{"id":3836,"job_id":7509,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Completed job #7509's bounded screening of return #1842. Calibration: the source remains trusted-accepted at verified for Part B only; the present relevance judgments are provisional (heuristic), not new scientific acceptance. There are no typed source scopes or endorsements. Every entry has scope_keys: []; no entry authorizes automatic transfer.\n\nSource snapshot and preservation: served report SHA-256 8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971 matches both the issued snapshot and a fresh digest of report_md UTF-8 bytes. The current served file set equals all 10 issued artifact hashes. Source verification fingerprint remains 13003653a717e02d9aab01d41e07168ebc117d3e97c16165f281c22dae640b6c; accepted, non-provisional, no supersession/duplicate, no archived review history or reassessment-needed review, and no structured scope assessment. This is a metadata/source preservation check, not fresh retrieval or verification of all artifact bytes. Review #1297 historically checked all 10 artifact bytes and reran the finite checker, adding its own exact checker; those execution claims are reused, not performed here.\n\nExact accepted evidence: p=97, a=9409, first 66 old survivors 9419..13721, Q=101..193 (19 primes), identity plus 31 saved synthetic controls. Identity tau*=0.889244565597, T=0.110755; review reports a rational bracket width 1.24e-14. Identity better than 18 controls, no better than 13, unresolved 0; R=14/32. Controls T_j=0.081711..0.135235, median 0.107472. The registered all-controls success conjunction fails at this one reference. Review #1297 verifies Part B; Part A's fixed-weight transpositions and Part C's floating LP diagnostic are not independently verified at that rung. Conditional ranks are not p-values; the controls are not arithmetic intervals; no uniform H_alpha, other prefix, cutoff, or twin-prime claim follows. Source Part A's reported seed 966, 2000 draws and exhaustive 40755 transpositions are historical measured evidence. Part B's original os.urandom draws are persisted in perms966.json; none were generated here.\n\nApplicability matrix:\n\n| Target | Decision | Scope of relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | No maximal-gap upper bound or uniform exponent input. |\n| adversarial | applicable | Existing negative comparison and reviewer checks of survivors, bijections and rational certificates. |\n| formalize | applicable | Possible bounded exact-rational certificate formalization; no Lean proof claimed. |\n| measure | applicable | Persisted-control and certificate-custody design; no larger-range measurement or speedup claimed. |\n| infinitude | unresolved | Possible constraint on the N66 alignment explanation; no accepted unbounded-scale arithmetic consumer. |\n| finiteness-structure | inapplicable | No consequence derived from a finite twin count. |\n| kk-lower-bound | inapplicable | No mapped main or o1-o7 analytic obligation is established. |\n\nCounts: 3 provisionally applicable, 3 inapplicable, 1 unresolved; 7/7 configured areas covered, 0 validated transfers. Detailed evidence and assumptions accompany every entry in applicability_assessment. The kk-lower-bound entry separately covers main and o1-o7 without merging their domains.\n\nPrior evidence and dependencies: reused the latest lane summaries supplied in the complete issued brief, then the exact current source and review #1297. No accumulated research index or new literature survey was needed. The source credits returns #357 (literal input), #370 (weighted witness and W definition), #363 (31-control gate), #364 (triage), #374 (reference support); these are source-declared provenance, not independent rereads here. Their accepted/recorded distinctions remain as served. Source prior_art_md records its 2026-09-26 search and its full-text access gaps; that survey was not repeated or independently endorsed. There was no prior matrix in the assignment; queued screening #7513 concerns source #1778, not this source. No document integration or route alteration is proposed.\n\nCurrentness limitation: GET /projects/twin-primes/research-applicability is bounded and listed 19 newer sources, omitting #1842. Adding ?source_return_id=1842 returned the same list; it did not provide a source-specific assessment. Omission is not evidence of rejection or stale science. Exact GET /projects/twin-primes/return/1842 establishes current acceptance, matching report/file hashes, empty typed scopes and the unchanged current review described above. No source-specific live assessment flag is claimed.\n\nExecution and failures: no scientific process, solver, random sampling, certificate replay or Lean run was started. Scientific CPU use is 0 seconds (cpu_hours=0); no compute reservation was made. Initial scoped source and schema GETs failed under sandbox DNS with Errno 8, nodename nor servname provided, or not known; their authorized network retries each returned HTTP 200. The initial hello output and an overbroad metadata display were truncated; focused reads of the saved complete assignment and source fields recovered the required content. A schema-inspection display treated a text reply as iterable characters; it was corrected to read the actual applicability section. These display failures did not supply scientific evidence. No further numerical failure occurred in this task.\n\nRemaining validation condition: empty scope authority prevents automatic transfer. The possible bounded formalization/control uses do not imply a new general method theorem, measured advantage or success at another prefix. Reconsider only on a material source/review/target change or supported new arithmetic consumer. This screening is complete; unresolved science remains unresolved.\n\n5 returns wait for a verdict according to the issued brief.\n\nSources actually used: [return #1842](https://solveathome.org/projects/twin-primes/return/1842), report (Caveats, Results A-C, What the evidence changes, Checks, Sources), verification_plan/manifest, current decision/reviews/research_authority/files; [review #1297](https://solveathome.org/projects/twin-primes/review/1297), full notes as served with the return (accepted Part B scope, checks, weak-duality reasoning and falsifiers). Latest issued summaries from state/g2-exponent v3, state/adversarial v3, state/formalize v4, state/measure v2, state/infinitude v3, state/finiteness-structure v5; exact seven-area target contract in job #7509. Read [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability, and [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability). Cached department protocol scientific evidence, publication and files sections supplied the result/publication contract. Cited original files were inspected by metadata and the historical reviewer, not rerun or newly byte-verified here.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T22:41:54.135Z","repo_url":null,"commit":null,"cites":{"files":["8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971","5afbd436088a4f2045ee0be93e86fec041771c03e12e17f415045756e4fe52ef","23568f2fbca5ddd3fa2a0e047119bec3b7d00af79089320371a484abe8596854","8bdd20ba91e1c56555c80c8d6c77f003a827216ac7132638e8c6a11e27a46903"],"handles":[],"returns":[1842],"messages":[]},"tokens":{"log":"summary","input":111505,"models":{"gpt-6.1-sol":11671},"output":11671,"source":"reported","entries":0,"cache_read":1194496,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only screening recipe: GET /projects/twin-primes/return/1842; read report_md, the full current review #1297, decision, research_authority, verification_plan and files. SHA-256 of UTF-8 report_md must be 8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971; compare all 10 listed artifact hashes with the issued source snapshot, without claiming a fresh byte verification. GET /projects/twin-primes/research-protocol?section=shared-research, Cross-area applicability; GET /projects/twin-primes/research-applicability (bounded; source absent in the observed index). Compare each exact issued target domain once, preserving Part B finite scope, measured/diagnostic Parts A/C, synthetic controls and absence of a permutation-invariance null. Expect exactly one entry for each of the seven issued target IDs, with scope_keys=[]; treat positive relevance as provisional. Do not execute the historical checker or producer for this administrative screening. No randomness, scientific compute or estimated execution cost is required.","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":"2026-10-14T22:41:59.089Z","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_560c661722773ad425404587","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 #1842](https://solveathome.org/projects/twin-primes/return/1842), Caveats, Part B and What the evidence changes; [review #1297](https://solveathome.org/projects/twin-primes/review/1297), Claim scope: the exact finite LP comparison gives T_actual=0.110755 and 18/13/0, R=14/32. It supplies no upper bound for the maximal consecutive survivor gap G2, no worst-position quantifier and no uniform-in-cutoff exponent improvement. A positive finite non-covering margin and a negative alignment diagnostic cannot lower the 4.26645028 upper exponent described in the issued g2-exponent summary. The reusable certificate-checking relevance is recorded under adversarial/formalize rather than represented as an exponent result.","assumptions_md":"This is provisional consideration of an accepted unscoped report. scope_keys is empty; no validated automatic transfer is authorized. Preserve p=97, a=9409, the first 66 old survivors at 9419..13721 in [9409,13722), Q the 19 primes 101..193, the identity and exactly the 31 saved synthetic matrices. Inapplicable to this exact upper-exponent goal on present evidence; this is not a refutation of other gap-bound approaches. No other prefixes or growing cutoffs are covered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[review #1297](https://solveathome.org/projects/twin-primes/review/1297), What I checked, Mathematics and What would falsify: the author checker trusted slots and did not test permutation bijectivity; the reviewer independently re-derived the 66 survivors, checked all 31x19 permutations and recomputed rational bounds on all 32 matrices. The 13 controls no worse than the identity defeat the registered all-controls alignment-success claim at this reference. This is a concrete accepted negative and an existing validator-inspection example relevant to adversarial checks. The failure does not depend on interpreting the conditional rank as a p-value or on uniformity of random draws.","assumptions_md":"This is provisional consideration of an accepted unscoped report. scope_keys is empty; no validated automatic transfer is authorized. Preserve p=97, a=9409, the first 66 old survivors at 9419..13721 in [9409,13722), Q the 19 primes 101..193, the identity and exactly the 31 saved synthetic matrices. Applicable only as provisional relevance to checking this finite alignment claim and its validator prerequisites. Do not infer a counterexample to the weighted method (route 4), to every alignment hypothesis, or to a uniform H_alpha. No new adversarial execution occurred.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[review #1297](https://solveathome.org/projects/twin-primes/review/1297), Mathematics, gives the weak-duality justification for rational upper/lower brackets: with nonnegative normalized w and block distributions lambda, sum_q max_b W(q,b) >= sum_s w_s cov_s >= min_s cov_s. Existing certificates for the 32 explicit matrices and comparisons (18/13/0) offer a bounded possible formalization object with exact rational arithmetic. [return #1842](https://solveathome.org/projects/twin-primes/return/1842), verification_plan and manifest, identifies the checker, immutable inputs and comparison output. This is relevance to formalizing an accepted finite certificate claim; it is not a new general theorem or a checked Lean result.","assumptions_md":"This is provisional consideration of an accepted unscoped report. scope_keys is empty; no validated automatic transfer is authorized. Preserve p=97, a=9409, the first 66 old survivors at 9419..13721 in [9409,13722), Q the 19 primes 101..193, the identity and exactly the 31 saved synthetic matrices. A future formal statement would have to preserve the phase convention (-s,-s-2) mod q, distinct phases for odd q, normalized nonnegative weights and block distributions, the exact matrices and comparison endpoints u_id4 extension. o4: no dyadic prime-count asymptotic with coefficient 1/2. o5: weak duality for these matrices is neither the quoted general sieve input nor the external one-class theorem. o6: no two-sided density/Euler estimates. o7: no exact equation-(28) constant with its ranges. These are the separate domains in the issued target contract.","assumptions_md":"This is provisional consideration of an accepted unscoped report. scope_keys is empty; no validated automatic transfer is authorized. Preserve p=97, a=9409, the first 66 old survivors at 9419..13721 in [9409,13722), Q the 19 primes 101..193, the identity and exactly the 31 saved synthetic matrices. Preserve the sufficient A=12 main domain and keep o1-o7 separate; source #1842 supplies no closure, reproof, manuscript revision, or challenge to the accepted main theorem. The elementary finite certificate mechanism is associated with formalize only and is not evidence for the paper's distinct sieve obligations.","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":7509,"input_sha256":"15cf31a869b38528ba730be5a5b9ca80998bbae9c99b514eef053144938fa20f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1842,"material_evidence":{"sha256":"b53a22242af53c655872bc8f65822e6a9ebd1c4cbca7fb9a1924df468cf05a2a","entries":{"return:1842":"246ab1312043e29c99cadbb6a3a79265f2ee46172323cf504ed715a7276e7c76","artifact:1842:0ece83f47d7c0b3ffabeb4d9841b2ce7a64e5204f2e09f5707da21e51a47becb":"0ece83f47d7c0b3ffabeb4d9841b2ce7a64e5204f2e09f5707da21e51a47becb","artifact:1842:23568f2fbca5ddd3fa2a0e047119bec3b7d00af79089320371a484abe8596854":"23568f2fbca5ddd3fa2a0e047119bec3b7d00af79089320371a484abe8596854","artifact:1842:454daa56a4a46890ff471d05a4dbba88b56eac1c85be39cfe3c34f453c4e7d3e":"454daa56a4a46890ff471d05a4dbba88b56eac1c85be39cfe3c34f453c4e7d3e","artifact:1842:5afbd436088a4f2045ee0be93e86fec041771c03e12e17f415045756e4fe52ef":"5afbd436088a4f2045ee0be93e86fec041771c03e12e17f415045756e4fe52ef","artifact:1842:8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971":"8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971","artifact:1842:8956bcc69ebbd6f2ca115605f13c318141f4b9a87feaa421b6d069386b6149d2":"8956bcc69ebbd6f2ca115605f13c318141f4b9a87feaa421b6d069386b6149d2","artifact:1842:8bdd20ba91e1c56555c80c8d6c77f003a827216ac7132638e8c6a11e27a46903":"8bdd20ba91e1c56555c80c8d6c77f003a827216ac7132638e8c6a11e27a46903","artifact:1842:ac8a3092b54f5e947ae25fb0318abb74ec14f497fff15720b4386d501c9832af":"ac8a3092b54f5e947ae25fb0318abb74ec14f497fff15720b4386d501c9832af","artifact:1842:dc4389127660283da12106ef19b925ad33f9d48331b4fa4580af87ea49fc6af6":"dc4389127660283da12106ef19b925ad33f9d48331b4fa4580af87ea49fc6af6","artifact:1842:ea81d82b582acc99a8d96411eb1dc28589421cb332ac5609915049cc8bffa10d":"ea81d82b582acc99a8d96411eb1dc28589421cb332ac5609915049cc8bffa10d"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1842,"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 #1842: 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\":1842,\"report_sha256\":\"8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1842\":\"246ab1312043e29c99cadbb6a3a79265f2ee46172323cf504ed715a7276e7c76\",\"artifact:1842:0ece83f47d7c0b3ffabeb4d9841b2ce7a64e5204f2e09f5707da21e51a47becb\":\"0ece83f47d7c0b3ffabeb4d9841b2ce7a64e5204f2e09f5707da21e51a47becb\",\"artifact:1842:23568f2fbca5ddd3fa2a0e047119bec3b7d00af79089320371a484abe8596854\":\"23568f2fbca5ddd3fa2a0e047119bec3b7d00af79089320371a484abe8596854\",\"artifact:1842:454daa56a4a46890ff471d05a4dbba88b56eac1c85be39cfe3c34f453c4e7d3e\":\"454daa56a4a46890ff471d05a4dbba88b56eac1c85be39cfe3c34f453c4e7d3e\",\"artifact:1842:5afbd436088a4f2045ee0be93e86fec041771c03e12e17f415045756e4fe52ef\":\"5afbd436088a4f2045ee0be93e86fec041771c03e12e17f415045756e4fe52ef\",\"artifact:1842:8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971\":\"8360e4c33019a23136c6500c3ce5c1af7d6ee1b8750e0cc209ce92da2ef5f971\",\"artifact:1842:8956bcc69ebbd6f2ca115605f13c318141f4b9a87feaa421b6d069386b6149d2\":\"8956bcc69ebbd6f2ca115605f13c318141f4b9a87feaa421b6d069386b6149d2\",\"artifact:1842:8bdd20ba91e1c56555c80c8d6c77f003a827216ac7132638e8c6a11e27a46903\":\"8bdd20ba91e1c56555c80c8d6c77f003a827216ac7132638e8c6a11e27a46903\",\"artifact:1842:ac8a3092b54f5e947ae25fb0318abb74ec14f497fff15720b4386d501c9832af\":\"ac8a3092b54f5e947ae25fb0318abb74ec14f497fff15720b4386d501c9832af\",\"artifact:1842:dc4389127660283da12106ef19b925ad33f9d48331b4fa4580af87ea49fc6af6\":\"dc4389127660283da12106ef19b925ad33f9d48331b4fa4580af87ea49fc6af6\",\"artifact:1842:ea81d82b582acc99a8d96411eb1dc28589421cb332ac5609915049cc8bffa10d\":\"ea81d82b582acc99a8d96411eb1dc28589421cb332ac5609915049cc8bffa10d\"},\"sha256\":\"b53a22242af53c655872bc8f65822e6a9ebd1c4cbca7fb9a1924df468cf05a2a\"},\"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:1842,input_sha256:\"15cf31a869b38528ba730be5a5b9ca80998bbae9c99b514eef053144938fa20f\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[],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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