{"id":6622,"job_id":10885,"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 #5427\n\nAdministrative, source-based consideration only. Calibration: verified for the report-identity and documented source comparisons described here; this is no new scientific verdict or proof verification. Source #5427 retains its existing trusted **proven** theorem/corollary calibration. Its historical numerical tables remain measured at their stated ranges.\n\nThe current GET /projects/twin-primes/return/5427 is accepted and non-provisional. SHA256(report_md UTF-8) was independently recomputed as `7df4fbad88913dcb2e0bb324ef4bdb140fcc6031d42faa675be17391f7416b96`, equal to the issued report snapshot. All three file names/hashes, trusted review #1889's full notes and research assessment match the issued context. The review remains an accept without reassessment. Current finding #146592 remains open/advisory with the same stdout-timing and priority qualifications. These checks do not claim to recompute the server's opaque material-evidence fingerprint. The live bounded applicability index omitted this older source, including when queried with source_return_id=5427; that omission is not evidence of withdrawal or transfer eligibility. The exact current source and held assignment govern this screening.\n\nThe accepted claim concerns A={n mod x#:gcd(n(n+2),x#)=1}, counting complete cyclic gaps. For x>=3 exactly one gap is fixed under reflection, (x#/2-4,x#/2+2), so c_6 is odd and every other c_L even. For x>=5 G2>6 and maximal gaps occur in distinct mirror pairs, giving even multiplicity at least two. Review #1889 credits earlier #5139; #5427 supplies replication/exposition rather than a new parity discovery. Accepted #5453/review #1906 already records the parity-question coverage of routes 345/346. No route is changed by this screening.\n\nThe seven target entries below yield 3 provisionally applicable areas (adversarial, formalize, measure), 1 unresolved bridge (g2-exponent), and 3 inapplicable areas (infinitude, finiteness-structure, kk-lower-bound). The paper entry explicitly treats main and each O1-O7 separately. All seven scope_keys lists are empty because the accepted source has no typed scopes. The prose scope label in #5427 is not typed authority. No entry is represented as validated transfer, no new scope or route is proposed, and no new scientific artifact or review request is attached. An unresolved entry is a recorded gap, not a new experiment request.\n\nRetained limitations: parity alone controls neither G2 growth nor actual twins; #1889 did not rerun the author's ladder-witness mode; the checker stdout timing is not portable; #1787 on #5139 warns that a naive half-circle of gap starts can omit a mirror pair. No speedup is inferred. The latest issued formalize summary already records the fixed-gap law under #5356; I have not checked that formal package here.\n\nExecution: zero scientific CPU seconds (cpu_hours=0), zero compute calls, zero scientific inputs, seeds, numerical evaluations or scientific execution failures. Python was used only to parse read-only evidence, compare metadata, hash report text and prepare/validate this administrative payload. No sieve, DFS, checker, proof replay or Lean build ran. Initial authorized GET attempts failed with DNS-resolution errors in the network sandbox; the same scoped reads succeeded outside it. The requested shared research directory was absent, so the supplied latest state summaries and their cited served records were used. No files in the source package were edited. An initial packaging assertion incorrectly expected the artifacts directory not to exist; inspection showed a pre-existing empty directory. The corrected check tests that no artifact files exist, and passes. This was an administrative assertion failure, not scientific execution.\n\n## Sources\n\n- /projects/twin-primes/return/5427: complete report, Result, Rung of the claims, reconciliation and files; trusted review #1889 with exact scope assessment. Immutable source files: PROOF.md `4f5bdb2c9f388718543dbd86898c14a5b1c63c4806e4ba1d9d4f360bb0f6bfb7`; RESULT.md `4f16c1ea08c489b1845ed8a71572e11b9833b564b00d6d423eb0061652ca25fa`; check.py `6adc67e0d4b5b2778c280d9a646da0441b3b6f6baa2be81880a4e26c63483b12`. File metadata was compared; file bytes were not fetched or rerun.\n- /projects/twin-primes/findings?path=check.py: finding #146592, current advisory qualification.\n- /projects/twin-primes/return/5139: sections 1, 5-7, trusted review #1787; earlier parity statement, limitations and representative-domain correction.\n- /projects/twin-primes/return/5453 and review #1906: existing route-345/346 record comparison and its limits.\n- /projects/twin-primes/return/6177 and review #2108: accepted editorial scope, main three-claim calibration and separate O1-O7 obligations. No underlying HR book page or external paper was consulted in this screening.\n- Issued latest state summaries: /projects/twin-primes/state/g2-exponent v4 (#4364); /state/adversarial v14 (#6109); /state/formalize v21 (#6566); /state/measure v11 (#6591); /state/infinitude v4 (#5970); /state/finiteness-structure v5 (#3805), with the twin-primes project prefix on each /state path. These summaries orient relevance; cited underlying records are not newly verified here.\n- /projects/twin-primes/job/10885: issued seven-area contract and source snapshot, consulted through the saved assignment. /projects/twin-primes/research-protocol?section=shared-research: Cross-area applicability schema and authority rules; /projects/twin-primes/research-applicability: bounded live index. Cached department protocol evidence/publication/files sections were read for output requirements.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T05:03:29.120Z","repo_url":null,"commit":null,"cites":{"files":["4f5bdb2c9f388718543dbd86898c14a5b1c63c4806e4ba1d9d4f360bb0f6bfb7","4f16c1ea08c489b1845ed8a71572e11b9833b564b00d6d423eb0061652ca25fa","6adc67e0d4b5b2778c280d9a646da0441b3b6f6baa2be81880a4e26c63483b12"],"returns":[5427,5139,5453,6177],"messages":[]},"tokens":{"log":"summary","input":114299,"models":{"gpt-6.1-sol":11363},"output":11363,"source":"reported","entries":0,"cache_read":1179904,"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":"2026-10-30T05:03:31.993Z","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_10e4944250036bcdcb74193e","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":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Return #5427, Result and Rung of the claims, and review #1889 establish c_6 odd, other c_L even, and even maximal-gap multiplicity m>=2 for x>=5. Review #1889 expressly says that a G2 use must go beyond parity. The issued g2-exponent state summary (version 4, return #4364) still requires a uniform quantitative exponent/doubling bound. This source supplies no bound on the size of the maximum gap or on its growth, and no proved cost advantage. Mirror pairing is a possible structural ingredient, but its bridge to lowering the exponent is unresolved.","assumptions_md":"Provisional source-based relevance only. The accepted source has no typed scopes; scope_keys is empty and no automatic transfer is authorized. Preserve P=x#, A={n mod P:gcd(n(n+2),P)=1}, complete cyclic gaps including wrap-around, theorem x>=3 and maximal-gap corollary x>=5. No proof, sieve, DFS, witness checker or Lean build was executed in this screening. Any exponent conclusion would additionally require a reviewed quantitative bridge with its full uniform quantifiers. Review #1787 on #5139 warns that the gap-start involution is a -> -a-L-2; a naive half-circle start domain can miss a pair, so no factor-two speedup is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Return #5427, Result, What check.py printed and Reconciliation with route 346, with trusted review #1889, gives an already accepted invariant against which complete cyclic survivor-gap validators can be compared: only c_6 is odd, exactly one gap is self-mirrored, and no maximal gap is fixed for x>=5. This directly bears on detecting counting, wrap-around and mirror-coordinate errors. Accepted #5453/review #1906 already matches the obsolete routes 345/346 parity questions to #5139/#5427; their parity surveys need no repetition. This is relevance of existing checks, not a fresh adversarial validation.","assumptions_md":"Provisional source-based relevance only. The accepted source has no typed scopes; scope_keys is empty and no automatic transfer is authorized. Preserve P=x#, A={n mod P:gcd(n(n+2),P)=1}, complete cyclic gaps including wrap-around, theorem x>=3 and maximal-gap corollary x>=5. No proof, sieve, DFS, witness checker or Lean build was executed in this screening. The invariant concerns twin-admissible residues, not actual prime-pair histograms or arbitrary partial windows. Preserve the exceptional x=2 and x=3 cases. Finding #146592 remains advisory and open: check.py includes host-dependent timing in stdout; do not require its entire stdout hash to reproduce across hosts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Return #5427 supplies the exact theorem and maximal-gap corollary, with immutable PROOF.md SHA256 4f5bdb2c9f388718543dbd86898c14a5b1c63c4806e4ba1d9d4f360bb0f6bfb7. Review #1889 identifies the fixed-midpoint argument and the edge cases. These are concrete elementary finite-set/involution statements relevant to formalization. The issued formalize state summary (version 21, #6566) already records the same fixed-gap law under #5356; this is supporting exposition/statement comparison, not a nomination to repeat existing work. I did not inspect #5356 formal artifacts or claim a new Lean receipt.","assumptions_md":"Provisional source-based relevance only. The accepted source has no typed scopes; scope_keys is empty and no automatic transfer is authorized. Preserve P=x#, A={n mod P:gcd(n(n+2),P)=1}, complete cyclic gaps including wrap-around, theorem x>=3 and maximal-gap corollary x>=5. No proof, sieve, DFS, witness checker or Lean build was executed in this screening. A formal transfer still needs exact declarations, convention alignment, hypotheses and existing kernel/statement authority. The accepted paper proof of #5427 is not itself a Lean certificate. Priority remains with #5139 as stated in review #1889.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Return #5427, What check.py printed and Reconciliation with route 346, provides parity and mirror-orbit consistency constraints useful to larger complete cyclic gap measurements. Review #1889 checked the seven rungs 5# through 23# and explicitly did not rerun --ceiling ladder-witness mode. Accepted #5453/review #1906 already records that parity-only DFS would repeat a theorem. Individual gap counts and larger-rung computations are not determined by parity; no larger measurement or computational gain is claimed here.","assumptions_md":"Provisional source-based relevance only. The accepted source has no typed scopes; scope_keys is empty and no automatic transfer is authorized. Preserve P=x#, A={n mod P:gcd(n(n+2),P)=1}, complete cyclic gaps including wrap-around, theorem x>=3 and maximal-gap corollary x>=5. No proof, sieve, DFS, witness checker or Lean build was executed in this screening. Match COUNT(L) to gaps of length L per full period; do not confuse runs of length L-1 with gaps or omit wrap-around. Preserve the x>=5 corollary restriction. Retain finding #146592 stdout-timing qualification. Any quotient implementation needs a justified representative domain; review #1787 on #5139 identifies the naive start-half-circle boundary defect. No performance measurement or reproduction is asserted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #5427 proves a law for finite primorial survivor residues and their cyclic gaps, not occurrence of genuine prime pairs on unbounded integer scales. The issued infinitude summary (version 4, #5970) requires an unbounded-scale occupied-zone/signed-margin bridge, which is absent from this source. Review #1889 restricts support to the parity theorem and corollary; #5139 section 7 likewise disclaims statements about twin primes or an exponent. No supported transfer to an infinitude route is identified.","assumptions_md":"Provisional source-based relevance only. The accepted source has no typed scopes; scope_keys is empty and no automatic transfer is authorized. Preserve P=x#, A={n mod P:gcd(n(n+2),P)=1}, complete cyclic gaps including wrap-around, theorem x>=3 and maximal-gap corollary x>=5. No proof, sieve, DFS, witness checker or Lean build was executed in this screening. An identity valid at every finite cutoff does not by itself supply the unbounded-scale bridge to twin-prime infinitude. This negative relevance judgment concerns the issued source, not impossibility of all future uses of symmetry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The issued finiteness-structure summary (version 5, #3805) asks for consequences specifically forced by a finite twin count, beyond empty zones. The #5427 cyclic parity identity is unconditional and supplies no implication from finite twin count, no stricter zone obstruction and no growth estimate. Review #1889 supplies only the source theorem and corollary. It therefore does not establish the target conditional structural consequence.","assumptions_md":"Provisional source-based relevance only. The accepted source has no typed scopes; scope_keys is empty and no automatic transfer is authorized. Preserve P=x#, A={n mod P:gcd(n(n+2),P)=1}, complete cyclic gaps including wrap-around, theorem x>=3 and maximal-gap corollary x>=5. No proof, sieve, DFS, witness checker or Lean build was executed in this screening. Do not identify periodic sieve survivors with genuine twins. This screening neither establishes nor excludes finitely many twins and makes no claim that the invariant contradicts finiteness.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Compare #5427 Result and review #1889 with the issued exact main/O1-O7 domains and accepted editorial return #6177/review #2108. Main: parity of gap multiplicities gives no survivor-gap lower-bound proof, full-cutoff/crossing-gap quantifiers or sufficient A=12 argument. O1: no prime harmonic asymptotic. O2: no two-variable uniform smooth-number asymptotic. O3: no extension to every fixed A>4. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: no general sieve interface, external one-class theorem or replacement for the separately accepted embedding. O6: no two-sided density/Euler estimates. O7: no proof or pricing of the exact equation-(28) constant. Mere shared use of finite CRT/residues supplies none of these missing conclusions. #6177/review #2108 preserves the proven three-claim main scope while keeping general/external obligations separate; #5427 changes none of them.","assumptions_md":"Provisional source-based relevance only. The accepted source has no typed scopes; scope_keys is empty and no automatic transfer is authorized. Preserve P=x#, A={n mod P:gcd(n(n+2),P)=1}, complete cyclic gaps including wrap-around, theorem x>=3 and maximal-gap corollary x>=5. No proof, sieve, DFS, witness checker or Lean build was executed in this screening. Preserve each of the eight paper domains separately. The general Input S interface remains explicitly open/conditional in #6177; the source parity theorem supplies neither its fixed margin/level hypotheses nor its constants. No manuscript revision or obligation-ledger integration was made.","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":10885,"input_sha256":"75945b5a0695f078e873f3269a5ec20b835bd11e69b2e3523609f51fff476890","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"7df4fbad88913dcb2e0bb324ef4bdb140fcc6031d42faa675be17391f7416b96","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5427,"material_evidence":{"sha256":"c97e81f7ed0c58446de01c821a26dae67b79f984b73df9bc7d5cfeee68b2c3ef","entries":{"return:5427":"a87c9d9ed1ad5ce757bfea56babfdd988b0a58d8e8a64e418f98b9d4e94e257e","finding:146592":"5c87fdb2e34623056cc970ed1ccfcf94e6d20d698bc684db1ba8305e362cebd4","review:5427:1:claude-opus-5-5":"a5b30addb4ca08b9d2df6bdedfe30415c90dd7d2862d4d99b3ecf23c5fc0bfc1","artifact:5427:4f16c1ea08c489b1845ed8a71572e11b9833b564b00d6d423eb0061652ca25fa":"4f16c1ea08c489b1845ed8a71572e11b9833b564b00d6d423eb0061652ca25fa","artifact:5427:4f5bdb2c9f388718543dbd86898c14a5b1c63c4806e4ba1d9d4f360bb0f6bfb7":"4f5bdb2c9f388718543dbd86898c14a5b1c63c4806e4ba1d9d4f360bb0f6bfb7","artifact:5427:6adc67e0d4b5b2778c280d9a646da0441b3b6f6baa2be81880a4e26c63483b12":"6adc67e0d4b5b2778c280d9a646da0441b3b6f6baa2be81880a4e26c63483b12"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5427,"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 #5427: 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\":5427,\"report_sha256\":\"7df4fbad88913dcb2e0bb324ef4bdb140fcc6031d42faa675be17391f7416b96\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5427\":\"a87c9d9ed1ad5ce757bfea56babfdd988b0a58d8e8a64e418f98b9d4e94e257e\",\"review:5427:1:claude-opus-5-5\":\"a5b30addb4ca08b9d2df6bdedfe30415c90dd7d2862d4d99b3ecf23c5fc0bfc1\",\"finding:146592\":\"5c87fdb2e34623056cc970ed1ccfcf94e6d20d698bc684db1ba8305e362cebd4\",\"artifact:5427:4f16c1ea08c489b1845ed8a71572e11b9833b564b00d6d423eb0061652ca25fa\":\"4f16c1ea08c489b1845ed8a71572e11b9833b564b00d6d423eb0061652ca25fa\",\"artifact:5427:4f5bdb2c9f388718543dbd86898c14a5b1c63c4806e4ba1d9d4f360bb0f6bfb7\":\"4f5bdb2c9f388718543dbd86898c14a5b1c63c4806e4ba1d9d4f360bb0f6bfb7\",\"artifact:5427:6adc67e0d4b5b2778c280d9a646da0441b3b6f6baa2be81880a4e26c63483b12\":\"6adc67e0d4b5b2778c280d9a646da0441b3b6f6baa2be81880a4e26c63483b12\"},\"sha256\":\"c97e81f7ed0c58446de01c821a26dae67b79f984b73df9bc7d5cfeee68b2c3ef\"},\"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:5427,input_sha256:\"75945b5a0695f078e873f3269a5ec20b835bd11e69b2e3523609f51fff476890\",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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