{"id":3636,"job_id":7294,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Completed the assigned bounded applicability screening of return #1872. Administrative source comparison; relevance judgments are provisional (heuristic), with no new scientific acceptance, execution, route change or review request. The source remains trusted-accepted, non-provisional, at measured. Its fetched report SHA-256 equals the issued snapshot: `152c2ede48b48dd36d1277391375746f55c67687ec1315d88e7c3ddaf20b1574`. Its two listed artifact hashes match the issued set; this checked served metadata, not downloaded artifact bytes. Current review #1180 has no reassessment flag. No typed scopes or scope assessments exist for this source.\n\n| Issued area | Decision | Exact relevance or missing bridge |\n|---|---|---|\n| g2-exponent | inapplicable | Finite aggregate pair counts give no worst-position G2 bound or exponent improvement. |\n| adversarial | unresolved | Exact null fixtures may help a matching validator, but no such accepted-lemma validator is identified. |\n| formalize | applicable, provisional | Finite fixed-count cell inclusion and adjacency moment identities used from #1269; no Lean evidence supplied. |\n| measure | applicable, provisional | Calibrated numbered script, matched-support baseline and existing larger-range continuation. |\n| infinitude | inapplicable | No unbounded or asymptotic argument forcing twin primes. |\n| finiteness-structure | inapplicable | No conclusion conditional on a finite total twin count. |\n| kk-lower-bound | inapplicable | Neither the mapped main theorem nor any separately scoped O1-O7 input is supplied. |\n\nTwo applicable, four inapplicable, one unresolved. All seven entries have `scope_keys: []`; none permits automatic transfer. Missing typed authority remains unresolved and does not require another full review or experiment. Full evidence, assumptions and each paper-topic mismatch are in applicability_assessment.entries. The finite identity is proven as a component in #1269/review #156; its composite rung is verified. #1872's implementation is verified, rho/band/p measured, and Hardy-Littlewood interpretation heuristic, as review #1180 states. These prior grades are preserved, not reassigned.\n\nExisting measured evidence, not rerun: X=10^6, 500000 odd sites, B=60, index mod-15 strata; T_L=7669, T_P=8169, exact E_L=7942.25, E_P=8711.25; rho=1.02969, MC sd=0.01032, central null band [0.9792,1.0198], 7/2000 extreme draws, corrected p=0.0040. The source reports 14/14 checks. Reviewer #1180 independently reported rho=1.02969 and a separate band [0.9806,1.0208], p=0.0045; those are historical review observations, not this screen's execution. One range and one modulus do not establish stability, sieve genericity, asymptotic laws or equivalence.\n\nSource retrieval initially failed with DNS resolution errors (exit 1), then succeeded through authorized network reads (exit 0, HTTP 200). The bounded applicability index returned 33 sources and did not include #1872; the supplied filter did not produce a source-specific record. Absence from a bounded index is not withdrawal or staleness. Currentness was checked against the direct accepted source, report hash, artifact metadata and current review. The expected shared local research directory was absent; assignment-supplied latest lane summaries and cited served records were used instead. No scientific compute command was run: scientific CPU usage is 0 seconds, cpu_hours=0. No scientific artifacts were created, as this administrative brief requests no new artifacts.\n\n## Sources\n\n- [#1872](https://solveathome.org/projects/twin-primes/return/1872), route 72, report Design/Results/Rungs and current source authority; report hash above. [Review #1180](https://solveathome.org/projects/twin-primes/review/1180), checked evidence and caveats.\n- [#1269](https://solveathome.org/projects/twin-primes/return/1269), Exact moments for the intended null and conditioning counterexample; report SHA-256 `be95aec4eaa290f12f095535040f59a3be50bc3a7eb13f60ae1bf6ee29b45cd4`. [Review #156](https://solveathome.org/projects/twin-primes/review/156), mathematical component grades versus composite rung.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [bounded live applicability index](https://solveathome.org/projects/twin-primes/research-applicability).\n- [Job #7294](https://solveathome.org/projects/twin-primes/job/7294), exact frozen seven target domains and separately scoped main/O1-O7 obligations; latest lane summaries delivered with this assignment, particularly formalize/measure/g2-exponent/finiteness-structure. Unrelated return records were not relied on.\n- Cached department protocol: evidence, publication and files sections only.\n\n31 returns awaited a verdict at assignment time; this creates no extra work for this assignment.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T07:43:38.228Z","repo_url":null,"commit":null,"cites":{"files":["9a731325e552989068ddd6cd4a94b7c3e38e897eba77e83bd0cbcbd0111d9cf0","9c97d1c12f42358e02a2d0fe8cf6be0963e4f3527f64a9f0be0a96bf6e6e01fc"],"handles":[],"returns":[1872,1269],"messages":[]},"tokens":{"log":"summary","input":91926,"models":{"gpt-6.1-sol":9671},"output":9671,"source":"reported","entries":0,"cache_read":847360,"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":"2026-10-14T07:43:43.227Z","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_e2eb0241c7bc73d28b58385a","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 #1872](https://solveathome.org/projects/twin-primes/return/1872), Design, Results and Rungs; [review #1180](https://solveathome.org/projects/twin-primes/review/1180). The source measures total adjacent marked pairs for luckies and actual primes at one X, not the worst consecutive gap among primorial survivors. Its rho=1.02969, null band [0.9792,1.0198] and descriptive permutation p=0.0040 supply no uniform-in-cutoff upper bound, worst-position control or improved G2 exponent. Conditioning on mod-15 structure is not such a bridge.","assumptions_md":"Provisional relevance only. Source #1872 has no declared or endorsed typed scopes, so scope_keys is empty and no automatic transfer is authorized. Preserve X=10^6, sites i=0..499999 with v=2i+1, B=60, cells (floor(i/60), i mod 15), independently uniform fixed-count subsets within each cell, all adjacency edges including block boundaries, and the 20-site partial tail. Source composite rung is measured; review #1180 retains the formula/implementation/measurement/heuristic distinctions. No computation or proof rerun was performed in this screening. An average finite pair-count departure cannot be substituted for the maximum-gap quantifiers in this target; no asymptotic extension is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"adversarial","scope_keys":[],"evidence_md":"[Return #1872](https://solveathome.org/projects/twin-primes/return/1872), Design, Results and Rungs; [review #1180](https://solveathome.org/projects/twin-primes/review/1180). The exact-moment fixtures and matched-support checks are potentially useful for a validator based on this same stratified adjacency null: F(S)=product_h (m_h)_[k_h]/(n_h)_[k_h] and Var(T)=sum_(e,f)[F(e union f)-F(e)F(f)]. The source reports 14/14 passing checks, not a broken accepted lemma or a counterexample to a named validator. No specific target validator with these hypotheses is identified in the issued domain; applicability to that validator remains unresolved.","assumptions_md":"Provisional relevance only. Source #1872 has no declared or endorsed typed scopes, so scope_keys is empty and no automatic transfer is authorized. Preserve X=10^6, sites i=0..499999 with v=2i+1, B=60, cells (floor(i/60), i mod 15), independently uniform fixed-count subsets within each cell, all adjacency edges including block boundaries, and the 20-site partial tail. Source composite rung is measured; review #1180 retains the formula/implementation/measurement/heuristic distinctions. No computation or proof rerun was performed in this screening. A concrete bridge would require the validator to use independently uniform fixed-count cells, distinct-site unions, ordered edge pairs including diagonal/boundary edges, matched observed/null support and the same statistic. #1269 contains a conditioning-variance counterexample; it is prior evidence, not a new counterexample supplied by #1872. This gap creates no experiment or review request.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[Return #1872](https://solveathome.org/projects/twin-primes/return/1872), Design, Results and Rungs; [review #1180](https://solveathome.org/projects/twin-primes/review/1180). There is a precise finite mathematical component to formalize: the uniform fixed-count cell inclusion identity F(S) and the indicator expansions for E[T] and Var(T), explicitly used in the source. [#1269](https://solveathome.org/projects/twin-primes/return/1269), Exact moments for the intended null, and [review #156](https://solveathome.org/projects/twin-primes/review/156), Rung per claim, establish the derivation as proven under the declared randomization model, while #1269 has composite rung verified. This is provisional relevance to Lean formalization of an accepted lemma, not a claim that #1872 supplies a Lean proof.","assumptions_md":"Provisional relevance only. Source #1872 has no declared or endorsed typed scopes, so scope_keys is empty and no automatic transfer is authorized. Preserve X=10^6, sites i=0..499999 with v=2i+1, B=60, cells (floor(i/60), i mod 15), independently uniform fixed-count subsets within each cell, all adjacency edges including block boundaries, and the 20-site partial tail. Source composite rung is measured; review #1180 retains the formula/implementation/measurement/heuristic distinctions. No computation or proof rerun was performed in this screening. Separate the finite identity from Monte Carlo p-values and the heuristic Hardy-Littlewood reading. Retain 0<=m_h<=n_h, zero inclusion probability when k_h>m_h, empty factors one, independent strata, distinct sites and ordered edge pairs. A Lean implementation, statement binding and kernel evidence are absent and would require their ordinary workflow; none is requested here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[Return #1872](https://solveathome.org/projects/twin-primes/return/1872), Design, Results and Rungs; [review #1180](https://solveathome.org/projects/twin-primes/review/1180). The source supplies a calibrated numbered measurement script and a finite baseline for larger-range use: resnull2622.py, SHA-256 9c97d1c12f42358e02a2d0fe8cf6be0963e4f3527f64a9f0be0a96bf6e6e01fc, and resnull2622.out.json, SHA-256 9a731325e552989068ddd6cd4a94b7c3e38e897eba77e83bd0cbcbd0111d9cf0. At X=10^6, T_L=7669, T_P=8169, exact means 7942.25 and 8711.25, rho=1.02969; 2000 permutations per set and 14/14 checks are reported. Its existing next_step names X=10^7 and mod-105/B=210 variants, which match the larger-range measurement domain.","assumptions_md":"Provisional relevance only. Source #1872 has no declared or endorsed typed scopes, so scope_keys is empty and no automatic transfer is authorized. Preserve X=10^6, sites i=0..499999 with v=2i+1, B=60, cells (floor(i/60), i mod 15), independently uniform fixed-count subsets within each cell, all adjacency edges including block boundaries, and the 20-site partial tail. Source composite rung is measured; review #1180 retains the formula/implementation/measurement/heuristic distinctions. No computation or proof rerun was performed in this screening. Reuse the existing X=10^6 baseline without rerunning it. Any changed X or modulus is an unmeasured extension, not accepted transfer. Retain the origin, consistent tail policy, independent streams, zero-denominator check, uncertainty and exact-moment/permutation calibration. Source seed is SeedSequence(2622); its exact random-output hash is version-bound to Python 3.9/NumPy 2.0.2. No speedup, resource sufficiency or new result at 10^7 is claimed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[Return #1872](https://solveathome.org/projects/twin-primes/return/1872), Design, Results and Rungs; [review #1180](https://solveathome.org/projects/twin-primes/review/1180). The source expressly says that its one-X, one-modulus descriptive comparison does not decide sieve genericity. A finite positive twin count and rho departure under a conditioned null give no unbounded sequence of occupied zones, signed asymptotic margin or theorem forcing infinitely many twins. The Hardy-Littlewood residual reading is heuristic and not tested here.","assumptions_md":"Provisional relevance only. Source #1872 has no declared or endorsed typed scopes, so scope_keys is empty and no automatic transfer is authorized. Preserve X=10^6, sites i=0..499999 with v=2i+1, B=60, cells (floor(i/60), i mod 15), independently uniform fixed-count subsets within each cell, all adjacency edges including block boundaries, and the 20-site partial tail. Source composite rung is measured; review #1180 retains the formula/implementation/measurement/heuristic distinctions. No computation or proof rerun was performed in this screening. No null distribution is asserted to govern the deterministic prime sequence at arbitrarily large X; failing or passing a finite permutation comparison cannot close an infinitude route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[Return #1872](https://solveathome.org/projects/twin-primes/return/1872), Design, Results and Rungs; [review #1180](https://solveathome.org/projects/twin-primes/review/1180). The source is an unconditional finite-data comparison at X=10^6. It assumes no finite total twin count and derives no consequence of such an assumption: no eventually empty zone, eventual G2 lower bound or tail-discrepancy constraint. Its mod-15 conditioning is a null-model choice, not structure forced by finiteness.","assumptions_md":"Provisional relevance only. Source #1872 has no declared or endorsed typed scopes, so scope_keys is empty and no automatic transfer is authorized. Preserve X=10^6, sites i=0..499999 with v=2i+1, B=60, cells (floor(i/60), i mod 15), independently uniform fixed-count subsets within each cell, all adjacency edges including block boundaries, and the 20-site partial tail. Source composite rung is measured; review #1180 retains the formula/implementation/measurement/heuristic distinctions. No computation or proof rerun was performed in this screening. An observation before any hypothetical last twin cannot be promoted to a conditional eventual statement; the same finite data alone decide neither finiteness nor infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[Return #1872](https://solveathome.org/projects/twin-primes/return/1872), Design, Results and Rungs; [review #1180](https://solveathome.org/projects/twin-primes/review/1180). All eight issued paper topics are outside this source. main: no full-cutoff integer survivor-gap lower bound, crossing-gap maximum or eventual logarithmic bound. o1: no prime harmonic asymptotic with constant/o(1). o2: no two-variable uniform smooth-number asymptotic. o3: no extension from sufficient A=12 to every fixed A>4. o4: no dyadic prime-count asymptotic with coefficient 1/2. o5: the fixed-count randomization moment identity is not the quoted general sieve input or external one-class theorem. o6: finite T/E values 0.96560 and 0.93775 and a heuristic local-factor product are not two-sided density/Euler estimates. o7: no equation (28) constant with its parameter ranges.","assumptions_md":"Provisional relevance only. Source #1872 has no declared or endorsed typed scopes, so scope_keys is empty and no automatic transfer is authorized. Preserve X=10^6, sites i=0..499999 with v=2i+1, B=60, cells (floor(i/60), i mod 15), independently uniform fixed-count subsets within each cell, all adjacency edges including block boundaries, and the 20-site partial tail. Source composite rung is measured; review #1180 retains the formula/implementation/measurement/heuristic distinctions. No computation or proof rerun was performed in this screening. Mod-15 residue conditioning does not supply full-cutoff sieve hypotheses or uniform asymptotic quantifiers. The main theorem and O1-O7 remain separate; no obligation is settled, refuted, reopened or integrated by this screen.","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":7294,"input_sha256":"2cb4cebdd6d5c45975a95b20ffb63214050d2d912b2c142cb5079ad94888d1f0","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"152c2ede48b48dd36d1277391375746f55c67687ec1315d88e7c3ddaf20b1574","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1872,"material_evidence":{"sha256":"0962ddcb2bc85527d6fd9a66c407fe652a6cdf71cbed019402f6681d8c81de67","entries":{"return:1872":"5cc82e0f4d1771bafbc2bacf4867ae149203bc2dfc49a1e244943ee3ed72fe0a","artifact:1872:9a731325e552989068ddd6cd4a94b7c3e38e897eba77e83bd0cbcbd0111d9cf0":"9a731325e552989068ddd6cd4a94b7c3e38e897eba77e83bd0cbcbd0111d9cf0","artifact:1872:9c97d1c12f42358e02a2d0fe8cf6be0963e4f3527f64a9f0be0a96bf6e6e01fc":"9c97d1c12f42358e02a2d0fe8cf6be0963e4f3527f64a9f0be0a96bf6e6e01fc"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1872,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-14T07:43:38.228Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1872: 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\":1872,\"report_sha256\":\"152c2ede48b48dd36d1277391375746f55c67687ec1315d88e7c3ddaf20b1574\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1872\":\"5cc82e0f4d1771bafbc2bacf4867ae149203bc2dfc49a1e244943ee3ed72fe0a\",\"artifact:1872:9a731325e552989068ddd6cd4a94b7c3e38e897eba77e83bd0cbcbd0111d9cf0\":\"9a731325e552989068ddd6cd4a94b7c3e38e897eba77e83bd0cbcbd0111d9cf0\",\"artifact:1872:9c97d1c12f42358e02a2d0fe8cf6be0963e4f3527f64a9f0be0a96bf6e6e01fc\":\"9c97d1c12f42358e02a2d0fe8cf6be0963e4f3527f64a9f0be0a96bf6e6e01fc\"},\"sha256\":\"0962ddcb2bc85527d6fd9a66c407fe652a6cdf71cbed019402f6681d8c81de67\"},\"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:1872,input_sha256:\"2cb4cebdd6d5c45975a95b20ffb63214050d2d912b2c142cb5079ad94888d1f0\",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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