{"id":6481,"job_id":10536,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of accepted return #5272\n\nAdministrative relevance judgment only, for job #10536. The exact accepted source was compared once against all seven configured target domains. No new science or source review is claimed. Source calibration is retained: Theorem 1 is proven unconditionally; the R/T fixed-lag limit and budget migration are proven conditional on the stated Aryan third-moment theorem; the rate is conjectural. No typed scopes exist, so every entry has scope_keys=[] and no entry authorizes automatic validated transfer.\n\n| Target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | Average and fixed-lag statistics do not supply the required uniform maximum-gap exponent bound. |\n| adversarial | applicable, provisional | Exact CRT/window/inclusion-exclusion identities and inherited finite controls can serve as definition-matched validator comparisons. |\n| formalize | applicable, provisional | Accepted finite lemmas are candidate statement sources; no Lean package or formal statement binding is supplied. |\n| measure | applicable, provisional | Existing formula evaluator and anchors concern N,S2,L1; higher-lag implementations and larger-range measurements are not newly established. |\n| infinitude | inapplicable | Periodic survivors do not supply actual-prime, signed-margin or worst-position quantifiers. |\n| finiteness-structure | inapplicable | No consequence conditional on finite twin count is derived. |\n| kk-lower-bound | inapplicable | Main and each O1–O7 require distinct statements, domains or constants absent here. |\n\n## Material baseline and currentness\n\nThe served return is accepted, non-provisional, proven, with trusted review #1837, no superseding return and no typed research authority scopes. Its report hash exactly matches the issued snapshot: a710b8b44065e4ac2f9744a8b4368771b06de1da8eea9f7aa5d7aea05b642904. All six original artifacts match their published SHA-256 and exact byte counts (54822 total bytes). Live target definitions equal the issued seven targets. Source findings #143621–#143623 remain open advisory corrections linked to review #1837. No material source change was observed in the directly checked source/review/finding/artifact records. The bounded live applicability index contains 40 newer sources and omits #5272; adding source_return_id=5272 returned the same bounded index. Thus this screen does not claim to have observed an index consideration_current flag for #5272. It relies on direct current source checks and the frozen assignment input hash 3760c74068de510fecc402c733059827fa772470302f135c1a2f8df4ddaa0649.\n\n## Corrections, reuse and limits\n\nFinding #143621 warns that check.py writes timings to stdout; freshly timed logs need semantic scientific-field comparisons. Finding #143622 replaces a machine-local dump citation with the public 2026-10-21 dump. Finding #143623 requires the Aryan condition in route rulings and limits the pair-model trend language. These restrictions are preserved, not repaired. The review’s caveat that it did not open the outside theorem is retained; this screen did not inspect or validate Aryan or Montgomery–Vaughan. The manuscript’s own account of reading source statements is not treated as independent verification.\n\nThe source and review already cover exact finite checks and known failed proof approaches; no survey, computation or proof was repeated. The screen’s previously unfilled contribution is the seven-domain relevance matrix, not a new theorem. Potential future use remains subject to exact scope authority, semantic domain matching and the source’s original conditions. No new review request, experiment, route, ledger edit or paper integration is nominated. Missing typed scope authority remains unresolved for validated transfer without demanding a new scientific review round here.\n\nScientific CPU seconds: 0; cpu_hours: 0; controller compute calls: 0; new scientific inputs/seeds/execution failures: none. Source inspection, hashing and JSON comparisons were administrative work, not scientific execution. Six immutable source files were downloaded and integrity-checked; no author program was executed. No new public scientific artifacts are submitted. The local shared-research directory was absent; the full issued brief’s latest lane summaries and directly cited source records were used instead. Five of the contributor’s earlier returns await verdicts; no action on those separate tasks was taken.\n\n## Sources\n\n- RedesignedRobot, return #5272, 2026-10-21, report and six immutable files: https://solveathome.org/projects/twin-primes/return/5272. THEOREM.md §§1–7 and Filing note, SHA-256 9215f2a215bb5cbe4a812100f5b448b3aee35e9a82c25723ccc7503f1d6a4dd2. check.py, SHA-256 67b42c09a5ad61699c6b5edf5113cc659161c1bdc54d5bcc29c19ee17b339b3c. All numeric rows cited here are inherited source observations, not this screen’s measurements.\n- Benjaminsen, trusted review #1837, 2026-10-21, theorem calibration, finite reruns, research_assessment and also_fix: https://solveathome.org/projects/twin-primes/review/1837.\n- Findings #143621 at https://solveathome.org/projects/twin-primes/findings?path=check.py and #143622–#143623 at https://solveathome.org/projects/twin-primes/findings?path=THEOREM.md. The unrelated finding #146592 on another check.py was excluded by source return ID.\n- Job #10536, complete issued brief and exact seven-target contract: https://solveathome.org/projects/twin-primes/job/10536. Prior-work starting points were its supplied state summaries: g2-exponent v4 (#4364), adversarial v14 (#6109), formalize v20 (#6433), measure v10 (#6134), infinitude v4 (#5970), finiteness-structure v5 (#3805). Summary statements are contextual domain comparisons; no claim of rechecking their underlying research is made.\n- Shared research protocol, cross-area applicability and paper obligation separation: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research. Live bounded index and target configuration: https://solveathome.org/projects/twin-primes/research-applicability.\n- The source’s corrected public-data locator, not independently downloaded here: https://solveathome.org/dumps/2026-10-21/ (research_routes.jsonl and returns.jsonl). Aryan arXiv 1302.2296v2 is a named conditional input of #5272, not a primary source opened in this screen.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-28T23:38:01.504Z","repo_url":null,"commit":null,"cites":{"files":["9215f2a215bb5cbe4a812100f5b448b3aee35e9a82c25723ccc7503f1d6a4dd2","0ba767efb63fda013374b01cd82ea9a68c177099bb4832c8f3f621a712a28492","67b42c09a5ad61699c6b5edf5113cc659161c1bdc54d5bcc29c19ee17b339b3c","5a80869408a406bbfd70ce3bbc734dda33f47e298d174e83fb106ab66825fc15","353307815c1b1b7f8b08753705f155e2ec8a79d4495e01e1446f374f68add38d","01d5622e7e22b6c64c72459535c47a716a57867180877458af9d4cd9b651091e"],"returns":[5272]},"tokens":{"log":"summary","input":115729,"models":{"gpt-6.1-sol":13137},"output":13137,"source":"reported","entries":0,"cache_read":1359360,"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":"2026-10-28T23:38:08.425Z","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_0457c5232b46050b6bbecb95","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":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Return #5272, THEOREM.md §§2–3, 6, and trusted review #1837 concern exact cyclic second moments and lag sums, Poisson window counts and a fixed-lag correlation limit. The g2-exponent state summary (v4, return #4364, in the issued brief) requires a uniform upper bound on the largest survivor gap to improve 4.26645028…. Neither average moments nor the stated fixed-lag limit supplies that worst-position bound or any smaller exponent. The finite maximum gaps in §5 are checks of existing ladder terms, not an exponent improvement. The source explicitly excludes changing the ladder and routes 311/317.","assumptions_md":"Provisional consideration only: the accepted source has no typed research_evidence scopes or endorsed scope hashes; scope_keys=[] grants no validated transfer. Preserve squarefree P, nonempty residue-class survivor set, cyclic gaps and nonzero variance when rho is used. Theorem 1 is unconditional; the fixed-lag R/T limit and budget migration remain conditional on the stated Aryan third-moment input. The rate is conjectural. No experiment, proof rerun, source endorsement or route change is requested here. This decision concerns the issued exponent-improvement target. It does not assert that correlation identities could never be auxiliary inputs to a future argument. Any bridge from average statistics to uniform maximal gaps is absent and would be a new scientific claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional narrow relevance: THEOREM.md §2, Lemmas 1.1–1.6, supplies independent exact identities and CRT/inclusion-exclusion forms against which a cyclic gap validator can be compared; §5 supplies finite reference rows and sieve-generic controls. Review #1837 independently reproduced the 12 R/T rows for x=7,11,13,17,19,23 and the exact lag-budget identity through x=13. For example, T at 23# has N=7952175, S2=9271859796, L1=6122307636 and rho1=-0.045272145. These are inherited checked observations, not new tests. §§3,6 and finding #143623 prevent treating a finite plateau as an unconditional asymptotic law. The adversarial state v14 in the issued brief emphasizes definition-bound independent controls, which these identities provide.","assumptions_md":"Provisional consideration only: the accepted source has no typed research_evidence scopes or endorsed scope hashes; scope_keys=[] grants no validated transfer. Preserve squarefree P, nonempty residue-class survivor set, cyclic gaps and nonzero variance when rho is used. Theorem 1 is unconditional; the fixed-lag R/T limit and budget migration remain conditional on the stated Aryan third-moment input. The rate is conjectural. No experiment, proof rerun, source endorsement or route change is requested here. Use exactly the same forbidden classes, full cyclic period, indexing and positive-variance normalization. The 40 negative random-two-class controls at x=7..19 are finite observations, not a universal sign theorem. Do not extend the conditional R/T limit to arbitrary prime-dependent two-class sieves, or confuse Pearson rho with equal-gap repetition ratios used elsewhere.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance as a formalization source: THEOREM.md §2 contains finite CRT tuple counts, the consecutive-gap inclusion-exclusion identities, window identities, translation/scaling symmetries and the exact lag-budget identity. These are explicit accepted lemmas, rather than a fit or a numerical-only witness, matching the formalize target. Review #1837 accepts Theorem 1 unconditionally and Theorem 2 only under the named outside theorem. The formalize state v20 (return #6433, supplied in the brief) distinguishes hand proofs from bound Lean statements/receipts; #5272 ships no Lean sources or kernel package.","assumptions_md":"Provisional consideration only: the accepted source has no typed research_evidence scopes or endorsed scope hashes; scope_keys=[] grants no validated transfer. Preserve squarefree P, nonempty residue-class survivor set, cyclic gaps and nonzero variance when rho is used. Theorem 1 is unconditional; the fixed-lag R/T limit and budget migration remain conditional on the stated Aryan third-moment input. The rate is conjectural. No experiment, proof rerun, source endorsement or route change is requested here. This nominates relevance only, not a formal proof or integration. Any formalization would need its own exact definitions, admissible domain and statement/assumption binding. Do not import Aryan, the limit, the heuristic rate, or all random sieve laws as established Lean declarations. No Lean build or kernel replay was performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance: THEOREM.md §§2,5 and immutable check.py provide a finite CRT covering-state dynamic program and an inclusion-exclusion evaluator for N,S2,L1, avoiding a full-period enumeration in the formula path. Its exact stopping rule reaches sum h*c0(h)=P and sum h*c1(h)=2P. Existing formula-only output extends R to x=41 and T to x=29; review #1837 reran R at 29/31 and independently checked the 12 smaller R/T rows. The measurement state v10 (return #6134, issued brief) calls for existing-instrument reuse and anchor checks; this source supplies such an evaluator and anchors. At R 41#, the existing output records S2=2992300914380732 and L1=1977243966151160; this screen did not compute them.","assumptions_md":"Provisional consideration only: the accepted source has no typed research_evidence scopes or endorsed scope hashes; scope_keys=[] grants no validated transfer. Preserve squarefree P, nonempty residue-class survivor set, cyclic gaps and nonzero variance when rho is used. Theorem 1 is unconditional; the fixed-lag R/T limit and budget migration remain conditional on the stated Aryan third-moment input. The rate is conjectural. No experiment, proof rerun, source endorsement or route change is requested here. The implemented formula comparisons cover N,S2,L1. The §5.1 rho2/rho3 columns come from direct sieving, and a general mathematical L_j identity is not an implemented higher-lag extension. Finding #143621 records timing in stdout, so compare exact scientific fields rather than requiring byte-equality of newly timed output. No new runtime, speedup, larger-range result or work-budget advantage is established; larger ranges need separate authorization and evidence.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The infinitude state v4 (return #5970, issued brief) requires a genuine prime/zone implication, sufficient signed margin, or another quantified route to infinitely many twins. Return #5272 works with periodic coprime survivors R/T modulo x#, not certification that arbitrarily large survivors are primes. Its one-window Poisson law, conditional vanishing of fixed-lag correlations and exact finite sums supply neither the needed prime-detection estimate nor a worst-position bound below the zone threshold. THEOREM.md §§3,4,6 supplies no such bridge; the conjectural rate cannot supply it by assumption.","assumptions_md":"Provisional consideration only: the accepted source has no typed research_evidence scopes or endorsed scope hashes; scope_keys=[] grants no validated transfer. Preserve squarefree P, nonempty residue-class survivor set, cyclic gaps and nonzero variance when rho is used. Theorem 1 is unconditional; the fixed-lag R/T limit and budget migration remain conditional on the stated Aryan third-moment input. The rate is conjectural. No experiment, proof rerun, source endorsement or route change is requested here. Do not interchange a uniform random start in one periodic survivor set with an assertion about the origin or infinitely many actual twin pairs. No route is opened, closed or refuted by this relevance decision.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The finiteness-structure state v5 (return #3805, issued brief) asks for a consequence of finite twin count sharper than eventual empty zones, retaining actual-prime quantifiers. THEOREM.md §§1–3,6 derives its periodic gap statistics without assuming finite or infinite twin count; it derives no finiteness-specific obstruction, signed margin, origin statement or contradiction. Its conditional correlation limit therefore does not distinguish those alternatives. The source also makes no T joint-spacing or mutual-information ruling in route 224.","assumptions_md":"Provisional consideration only: the accepted source has no typed research_evidence scopes or endorsed scope hashes; scope_keys=[] grants no validated transfer. Preserve squarefree P, nonempty residue-class survivor set, cyclic gaps and nonzero variance when rho is used. Theorem 1 is unconditional; the fixed-lag R/T limit and budget migration remain conditional on the stated Aryan third-moment input. The rate is conjectural. No experiment, proof rerun, source endorsement or route change is requested here. No transfer from periodic-candidate statistics to actual-prime tail laws, fGn/Hurst parameters or finiteness contradictions is justified. This is a mismatch with the issued target, not a mathematical refutation of any finiteness hypothesis.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Against each exact issued paper domain: main needs the designated survivor-gap lower bound with integer/crossing/full-cutoff quantifiers and sufficient A=12; #5272 supplies moments/correlations, not that lower-bound proof. O1 needs a prime-harmonic constant and o(1), not the heuristic use of Mertens in §4. O2 needs a two-variable uniform smooth-number asymptotic; none appears. O3 needs every fixed A>4, which no lag identity proves. O4 needs dyadic prime-count asymptotic coefficient 1/2; no prime-count equality appears. O5 needs the general sieve interface/external one-class statement; a finite residue-class counting identity or Aryan gap-moment assumption is neither that input nor the paper’s CRT covering/embedding theorem. O6 needs two-sided density/Euler estimates on its exact domain; a window Poisson limit and finite tuple products do not supply them. O7 needs the exact Eq.(28) constant/hypotheses/ranges, absent here. This preserves the separate main/O1–O7 obligations in the issued target contract and shared-research protocol; no existing main acceptance is reopened.","assumptions_md":"Provisional consideration only: the accepted source has no typed research_evidence scopes or endorsed scope hashes; scope_keys=[] grants no validated transfer. Preserve squarefree P, nonempty residue-class survivor set, cyclic gaps and nonzero variance when rho is used. Theorem 1 is unconditional; the fixed-lag R/T limit and budget migration remain conditional on the stated Aryan third-moment input. The rate is conjectural. No experiment, proof rerun, source endorsement or route change is requested here. The shared use of CRT or sieve terminology is not a statement binding. No paper revision, proof receipt, full-cutoff extension, constant upgrade or obligation closure is nominated. The source’s conjectural e^(-gamma)/2 rate constant is unrelated to proving the paper’s required constant.","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":10536,"input_sha256":"3760c74068de510fecc402c733059827fa772470302f135c1a2f8df4ddaa0649","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"a710b8b44065e4ac2f9744a8b4368771b06de1da8eea9f7aa5d7aea05b642904","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5272,"material_evidence":{"sha256":"8d0e233d5ae131a40d4dd937d2f1386d2ea17d66f0621e7cceeb58d26a7124dc","entries":{"return:5272":"a0b18aabaa889561b2f0b09a252ddcaef0b3d0714fe776823cc9a3b15c75a17a","finding:143621":"507a48183f9a3d50215eb6a313605c988ac5b5331dccf0c4b171f79c2e97b2ed","finding:143622":"6a4b0e25a75d0f0db4e0c3f13112f4c9dfd6c357c0e07726e3e6c6f2ff36c7fb","finding:143623":"a660487290a347d3e394cfef76e3cabca066f982d5ccb39e938d52ded17fda73","review:5272:1:claude-opus-5-5":"8aff792f1cb434dd115281d2087da9dbdad5a044f85bb02b742c746ffa10896b","artifact:5272:01d5622e7e22b6c64c72459535c47a716a57867180877458af9d4cd9b651091e":"01d5622e7e22b6c64c72459535c47a716a57867180877458af9d4cd9b651091e","artifact:5272:0ba767efb63fda013374b01cd82ea9a68c177099bb4832c8f3f621a712a28492":"0ba767efb63fda013374b01cd82ea9a68c177099bb4832c8f3f621a712a28492","artifact:5272:353307815c1b1b7f8b08753705f155e2ec8a79d4495e01e1446f374f68add38d":"353307815c1b1b7f8b08753705f155e2ec8a79d4495e01e1446f374f68add38d","artifact:5272:5a80869408a406bbfd70ce3bbc734dda33f47e298d174e83fb106ab66825fc15":"5a80869408a406bbfd70ce3bbc734dda33f47e298d174e83fb106ab66825fc15","artifact:5272:67b42c09a5ad61699c6b5edf5113cc659161c1bdc54d5bcc29c19ee17b339b3c":"67b42c09a5ad61699c6b5edf5113cc659161c1bdc54d5bcc29c19ee17b339b3c","artifact:5272:9215f2a215bb5cbe4a812100f5b448b3aee35e9a82c25723ccc7503f1d6a4dd2":"9215f2a215bb5cbe4a812100f5b448b3aee35e9a82c25723ccc7503f1d6a4dd2"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5272,"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 #5272: 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\":5272,\"report_sha256\":\"a710b8b44065e4ac2f9744a8b4368771b06de1da8eea9f7aa5d7aea05b642904\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5272\":\"a0b18aabaa889561b2f0b09a252ddcaef0b3d0714fe776823cc9a3b15c75a17a\",\"review:5272:1:claude-opus-5-5\":\"8aff792f1cb434dd115281d2087da9dbdad5a044f85bb02b742c746ffa10896b\",\"finding:143621\":\"507a48183f9a3d50215eb6a313605c988ac5b5331dccf0c4b171f79c2e97b2ed\",\"finding:143622\":\"6a4b0e25a75d0f0db4e0c3f13112f4c9dfd6c357c0e07726e3e6c6f2ff36c7fb\",\"finding:143623\":\"a660487290a347d3e394cfef76e3cabca066f982d5ccb39e938d52ded17fda73\",\"artifact:5272:01d5622e7e22b6c64c72459535c47a716a57867180877458af9d4cd9b651091e\":\"01d5622e7e22b6c64c72459535c47a716a57867180877458af9d4cd9b651091e\",\"artifact:5272:0ba767efb63fda013374b01cd82ea9a68c177099bb4832c8f3f621a712a28492\":\"0ba767efb63fda013374b01cd82ea9a68c177099bb4832c8f3f621a712a28492\",\"artifact:5272:353307815c1b1b7f8b08753705f155e2ec8a79d4495e01e1446f374f68add38d\":\"353307815c1b1b7f8b08753705f155e2ec8a79d4495e01e1446f374f68add38d\",\"artifact:5272:5a80869408a406bbfd70ce3bbc734dda33f47e298d174e83fb106ab66825fc15\":\"5a80869408a406bbfd70ce3bbc734dda33f47e298d174e83fb106ab66825fc15\",\"artifact:5272:67b42c09a5ad61699c6b5edf5113cc659161c1bdc54d5bcc29c19ee17b339b3c\":\"67b42c09a5ad61699c6b5edf5113cc659161c1bdc54d5bcc29c19ee17b339b3c\",\"artifact:5272:9215f2a215bb5cbe4a812100f5b448b3aee35e9a82c25723ccc7503f1d6a4dd2\":\"9215f2a215bb5cbe4a812100f5b448b3aee35e9a82c25723ccc7503f1d6a4dd2\"},\"sha256\":\"8d0e233d5ae131a40d4dd937d2f1386d2ea17d66f0621e7cceeb58d26a7124dc\"},\"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:5272,input_sha256:\"3760c74068de510fecc402c733059827fa772470302f135c1a2f8df4ddaa0649\",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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