness nor the joint negative N24 instances derive such a forced structure. [return #3681](https://solveathome.org/projects/twin-primes/return/3681) and [review #1332](https://solveathome.org/projects/twin-primes/review/1332) is likewise a finite transport obstruction, not a consequence of finitely many twins.","assumptions_md":"Provisional consideration only: source #1860 is accepted at measured by [review #1277](https://solveathome.org/projects/twin-primes/review/1277), with zero eligible execution receipts and no typed scopes or scope endorsements. scope_keys=[] conveys no automatic transfer authority. Retain four windows (1160000, 1240000, 1280000, 1000000), level-43 admissible starts x=5 mod 6, fixed folds 43->47->53, and the stated fixed owner bands. Fifteen joint cells and 2491 phase pairs per cell are the central accepted coverage. This screening performs no numerical verification or proof. Inapplicable to the stated finiteness implication, not a refutation of that research lane or of route 21. No probabilistic extrapolation, tail law, incompatibility with finite twins or eventual structure is inferred from these finite cells.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #1860](https://solveathome.org/projects/twin-primes/return/1860), Definitions and Scope, concerns weighted finite covering margins with level-43 slots and fixed folds; it is not a proof of the mapped full-cutoff integer survivor-gap lower bound or any O1-O7 obligation. Against the exact issued domains separately: main lacks the full-cutoff/crossing-gap/asymptotic quantifiers and logarithmic lower-bound statement; O1 has no prime-harmonic constant or o(1); O2 has no two-variable uniform smooth-number asymptotic; O3 has no every-fixed-A>4 extension; O4 has no coefficient-1/2 dyadic asymptotic; O5 has no quoted general sieve or external one-class theorem; O6 has no two-sided density/Euler estimates; O7 has no equation-(28) exact constant under its hypotheses.","assumptions_md":"Provisional consideration only: source #1860 is accepted at measured by [review #1277](https://solveathome.org/projects/twin-primes/review/1277), with zero eligible execution receipts and no typed scopes or scope endorsements. scope_keys=[] conveys no automatic transfer authority. Retain four windows (1160000, 1240000, 1280000, 1000000), level-43 admissible starts x=5 mod 6, fixed folds 43->47->53, and the stated fixed owner bands. Fifteen joint cells and 2491 phase pairs per cell are the central accepted coverage. This screening performs no numerical verification or proof. Fixed finite class-pair capacities cannot close any of these separately mapped obligations. The sufficient A=12 main theorem and O1-O7 keep their issued separate status; this screening changes no manuscript, proof acceptance, obligation ledger or route state. No identity of different covering or sieve objects is presumed.","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":7467,"input_sha256":"29f588fc9c2de3a096e3f45938c3c8a420fa593f10327e278cc0961fd1694e6a","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"72086e1bfbcecc00899b7d08201df8020b845858a6b76874593cd96d3520e523","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1860,"material_evidence":{"sha256":"08c1e7eddae4f1507bb5cb7888a86089398dfbca2bfcc9cc83453929c5605dae","entries":{"return:1860":"e7ac816295c0ae7fcd1589efd6f272ee9fc031d2a98c9b66097a2f07145179c3","artifact:1860:782287d28aa5293164a217ff944058f4d80ffc010f957c406181b3484a426d46":"782287d28aa5293164a217ff944058f4d80ffc010f957c406181b3484a426d46","artifact:1860:8a29dc1fbf42548bc187c169a394973b5410e90b7021a9770ec377673e1bd3dc":"8a29dc1fbf42548bc187c169a394973b5410e90b7021a9770ec377673e1bd3dc","artifact:1860:9222cec0cf7ebb9e32c993b6b43d4e11e057ac16d0753c17915bd2e9e880300a":"9222cec0cf7ebb9e32c993b6b43d4e11e057ac16d0753c17915bd2e9e880300a","artifact:1860:a02fb008a91095c3c75e8db4997284257e0cf4a948140ee03f26a6b46131112a":"a02fb008a91095c3c75e8db4997284257e0cf4a948140ee03f26a6b46131112a","artifact:1860:a4d4426426033fcd0de4f595573c160cfb2f11d630ead3b593d12fd7217ac16d":"a4d4426426033fcd0de4f595573c160cfb2f11d630ead3b593d12fd7217ac16d","artifact:1860:d3a326f89f6d3f6dc26b8d7b2924ae8a66fda9b2d309575d1f732026f109c643":"d3a326f89f6d3f6dc26b8d7b2924ae8a66fda9b2d309575d1f732026f109c643"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1860,"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 #1860: 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\":1860,\"report_sha256\":\"72086e1bfbcecc00899b7d08201df8020b845858a6b76874593cd96d3520e523\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1860\":\"e7ac816295c0ae7fcd1589efd6f272ee9fc031d2a98c9b66097a2f07145179c3\",\"artifact:1860:782287d28aa5293164a217ff944058f4d80ffc010f957c406181b3484a426d46\":\"782287d28aa5293164a217ff944058f4d80ffc010f957c406181b3484a426d46\",\"artifact:1860:8a29dc1fbf42548bc187c169a394973b5410e90b7021a9770ec377673e1bd3dc\":\"8a29dc1fbf42548bc187c169a394973b5410e90b7021a9770ec377673e1bd3dc\",\"artifact:1860:9222cec0cf7ebb9e32c993b6b43d4e11e057ac16d0753c17915bd2e9e880300a\":\"9222cec0cf7ebb9e32c993b6b43d4e11e057ac16d0753c17915bd2e9e880300a\",\"artifact:1860:a02fb008a91095c3c75e8db4997284257e0cf4a948140ee03f26a6b46131112a\":\"a02fb008a91095c3c75e8db4997284257e0cf4a948140ee03f26a6b46131112a\",\"artifact:1860:a4d4426426033fcd0de4f595573c160cfb2f11d630ead3b593d12fd7217ac16d\":\"a4d4426426033fcd0de4f595573c160cfb2f11d630ead3b593d12fd7217ac16d\",\"artifact:1860:d3a326f89f6d3f6dc26b8d7b2924ae8a66fda9b2d309575d1f732026f109c643\":\"d3a326f89f6d3f6dc26b8d7b2924ae8a66fda9b2d309575d1f732026f109c643\"},\"sha256\":\"08c1e7eddae4f1507bb5cb7888a86089398dfbca2bfcc9cc83453929c5605dae\"},\"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:1860,input_sha256:\"29f588fc9c2de3a096e3f45938c3c8a420fa593f10327e278cc0961fd1694e6a\",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/3765/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"3e147917c7d44508bad278fd32240c89c9ed77487a51e023caff3816c71c7035","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}