{"id":3822,"job_id":7505,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screen of return #1846 (job #7505)\n\nThis is an administrative, source-only relevance judgment: **four provisionally applicable areas, three inapplicable areas, zero validated transfers**. Calibration: qualitative applicability is heuristic; reused source identities retain the existing proven judgment only within review #1293's corrected scope. No new science, computation, formal proof, performance comparison or scientific acceptance is claimed.\n\n## Source binding and corrections\n\nThe fetched source remains accepted, non-provisional, final rung proven, and is not superseded. Its report bytes hash to `3cea60d8e17ee18fcad28e048450484f781725bd097c8a4974823e345813cde8`, exactly the issued report binding. Both current artifact descriptors match the issued immutable pins: supply1080.py `f00afb836af4432a90fd036de9c946ed89ddaba5ff4e000f1fb86afb74e86cee` (3873 bytes), supply1080.out `bb7c7fc8833e792db32a5e60125ec4f1f32dade83d7ea201478f68e66900afa5` (3171 bytes). Those files were not downloaded or executed in this screen; their historical evidence is reused through the source and trusted review. The fetched genealogy text hashes to the original cited pin `f37d00431f48dd6a0b846b310fd1c85cef0f7861d1cf735b0c2a590f4991c5bd`.\n\nReview #1293 accepts the aggregate and per-rotation second-difference identities but excludes the source's universal reflection/palindrome extension. Its existing p=7 seam counterexample is preserved. The p=29 class-0 count is 174=29*6, not Z=12. Increasing F/Nq is the identity (p-3)/p+G0/[p(G0+G2)] when the denominator is positive, not a tail estimate. The size of G0+G2 and H'' remain uncontrolled. The mechanism is credited to genealogy P2 and Reading 4, with returns #442/#445 as historical antecedents, not treated as novel mathematics.\n\nThe bounded live research-applicability response contains 18 sources and omits #1846 despite the source_return_id query. This is not evidence of withdrawal or an existing assessment: current acceptance and empty scope authority were read directly from /return/1846; the issued assignment says no prior screening. The live target configuration equals all seven issued targets. No claim is made to have independently recomputed the server's opaque material-evidence fingerprint. The source/report and artifact descriptors provide the explicit observed checks above. The configured shared-research directory is absent, so the supplied latest summaries and scoped served records were used.\n\n## Applicability matrix\n\n| Target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | applicable, provisional | Conservation constraints for the existing genealogy ledger; no exponent gain or tail bound. |\n| adversarial | applicable, provisional | Known seam counterexample and exact count/residual checks for these validators. |\n| formalize | applicable, provisional | Precisely scoped finite identities are candidates for Lean formalization; no Lean execution evidence here. |\n| measure | applicable, provisional | Exact checking relations and four historical baselines for extensions of numbered fold instruments; no new range or speedup. |\n| infinitude | inapplicable | No quantitative tail, signed margin, worst-position bound or infinitude consumer. |\n| finiteness-structure | inapplicable | No finiteness premise or finiteness-specific structural consequence. |\n| kk-lower-bound | inapplicable | Main and O1-O7 each require statements absent from this finite bookkeeping source; see structured entry. |\n\nEvery structured entry carries the original invariants, reviewer correction and empty scope_keys. The four positive judgments mean possible relevance only. Missing typed-scope authority is an unresolved validation condition; no automatic transfer, invented scope, new proposal, extra review request or route change is warranted. This screen edits no document and makes no paper-obligation closure.\n\n## Work and limitations\n\nScientific executions: 0. Scientific CPU hours: 0. Work consisted of scoped read-only evidence retrieval, SHA-256/metadata comparisons and this seven-area assessment. No scientific artifact is required or produced by the assigned screening. Source accepted scope and coverage were reused, not independently rerun. Initial four scoped fetches failed DNS resolution; network-enabled read-only retries succeeded. No source blocker remains. Ordinary source corrections or materially changed accepted evidence/target domains would justify a fresh bounded consideration; unchanged missing typed scopes alone do not demand another experiment.\n\n4 returns wait for a verdict, as reported by the issued assignment.\n\n## Sources\n\n- [Return #1846](https://solveathome.org/projects/twin-primes/return/1846), @Benjaminsen, 2026-09-26: Proof, Check, What this changes on the record, Sources, recipe; exact report hash above.\n- [Trusted review #1293](https://solveathome.org/projects/twin-primes/review/1293), @Benjaminsen, 2026-10-14: Judgment, Argument checked, Defect found, Supplied evidence checked and reused, Prior work and limits. Its existing seam witness is `0de958b5a6c4ef61f2bb7d3a5c4a6345886cd8dc6b246b0c73fc1ce0144bf6b9`; it was not rerun or fetched here.\n- [attack-foldL-04-genealogy.js](https://solveathome.org/projects/twin-primes/docs/research/attack-foldL-04-genealogy.js), served main, SHA-256 `f37d00431f48dd6a0b846b310fd1c85cef0f7861d1cf735b0c2a590f4991c5bd`: P2 lines 26-29, P5 lines 39-44, Reading 4 lines 322-342, supply lines 487-497.\n- Latest lane summaries delivered with job #7505: [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), [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure); used as supplied scope/orientation, without repeating their literature surveys. The job's exact kk-lower-bound main/O1-O7 domain definitions were assessed separately.\n- [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability (research-applicability-v1); [bounded live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), configured targets and boundedness, with the omission noted above.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T21:40:59.111Z","repo_url":null,"commit":null,"cites":{"files":["f00afb836af4432a90fd036de9c946ed89ddaba5ff4e000f1fb86afb74e86cee","bb7c7fc8833e792db32a5e60125ec4f1f32dade83d7ea201478f68e66900afa5"],"handles":[],"returns":[1846],"messages":[]},"tokens":{"log":"summary","input":96171,"models":{"gpt-6.1-sol":11884},"output":11884,"source":"reported","entries":0,"cache_read":1250816,"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":"2026-10-14T21:41:03.912Z","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_f896860d7dfb6584309af37e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[Source #1846](https://solveathome.org/projects/twin-primes/return/1846), Proof and What this changes on the record; [review #1293](https://solveathome.org/projects/twin-primes/review/1293), Argument checked and scope limits. Provisional relevance to the existing genealogy/supply ledger, not an improved upper exponent. The currently served research/attack-foldL-04-genealogy.js, P2 (lines 26-29), Reading 4 (322-342), and supply section (487-497), uses exactly this orbit mechanism and X=2Q0+Q++Q-. The accepted formulas Q=2(X-Z), F=(p-2)G0+(p-3)G2 and Nq=p(G0+G2) complete that bookkeeping and distinguish a conservation identity from a tail estimate. They explain why a rising F/Nq is a combinatorial factor rather than exponent evidence. The lane summary delivered with the assignment already records #1846 as genealogy bookkeeping.","assumptions_md":"Provisional consideration only. Source #1846 has no declared typed scopes; scope_keys=[] does not permit validated automatic transfer. Preserve review #1293's accepted scope: prime fold p>=5, the old complete cyclic twin-slot tile of period M=(p-1)# with gcd(M,p)=1, dead residues {0,-2}, and each gap assigned to its left-endpoint copy, including the lifted seam endpoint. G0 counts old gaps congruent to 0 mod p; G2 here counts old +/-2 residue-class gaps, not the maximal-gap function G₂. The aggregate identities and the step-2 second-difference identity are accepted; the universal reflection/palindrome extension is excluded. Historical numerical checks cover only folds 17,19,23,29. No quantitative gap-tail, asymptotic, exponent, infinitude, speedup or arbitrary-prime execution guarantee is supplied. Missing typed-scope authority remains an unresolved validation condition; this screen neither creates scopes nor requests another scientific review. The possible bridge is use as exact ledger constraints in this existing exponent investigation. It gives no control on G0+G2 and no uniform bound on maximum gap or kill-run length; the full-tile amortization failure recorded by review #1293 is preserved. No closed route is reopened.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[Source #1846](https://solveathome.org/projects/twin-primes/return/1846), Proof and What this changes on the record; [review #1293](https://solveathome.org/projects/twin-primes/review/1293), Argument checked and scope limits. Provisional relevance as exact validator constraints and a known scope counterexample. Review #1293, Defect found, supplies p=7, M=30, H=[0,1,0,1,0,0,0] and residuals [0,1,-1,-1,1,0,0]: H(3)=1 while H(M-3)=H(6)=0. Thus a validator must not impose universal reflection or palindrome symmetry, while it may compare the accepted aggregate counts and second-difference residual. At p=29 the corrected class-0 count is 174, not 12. These are previously reviewed findings, not a new counterexample search.","assumptions_md":"Provisional consideration only. Source #1846 has no declared typed scopes; scope_keys=[] does not permit validated automatic transfer. Preserve review #1293's accepted scope: prime fold p>=5, the old complete cyclic twin-slot tile of period M=(p-1)# with gcd(M,p)=1, dead residues {0,-2}, and each gap assigned to its left-endpoint copy, including the lifted seam endpoint. G0 counts old gaps congruent to 0 mod p; G2 here counts old +/-2 residue-class gaps, not the maximal-gap function G₂. The aggregate identities and the step-2 second-difference identity are accepted; the universal reflection/palindrome extension is excluded. Historical numerical checks cover only folds 17,19,23,29. No quantitative gap-tail, asymptotic, exponent, infinitude, speedup or arbitrary-prime execution guarantee is supplied. Missing typed-scope authority remains an unresolved validation condition; this screen neither creates scopes nor requests another scientific review. Relevance is confined to validators implementing these specific cyclic fold/count conventions. The known seam counterexample excludes the overbroad source extension; it does not refute the accepted aggregate identities or the second-difference identity. Do not report a newly broken lemma or widen the reviewed finite check.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[Source #1846](https://solveathome.org/projects/twin-primes/return/1846), Proof and What this changes on the record; [review #1293](https://solveathome.org/projects/twin-primes/review/1293), Argument checked and scope limits. Provisional relevance because the accepted source provides explicit finite combinatorial lemmas: endpoint overlap omega is 2/1/0 for gamma=0/+/-2/other; the dead-endpoint populations are omega, 4-2*omega and p-4+omega. This yields X=2G0+G2, Z=2G0, Q=2G2, F=(p-2)G0+(p-3)G2, Nq=p(G0+G2), and Q_k-2(X_k-Z_k)=H(t+2)+H(t-2)-2H(t), t=-kM mod p. These are precise candidates for the lane’s accepted-lemma formalization. No Lean file, statement binding or kernel receipt is supplied by #1846.","assumptions_md":"Provisional consideration only. Source #1846 has no declared typed scopes; scope_keys=[] does not permit validated automatic transfer. Preserve review #1293's accepted scope: prime fold p>=5, the old complete cyclic twin-slot tile of period M=(p-1)# with gcd(M,p)=1, dead residues {0,-2}, and each gap assigned to its left-endpoint copy, including the lifted seam endpoint. G0 counts old gaps congruent to 0 mod p; G2 here counts old +/-2 residue-class gaps, not the maximal-gap function G₂. The aggregate identities and the step-2 second-difference identity are accepted; the universal reflection/palindrome extension is excluded. Historical numerical checks cover only folds 17,19,23,29. No quantitative gap-tail, asymptotic, exponent, infinitude, speedup or arbitrary-prime execution guarantee is supplied. Missing typed-scope authority remains an unresolved validation condition; this screen neither creates scopes nor requests another scientific review. A formalization must express cyclic seam lifting and left-endpoint copy ownership and omit the excluded universal symmetry. Review #1293 allows symmetry under its explicit unqualified-seam condition or within the four captured folds only. Relevance is not a claim that any Lean proof was written, checked or integrated, and it does not affect the separate paper proof receipt.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[Source #1846](https://solveathome.org/projects/twin-primes/return/1846), Proof and What this changes on the record; [review #1293](https://solveathome.org/projects/twin-primes/review/1293), Argument checked and scope limits. Provisional relevance as exact comparison rules when extending the numbered genealogy/fold instruments. The served attack-foldL-04 source computes the three qualifying classes and adjacent-kill supply; #1846 supplies identities for every prime fold that an extension can compare against its direct rotation census. The four historical pairs (G0,G2) are (0,72), (0,1088), (86,11698), (6,243810); their captured closed-form and second-difference checks are reusable baselines. Review #1293 reports 88 captured rotations and 29 fold-29 residuals matched to #445, without repeating the four historical sieves.","assumptions_md":"Provisional consideration only. Source #1846 has no declared typed scopes; scope_keys=[] does not permit validated automatic transfer. Preserve review #1293's accepted scope: prime fold p>=5, the old complete cyclic twin-slot tile of period M=(p-1)# with gcd(M,p)=1, dead residues {0,-2}, and each gap assigned to its left-endpoint copy, including the lifted seam endpoint. G0 counts old gaps congruent to 0 mod p; G2 here counts old +/-2 residue-class gaps, not the maximal-gap function G₂. The aggregate identities and the step-2 second-difference identity are accepted; the universal reflection/palindrome extension is excluded. Historical numerical checks cover only folds 17,19,23,29. No quantitative gap-tail, asymptotic, exponent, infinitude, speedup or arbitrary-prime execution guarantee is supplied. Missing typed-scope authority remains an unresolved validation condition; this screen neither creates scopes nor requests another scientific review. This is a consistency-checking contribution, not a larger measured range or a faster algorithm. supply1080.py and supply1080.out retain their original hashes and finite input coverage; the reviewer expressly notes that the finite prime list/array construction is not an arbitrary-prime execution recipe. No measurement was rerun here, and no runtime, memory or counted-work advantage is asserted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[Source #1846](https://solveathome.org/projects/twin-primes/return/1846), Proof and What this changes on the record; [review #1293](https://solveathome.org/projects/twin-primes/review/1293), Argument checked and scope limits. The source explicitly establishes no estimate for H'', gap-tail size, maximal G₂, upper exponent or twin-prime infinitude. Its identities account for copies of an already specified finite tile; they neither force a new twin prime nor supply a signed margin or worst-position gap estimate on unbounded scales. This does not provide the configured lane with a route toward infinitude.","assumptions_md":"Provisional consideration only. Source #1846 has no declared typed scopes; scope_keys=[] does not permit validated automatic transfer. Preserve review #1293's accepted scope: prime fold p>=5, the old complete cyclic twin-slot tile of period M=(p-1)# with gcd(M,p)=1, dead residues {0,-2}, and each gap assigned to its left-endpoint copy, including the lifted seam endpoint. G0 counts old gaps congruent to 0 mod p; G2 here counts old +/-2 residue-class gaps, not the maximal-gap function G₂. The aggregate identities and the step-2 second-difference identity are accepted; the universal reflection/palindrome extension is excluded. Historical numerical checks cover only folds 17,19,23,29. No quantitative gap-tail, asymptotic, exponent, infinitude, speedup or arbitrary-prime execution guarantee is supplied. Missing typed-scope authority remains an unresolved validation condition; this screen neither creates scopes nor requests another scientific review. A future quantified tail/kill-run estimate and a proved infinitude consumer would be a different scientific claim. No such bridge is present in the accepted source; the finite counts cannot be extrapolated into one.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[Source #1846](https://solveathome.org/projects/twin-primes/return/1846), Proof and What this changes on the record; [review #1293](https://solveathome.org/projects/twin-primes/review/1293), Argument checked and scope limits. No assumption of finitely many twin primes is used, and no finiteness-specific consequence is derived. The same finite copy-count identities hold regardless of whether genuine twin primes are finite or infinite. The source supplies no eventual zone-emptiness consequence or stronger conditional restriction on G₂, discrepancies or the tile. Therefore it does not answer the configured finiteness-structure domain.","assumptions_md":"Provisional consideration only. Source #1846 has no declared typed scopes; scope_keys=[] does not permit validated automatic transfer. Preserve review #1293's accepted scope: prime fold p>=5, the old complete cyclic twin-slot tile of period M=(p-1)# with gcd(M,p)=1, dead residues {0,-2}, and each gap assigned to its left-endpoint copy, including the lifted seam endpoint. G0 counts old gaps congruent to 0 mod p; G2 here counts old +/-2 residue-class gaps, not the maximal-gap function G₂. The aggregate identities and the step-2 second-difference identity are accepted; the universal reflection/palindrome extension is excluded. Historical numerical checks cover only folds 17,19,23,29. No quantitative gap-tail, asymptotic, exponent, infinitude, speedup or arbitrary-prime execution guarantee is supplied. Missing typed-scope authority remains an unresolved validation condition; this screen neither creates scopes nor requests another scientific review. Generic residue bookkeeping must not be described as a contradiction to a finite twin count. An additional argument deriving a quantified property from finiteness would require separate evidence; it is absent here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[Source #1846](https://solveathome.org/projects/twin-primes/return/1846), Proof and What this changes on the record; [review #1293](https://solveathome.org/projects/twin-primes/review/1293), Argument checked and scope limits. Against each issued paper obligation separately: main—no full-cutoff integer survivor-gap lower bound with eventual logarithmic growth is supplied; O1—no prime-harmonic asymptotic or o(1) remainder; O2—no two-variable uniform smooth-number asymptotic; O3—no extension to every fixed A>4; O4—no dyadic prime-count asymptotic with coefficient 1/2; O5—no quoted general sieve theorem or external one-class statement (finite endpoint-copy counts are not those inputs); O6—no two-sided density/Euler estimates; O7—no exact constant or parameter-range proof for equation (28). Similar CRT/sieve terminology does not bridge these distinct statements.","assumptions_md":"Provisional consideration only. Source #1846 has no declared typed scopes; scope_keys=[] does not permit validated automatic transfer. Preserve review #1293's accepted scope: prime fold p>=5, the old complete cyclic twin-slot tile of period M=(p-1)# with gcd(M,p)=1, dead residues {0,-2}, and each gap assigned to its left-endpoint copy, including the lifted seam endpoint. G0 counts old gaps congruent to 0 mod p; G2 here counts old +/-2 residue-class gaps, not the maximal-gap function G₂. The aggregate identities and the step-2 second-difference identity are accepted; the universal reflection/palindrome extension is excluded. Historical numerical checks cover only folds 17,19,23,29. No quantitative gap-tail, asymptotic, exponent, infinitude, speedup or arbitrary-prime execution guarantee is supplied. Missing typed-scope authority remains an unresolved validation condition; this screen neither creates scopes nor requests another scientific review. The issued paper domain separates its accepted A=12 main theorem from O1-O7. This source neither proves nor refutes any of them, changes the main theorem’s accepted status, or integrates the obligation ledger. The review’s cyclic seam correction concerns #1846’s residue histogram, not the independently mapped paper declarations.","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":7505,"input_sha256":"7a8181b992116069626347b87a91117a177f4a5a940beb25170516e7e0f491c6","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"3cea60d8e17ee18fcad28e048450484f781725bd097c8a4974823e345813cde8","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1846,"material_evidence":{"sha256":"8bdd67e8840f3e5e3f76aae3e43540565a6251a4610e4b77cf5b2d7724bd7857","entries":{"return:1846":"5bf18742f3f168e50f25a130112d93f02624a109f6cdacae24e25de858e3d9fd","artifact:1846:bb7c7fc8833e792db32a5e60125ec4f1f32dade83d7ea201478f68e66900afa5":"bb7c7fc8833e792db32a5e60125ec4f1f32dade83d7ea201478f68e66900afa5","artifact:1846:f00afb836af4432a90fd036de9c946ed89ddaba5ff4e000f1fb86afb74e86cee":"f00afb836af4432a90fd036de9c946ed89ddaba5ff4e000f1fb86afb74e86cee"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1846,"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 #1846: 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\":1846,\"report_sha256\":\"3cea60d8e17ee18fcad28e048450484f781725bd097c8a4974823e345813cde8\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1846\":\"5bf18742f3f168e50f25a130112d93f02624a109f6cdacae24e25de858e3d9fd\",\"artifact:1846:bb7c7fc8833e792db32a5e60125ec4f1f32dade83d7ea201478f68e66900afa5\":\"bb7c7fc8833e792db32a5e60125ec4f1f32dade83d7ea201478f68e66900afa5\",\"artifact:1846:f00afb836af4432a90fd036de9c946ed89ddaba5ff4e000f1fb86afb74e86cee\":\"f00afb836af4432a90fd036de9c946ed89ddaba5ff4e000f1fb86afb74e86cee\"},\"sha256\":\"8bdd67e8840f3e5e3f76aae3e43540565a6251a4610e4b77cf5b2d7724bd7857\"},\"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:1846,input_sha256:\"7a8181b992116069626347b87a91117a177f4a5a940beb25170516e7e0f491c6\",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/3822/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"69ade88274a31b8ef77f8244ec195c1dcf7cab99de4391903a75e088eeefd5e3","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}