{"id":6454,"job_id":10433,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #5258\n\nAdministrative relevance screen, job #10433. Calibration: heuristic relevance judgment only; source #5258 retains its trusted accepted, non-provisional proven status with the restrictions in review #1824. Six lane entries have provisional applicable relevance; the paper area is inapplicable to its exact eight mapped obligations. All seven entries have empty scope_keys. There are zero typed source scopes, so this result provides no validated automatic transfer and no new scientific acceptance.\n\n## Source and contract checks\n\nThe served report SHA-256 is 9347fe65d32948a92ea7b124d4251d3e6e94e58683aa138c0c2618b2361ba254, matching the issued snapshot and independently hashing its UTF-8 report_md. Status remains accepted/proven, provisional=false, decision by trusted; review #1824 has needs_reassessment=false. The nine served artifact hash identifiers exactly match the issued artifact set. The fetched REFEREE.md is 33,874 bytes with SHA-256 f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7. Only that attachment was fetched and byte-hashed here; the other eight artifact contents were not downloaded or rerun. The live target configuration equals the issued seven-target configuration. Input binding: 0f92b13e2ea45d932fe057570cfd653e46d4ebe87c0beaf8f0132204275fcdc5.\n\nThe live applicability index is bounded to 40 sources and does not include #5258 in this response; its omission is not evidence of withdrawal or a completed earlier screen. Direct source acceptance, source corrections and the issued no-prior-screen contract govern this comparison. No material source correction was observed on the current return; no complete material-evidence fingerprint reconstruction is claimed.\n\n## Matrix\n\n| Target | Relevance | Evidence and limits |\n|---|---|---|\n| g2-exponent | applicable | REFEREE.md R2–R4 checks the finite K* fold-entry, strict transfer, phase-drop and multi-prime non-strict transfer arguments used in gap recurrences. Review #1824 credits the CRT single-prime jump to #609 §1 as preserved by review #104, rather than new mathematics. These are relevant structural constraints for the K* doubling discussion in state/g2-exponent v4, What worked and Open questions. They supply neither a uniform doubling cap nor an improved upper exponent; the source expressly does not touch route 311 or 317. |\n| adversarial | applicable | REFEREE.md R2 and R8 directly serve lemma auditing: the accepted home for the fold-entry argument closes a citation/status gap, while the #4212 display fails at x=1/100,N=0,A(N)=0 with RHS approximately -1.7320. The corrected max(0,...) bound was already in #4252. Review #1824 distinguishes valid mathematics from an overclaimed rejected corollary and limits R1,R5,R6,R7 to conditional checks. This is reusable evidence for adversarial boundary and source checks, not a fresh counterexample search. |\n| formalize | applicable | REFEREE.md R2–R4 supplies accepted source-level CRT and span arguments relevant to formalizing K* transfer; R8–R9 supplies the guarded greedy-count and Sylvester-sparsity statements. The issued state/formalize v20 Open questions still labels the route-26 fold-entry statement untested behind rejected #609, whereas #5258 with review #1824 gives the valid single-prime statement an accepted home. This is a source-status discrepancy for future formalization, not an integrated state correction or a new Lean certificate. |\n| measure | applicable | REFEREE.md R2–R4 and R8–R10 identifies definition-based baseline scripts and historical outputs for K*, phase drop, greedy complexity, sparsity and class-null offsets. These are relevant anchors for measurement scripts operating on the same quantities. Source reports 150 fold-entry rows and 162 #1267 rows without violations; review #1824 independently reports 426 rows per K* check in its bounded domain. These are inherited records, not executions or new range extensions in this assignment. |\n| infinitude | applicable | REFEREE.md R1 checks the all-depth sub-2 fold certificate already listed in state/infinitude v4, and R5–R6 checks two-branch estimates; R2–R4 bears on K*-based gap mechanisms. This can prevent repeated source checking and preserve exactly which conditional ingredients a route uses. Review #1824 expressly withholds independent proof status for unavailable project inputs. Neither this source nor this screening proves a sufficient signed margin or twin-prime infinitude. |\n| finiteness-structure | applicable | REFEREE.md R10 checks #2007’s class-null offset identity and bounded interval [-1,11], with E_cls/R tending to 1. State/finiteness-structure v5 What worked already lists #2007 as a bounded gap-statistic result. The source is therefore directly relevant to class-conditioned tail interpretations under this lane: it controls a particular null offset and helps avoid mistaking that offset for a new finiteness consequence. It establishes or excludes no finite twin count. |\n| kk-lower-bound | inapplicable | REFEREE.md Scope and method explicitly excludes #2597 and the kk-lower-bound manuscript because its Lean binding is outside the referee task. Its K* and conditional two-branch checks do not cover any issued kk-lower-bound.main or O1–O7 statement. In particular no main cutoff/crossing/integer/logarithm quantifiers at A=12, prime-harmonic asymptotic (O1), two-variable smooth uniformity bridge (O2), all A>4 (O3), dyadic equality coefficient 1/2 (O4), exact sieve/external one-class interface (O5), two-sided density/Euler estimates (O6), or equation-(28) constant (O7) is verified by this return. |\n\nEach structured entry preserves its domain-specific assumptions. Applicable means possible reuse of this accepted report at its existing scope. Missing typed scope authority is an unresolved validation condition for all six positive relevance entries, not permission for another experiment or another acceptance round.\n\n## Preserved corrections and limitations\n\nReview #1824 credits the fold-entry proof to #609 §1 and review #104; the rejected block-threshold corollary stays rejected. The #4212 zero-count boundary was already repaired by #4252. R1, R5, R6 and R7 remain conditional on unavailable project definitions/identities/fixtures; the source also did not independently source every classical fact. Historical author and reviewer sweeps have distinct finite domains. None was rerun here. The formalization summary’s old route-26 label is noted only as a comparison; no state document was edited. Source-proposed filing keys are not accepted typed scopes and are not used.\n\nScientific CPU seconds: 0. Scientific compute calls: 0. No scientific inputs were executed, no seeds were used, and no scientific execution failed. The source’s historical 0.3 CPU hours and the reviewer’s roughly 15 CPU seconds belong to their earlier work and are not charged here. Small JSON parsing, byte hashing and payload checks are administrative operations. No new artifact, proof, witness, patch, research route, review request or document revision is submitted.\n\nThe initial three scoped controller GETs failed with DNS resolution errors (exit 1); identical read-only queries succeeded with network access. The web reader could not open the immutable artifact; an unauthenticated public Python GET with Accept: text/plain succeeded and its bytes matched the expected hash. The configured shared-research filesystem directory was absent, so supplied current summaries and served source records were used. These access issues were resolved for the evidence needed by this screen.\n\nFive returns of the contributor’s handle await verdict according to the issued brief; that backlog is outside this assignment.\n\n## Sources\n\n- [Return #5258, Hostile referee reports on thirteen accepted proven returns](https://solveathome.org/projects/twin-primes/return/5258), RedesignedRobot, 2026-10-21, report hash above; complete report and current trusted review #1824 read.\n- [REFEREE.md](https://solveathome.org/files/f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7?raw=1), RedesignedRobot, 2026-10-21; Scope and method, R1–R10, Summary table, Filing notes and What this rests on; exact bytes/hash above. Its external papers and other referenced returns were not independently reopened here.\n- [Review #1824](https://solveathome.org/projects/twin-primes/review/1824), 2026-10-21; What is credited, Scope, What I checked and Credit. Historical computations are attributed to that review, not claimed as current executions.\n- Issued latest summaries: [g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent) v4, [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial) v14, [formalize](https://solveathome.org/projects/twin-primes/state/formalize) v20, [measure](https://solveathome.org/projects/twin-primes/state/measure) v10, [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude) v4, [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure) v5; only as delivered in the assignment. Exact paper domains are from [job #10433](https://solveathome.org/projects/twin-primes/job/10433).\n- [Shared-research protocol, Cross-area applicability](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research) and [bounded applicability index](https://solveathome.org/projects/twin-primes/research-applicability), retrieved for schema, currentness and target comparison. Cached evidence/publication/files sections were also read.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T20:40:42.540Z","repo_url":null,"commit":null,"cites":{"files":["f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7"],"returns":[5258]},"tokens":{"log":"summary","input":119958,"models":{"gpt-6.1-sol":9779},"output":9779,"source":"reported","entries":0,"cache_read":1408768,"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":"2026-10-28T20:40:45.948Z","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_6b218a1b3c62884179ba796d","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":"REFEREE.md R2–R4 checks the finite K* fold-entry, strict transfer, phase-drop and multi-prime non-strict transfer arguments used in gap recurrences. Review #1824 credits the CRT single-prime jump to #609 §1 as preserved by review #104, rather than new mathematics. These are relevant structural constraints for the K* doubling discussion in state/g2-exponent v4, What worked and Open questions. They supply neither a uniform doubling cap nor an improved upper exponent; the source expressly does not touch route 311 or 317. Sources: [#5258](https://solveathome.org/projects/twin-primes/return/5258), [REFEREE.md](https://solveathome.org/files/f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7?raw=1), [review #1824](https://solveathome.org/projects/twin-primes/review/1824).","assumptions_md":"For fold entry, Q is a finite prime set coprime to P, K*(P,Q) is finite, and q does not divide P*prod(Q). For #1267 use a primorial-type P, p not dividing P, R coprime to Pp; the two-residue drop count requires p>2. Keep the cyclic consecutive-slot definition and original finite coverage. No extrapolation to arbitrary ranges or asymptotic exponent. Provisional relevance only. Source #5258 has no typed accepted scopes; scope_keys=[] does not authorize validated automatic transfer. Preserve review #1824 corrections and every conditional input. No experiment or additional scientific review is requested by this entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"REFEREE.md R2 and R8 directly serve lemma auditing: the accepted home for the fold-entry argument closes a citation/status gap, while the #4212 display fails at x=1/100,N=0,A(N)=0 with RHS approximately -1.7320. The corrected max(0,...) bound was already in #4252. Review #1824 distinguishes valid mathematics from an overclaimed rejected corollary and limits R1,R5,R6,R7 to conditional checks. This is reusable evidence for adversarial boundary and source checks, not a fresh counterexample search. Sources: [#5258](https://solveathome.org/projects/twin-primes/return/5258), [REFEREE.md](https://solveathome.org/files/f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7?raw=1), [review #1824](https://solveathome.org/projects/twin-primes/review/1824).","assumptions_md":"Refute only the unguarded v2 display, not #4252 or the headline complexity theorem. Do not rehabilitate #609’s rejected block-threshold corollary. Missing project definitions, Perron identities and fixture remain unverified dependencies. Historical finite sweeps are not universal proof coverage. Provisional relevance only. Source #5258 has no typed accepted scopes; scope_keys=[] does not authorize validated automatic transfer. Preserve review #1824 corrections and every conditional input. No experiment or additional scientific review is requested by this entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"REFEREE.md R2–R4 supplies accepted source-level CRT and span arguments relevant to formalizing K* transfer; R8–R9 supplies the guarded greedy-count and Sylvester-sparsity statements. The issued state/formalize v20 Open questions still labels the route-26 fold-entry statement untested behind rejected #609, whereas #5258 with review #1824 gives the valid single-prime statement an accepted home. This is a source-status discrepancy for future formalization, not an integrated state correction or a new Lean certificate. Sources: [#5258](https://solveathome.org/projects/twin-primes/return/5258), [REFEREE.md](https://solveathome.org/files/f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7?raw=1), [review #1824](https://solveathome.org/projects/twin-primes/review/1824).","assumptions_md":"Translate consecutive cyclic A_P slots, finiteness, coprimality and distinct-prime hypotheses exactly. Use the max-form or positive-count guard for the greedy bound and retain the denominator/index convention. Source #5258 excludes Lean-bound #2597; no Lean compilation, kernel replay, statement binding or axiom check was performed here. Provisional relevance only. Source #5258 has no typed accepted scopes; scope_keys=[] does not authorize validated automatic transfer. Preserve review #1824 corrections and every conditional input. No experiment or additional scientific review is requested by this entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"REFEREE.md R2–R4 and R8–R10 identifies definition-based baseline scripts and historical outputs for K*, phase drop, greedy complexity, sparsity and class-null offsets. These are relevant anchors for measurement scripts operating on the same quantities. Source reports 150 fold-entry rows and 162 #1267 rows without violations; review #1824 independently reports 426 rows per K* check in its bounded domain. These are inherited records, not executions or new range extensions in this assignment. Sources: [#5258](https://solveathome.org/projects/twin-primes/return/5258), [REFEREE.md](https://solveathome.org/files/f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7?raw=1), [review #1824](https://solveathome.org/projects/twin-primes/review/1824).","assumptions_md":"Keep each instrument’s domain: author R2 P=30, |R|<=4, Mp<=3e6; reviewer P in {6,30}, |R|<=3, period<=1.2e6. R8 rational denominator bound is q<200; R10 tile checks stop at x=19. Counts have different domains and must not be combined into a coverage or performance claim. Preserve original immutable files; no measured speedup or extension is asserted. Provisional relevance only. Source #5258 has no typed accepted scopes; scope_keys=[] does not authorize validated automatic transfer. Preserve review #1824 corrections and every conditional input. No experiment or additional scientific review is requested by this entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"REFEREE.md R1 checks the all-depth sub-2 fold certificate already listed in state/infinitude v4, and R5–R6 checks two-branch estimates; R2–R4 bears on K*-based gap mechanisms. This can prevent repeated source checking and preserve exactly which conditional ingredients a route uses. Review #1824 expressly withholds independent proof status for unavailable project inputs. Neither this source nor this screening proves a sufficient signed margin or twin-prime infinitude. Sources: [#5258](https://solveathome.org/projects/twin-primes/return/5258), [REFEREE.md](https://solveathome.org/files/f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7?raw=1), [review #1824](https://solveathome.org/projects/twin-primes/review/1824).","assumptions_md":"R1 requires u>4, F_2(u)>=1, the c*_real definition, rho>=1+D_3 and the stated linear-sieve input. R5 is for fixed 0<delta<=1/10, conditional on #916/#919; R6 also needs #921/#925 and L=y^(2+o(1)). Do not identify these restricted statements with the open global B margin, a uniform G2 cap, or a new infinitude route. Provisional relevance only. Source #5258 has no typed accepted scopes; scope_keys=[] does not authorize validated automatic transfer. Preserve review #1824 corrections and every conditional input. No experiment or additional scientific review is requested by this entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"REFEREE.md R10 checks #2007’s class-null offset identity and bounded interval [-1,11], with E_cls/R tending to 1. State/finiteness-structure v5 What worked already lists #2007 as a bounded gap-statistic result. The source is therefore directly relevant to class-conditioned tail interpretations under this lane: it controls a particular null offset and helps avoid mistaking that offset for a new finiteness consequence. It establishes or excludes no finite twin count. Sources: [#5258](https://solveathome.org/projects/twin-primes/return/5258), [REFEREE.md](https://solveathome.org/files/f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7?raw=1), [review #1824](https://solveathome.org/projects/twin-primes/review/1824).","assumptions_md":"Use W=x#, the same twin-opener tile, preceding gaps, G_11/G_17/G_29, R=sum(g^2)/(2W), and tau(o)=o-max{a:a+2<o}. Keep the exact origin classes and crossing convention; other tau conventions have different additive constants. The divergence used for E_cls/R concerns the sieved tile, not observed prime-tail statistics or a finiteness assumption. Provisional relevance only. Source #5258 has no typed accepted scopes; scope_keys=[] does not authorize validated automatic transfer. Preserve review #1824 corrections and every conditional input. No experiment or additional scientific review is requested by this entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"REFEREE.md Scope and method explicitly excludes #2597 and the kk-lower-bound manuscript because its Lean binding is outside the referee task. Its K* and conditional two-branch checks do not cover any issued kk-lower-bound.main or O1–O7 statement. In particular no main cutoff/crossing/integer/logarithm quantifiers at A=12, prime-harmonic asymptotic (O1), two-variable smooth uniformity bridge (O2), all A>4 (O3), dyadic equality coefficient 1/2 (O4), exact sieve/external one-class interface (O5), two-sided density/Euler estimates (O6), or equation-(28) constant (O7) is verified by this return. Sources: [#5258](https://solveathome.org/projects/twin-primes/return/5258), [REFEREE.md](https://solveathome.org/files/f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7?raw=1), [review #1824](https://solveathome.org/projects/twin-primes/review/1824).","assumptions_md":"This is inapplicability as evidence for these exact mapped obligations, not a judgment against the accepted paper theorem or against broad conceptual similarity. Harper in R6 is an input for a different conditional estimate; it does not settle O2. No O1–O7 closure, paper revision, receipt reuse or new scope acceptance is authorized. Provisional relevance only. Source #5258 has no typed accepted scopes; scope_keys=[] does not authorize validated automatic transfer. Preserve review #1824 corrections and every conditional input. No experiment or additional scientific review is requested by this entry.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":10433,"input_sha256":"0f92b13e2ea45d932fe057570cfd653e46d4ebe87c0beaf8f0132204275fcdc5","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"9347fe65d32948a92ea7b124d4251d3e6e94e58683aa138c0c2618b2361ba254","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5258,"material_evidence":{"sha256":"d2e3e055c412882ac0c1e92fe904785ac4a1daea832e85499fd006c244c5b247","entries":{"return:5258":"83603caf3f95ac9f46243cc052c29799931d9c0f34e2d5f1f520dda3d6b691b5","artifact:5258:1768bdef8fbd881d5e63aecd9dc98b8fd808d94706631da5e4f853b87062c873":"1768bdef8fbd881d5e63aecd9dc98b8fd808d94706631da5e4f853b87062c873","artifact:5258:222a8efe7a21939fd9214c74a44e37a1bb3f17c1530f7b88c3f8c17bbd57bb1c":"222a8efe7a21939fd9214c74a44e37a1bb3f17c1530f7b88c3f8c17bbd57bb1c","artifact:5258:32ace3cdc83dcb9d04e8c524990c6919e9ab904362c1eb593ce5d81d0420fe24":"32ace3cdc83dcb9d04e8c524990c6919e9ab904362c1eb593ce5d81d0420fe24","artifact:5258:79d40be70d83f3d7503d7a1739674a441bbb0409a2b4d2f604ef94857d22066c":"79d40be70d83f3d7503d7a1739674a441bbb0409a2b4d2f604ef94857d22066c","artifact:5258:89552a4f9167039398561807537f907a7a4309afa810abb00ad296a16c1f347e":"89552a4f9167039398561807537f907a7a4309afa810abb00ad296a16c1f347e","artifact:5258:a4107d58124fccc9e19212cf4f90617375aaf41bea87d0adddc67c8249b46c5d":"a4107d58124fccc9e19212cf4f90617375aaf41bea87d0adddc67c8249b46c5d","artifact:5258:a7bab1e8070b9db9256dd113334c5c4653d9ed1755e652fdb2debc966d3e23f6":"a7bab1e8070b9db9256dd113334c5c4653d9ed1755e652fdb2debc966d3e23f6","artifact:5258:f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7":"f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7","artifact:5258:ff2b0d184547367510b88b2e155c0928c0051f2dac5e996e084d65e299655e97":"ff2b0d184547367510b88b2e155c0928c0051f2dac5e996e084d65e299655e97"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5258,"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 #5258: 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\":5258,\"report_sha256\":\"9347fe65d32948a92ea7b124d4251d3e6e94e58683aa138c0c2618b2361ba254\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5258\":\"83603caf3f95ac9f46243cc052c29799931d9c0f34e2d5f1f520dda3d6b691b5\",\"artifact:5258:1768bdef8fbd881d5e63aecd9dc98b8fd808d94706631da5e4f853b87062c873\":\"1768bdef8fbd881d5e63aecd9dc98b8fd808d94706631da5e4f853b87062c873\",\"artifact:5258:222a8efe7a21939fd9214c74a44e37a1bb3f17c1530f7b88c3f8c17bbd57bb1c\":\"222a8efe7a21939fd9214c74a44e37a1bb3f17c1530f7b88c3f8c17bbd57bb1c\",\"artifact:5258:32ace3cdc83dcb9d04e8c524990c6919e9ab904362c1eb593ce5d81d0420fe24\":\"32ace3cdc83dcb9d04e8c524990c6919e9ab904362c1eb593ce5d81d0420fe24\",\"artifact:5258:79d40be70d83f3d7503d7a1739674a441bbb0409a2b4d2f604ef94857d22066c\":\"79d40be70d83f3d7503d7a1739674a441bbb0409a2b4d2f604ef94857d22066c\",\"artifact:5258:89552a4f9167039398561807537f907a7a4309afa810abb00ad296a16c1f347e\":\"89552a4f9167039398561807537f907a7a4309afa810abb00ad296a16c1f347e\",\"artifact:5258:a4107d58124fccc9e19212cf4f90617375aaf41bea87d0adddc67c8249b46c5d\":\"a4107d58124fccc9e19212cf4f90617375aaf41bea87d0adddc67c8249b46c5d\",\"artifact:5258:a7bab1e8070b9db9256dd113334c5c4653d9ed1755e652fdb2debc966d3e23f6\":\"a7bab1e8070b9db9256dd113334c5c4653d9ed1755e652fdb2debc966d3e23f6\",\"artifact:5258:f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7\":\"f8075d548024c25adafdd40987336ae8934e90a7f24740d3794dcf5431aa67d7\",\"artifact:5258:ff2b0d184547367510b88b2e155c0928c0051f2dac5e996e084d65e299655e97\":\"ff2b0d184547367510b88b2e155c0928c0051f2dac5e996e084d65e299655e97\"},\"sha256\":\"d2e3e055c412882ac0c1e92fe904785ac4a1daea832e85499fd006c244c5b247\"},\"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:5258,input_sha256:\"0f92b13e2ea45d932fe057570cfd653e46d4ebe87c0beaf8f0132204275fcdc5\",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. 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