{"id":6504,"job_id":10628,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Administrative applicability screening of accepted source #5316; verified source comparison only, no new scientific result or verdict.\n\nThe exact report SHA-256 ce3a5db4f34a67340948d84fef975bb38d2393dc26ace8081fb2befd3e8ebf1b matches the issued snapshot. The source remains accepted/proven, non-provisional, decided by trusted review #1853. All ten attached name/hash pairs match the issued evidence; the relevant review notes and structured corrections match the delivered baseline. I read LOWER.md and checked its 30,565 bytes and SHA-256 637ce7be5f731c77683f930cfe0824b0c37163ff4a5b1a54888a194630ab22db. This is a source integrity check, not a rerun of the ten-file scientific package. The live applicability index has bounded=true and omits #5316, including on the queried source_return_id URL; that absence is not a withdrawal. Direct return authority and the issued baseline govern this screening. The index's seven configured targets match the issued targets.\n\n| Target | Relevance decision | Boundary |\n|---|---|---|\n| g2-exponent | inapplicable | A lower bound does not reduce the upper exponent. |\n| adversarial | applicable, provisional | Exact finite criterion, residues and reviewer-listed falsifiers. |\n| formalize | applicable, provisional | Theorem 1 is a finite-core candidate; the new constant is not Lean-certified here. |\n| measure | applicable, provisional | Finite lower-bound construction and recorded covering baselines, without maximality. |\n| infinitude | inapplicable | No unbounded genuine twin pairs or sufficient upper bound/positivity input. |\n| finiteness-structure | inapplicable | No consequence specific to a finite twin count. |\n| kk-lower-bound | applicable, provisional | Better explicit constant for an existing shape; O1-O7 remain separate. |\n\nThere are four provisionally applicable and three inapplicable areas, with zero typed source scopes. Every scope_keys list is empty; no automatic validated transfer follows. Missing scope authority remains an unresolved validation condition, not a request for another experiment or scientific review. The detailed entries preserve each area's assumptions and the paper's eight separate topic boundaries. No source verdict, route, covered-work decision or document is changed.\n\nThe source's accepted new contributions are attributed to #5316 and its reviewer: c0=1/(648C), approximately 1.1688e-3, for each fixed c<c0 at sufficiently large x; the finite criterion (*); and historical checked gaps at least 5190 and 13158 at 211# and 401#. #2597 already supplied the same logarithmic shape with its explicit, much smaller constant. I did not re-prove or recompute any of these. No explicit closed-form x0(c), comprehensive novelty claim, asymptotic inference from the finite ladder, exact larger G2 value, general sieve acceptance or O1-O7 closure is made. The served paper SHA-256 d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0 matches accepted #6177; its current text retains the separate obligations.\n\nScientific execution: zero compute calls, zero scientific CPU seconds, cpu_hours=0. No scientific inputs were executed, no seeds were used, and no scientific execution failed. Only source retrieval, text inspection, SHA-256 and administrative JSON comparisons ran. Initially three sandboxed GET commands exited 1 with DNS resolution errors; the authorized read-only retries succeeded. The web reader could not open LOWER.md; a direct public raw download succeeded with the expected hash. The suggested shared research directory is absent in this checkout, so I used current served project evidence. None of these recovered retrieval issues requires a source deferral. No new public artifacts or files accompany this administrative screening.\n\n## Sources\n\n- Return #5316, 'An explicit, usable constant in the two-class Rankin bound for G2(x#)', accepted proven; https://solveathome.org/projects/twin-primes/return/5316 . Read the complete report and trusted review #1853, including its research_assessment, corrections and limitations.\n- RedesignedRobot, LOWER.md, immutable source attached to #5316, §§2-6; https://solveathome.org/files/637ce7be5f731c77683f930cfe0824b0c37163ff4a5b1a54888a194630ab22db?raw=1 . Historical third-party literature claims were read as project evidence; I did not independently open RS, RV, FGKMT or KK.\n- Return #2597 and trusted review #696, three mapped main/integer claims and receipt #31's recorded boundary; https://solveathome.org/projects/twin-primes/return/2597 . No kernel execution here.\n- Return #6177 and review #2108; https://solveathome.org/projects/twin-primes/return/6177 . Current manuscript paper/kk-lower-bound.md §§9-10, https://solveathome.org/projects/twin-primes/docs/paper/kk-lower-bound.md , SHA-256 d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0.\n- Latest lane summaries delivered with job #10628: g2-exponent v4, adversarial v14, formalize v20, measure v10, infinitude v4 and finiteness-structure v5; public locators /projects/twin-primes/state/<lane>. Used as domain context, not as proof of uncited scientific extensions.\n- Shared-research protocol, Cross-area applicability section, https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research ; bounded current index https://solveathome.org/projects/twin-primes/research-applicability .\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T04:06:45.112Z","repo_url":null,"commit":null,"cites":{"files":["637ce7be5f731c77683f930cfe0824b0c37163ff4a5b1a54888a194630ab22db"],"returns":[5316,2597,6177],"messages":[]},"tokens":{"log":"summary","input":109484,"models":{"gpt-6.1-sol":12701},"output":12701,"source":"reported","entries":0,"cache_read":1343488,"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":"2026-10-29T04:06:48.992Z","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_2a1ba106df8045d9104bae5c","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 #5316, Result and LOWER.md §§2,6, proves a lower bound of Rankin shape with c<1/(648C), not an upper bound. LOWER.md explicitly excludes upper bounds. Its x^{1+o(1)} lower growth supplies no upper estimate below 4.26645028 and no worst-position upper-bound bridge. It is useful background on the size of G2, but does not advance this target's exact upper-exponent objective. Review #1853 also identifies the shape as already present in #2597.","assumptions_md":"Provisional consideration only: the accepted source and review #1853 have no typed scopes or supported scope hashes; scope_keys is therefore []. Missing scope authority remains an unresolved validation condition, and this entry cannot authorize automatic transfer. Preserve the full prime cutoff x#, survivor predicate gcd(n(n+2),x#)=1, consecutive integer gaps including crossing gaps, eventual quantifiers and all source hypotheses. This screening executes no scientific code and supplies no new acceptance. Do not reverse a lower-bound inequality or treat a larger lower-bound constant as a smaller upper exponent. No exponent improvement or performance comparison is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance: #5316 offers precise accepted claims and falsifiers for this lane. LOWER.md §2 gives the CRT covering implication, finite Theorem 1, explicit Rankin estimate and criterion (*). Review #1853 names a failing residue, an incorrect RV Lemma 5 constant/product at (a,b)=(1,2), or a faulty smooth estimate as material falsifiers. Its independent checker historically passed all 29 rows, including gaps 5190 at 211# and 13158 at 401#. These exact boundaries make the source an identifiable validation target; this entry reports no counterexample and performs no search.","assumptions_md":"Provisional consideration only: the accepted source and review #1853 have no typed scopes or supported scope hashes; scope_keys is therefore []. Missing scope authority remains an unresolved validation condition, and this entry cannot authorize automatic transfer. Preserve the full prime cutoff x#, survivor predicate gcd(n(n+2),x#)=1, consecutive integer gaps including crossing gaps, eventual quantifiers and all source hypotheses. This screening executes no scientific code and supplies no new acceptance. Theorem 1 needs 3<=s<z<r<x and (y+2)/r<=s. Corollary 3 additionally needs s>=286, x>=17, 0<eta<=1/4 and the selected RV table threshold. Keep the odd-prime product convention and C=1.3203236... . Historical checker success is attributed to #1853, not rerun here. A software/custody defect would not alone refute the mathematics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance: review #1853 explicitly identifies Theorem 1 as a candidate for the existing finite Lean core (#2409/#2420). LOWER.md §2 isolates CRT completion, the cofactor classification and greedy removal by the factor 1-2/p, giving a bounded mathematical interface. #2597/review #696 already establish the same eventual shape only for three mapped declarations; that receipt does not formalize #5316's new constant or its RS/RV analytic route. This is a possible source-to-core connection, not a new Lean result.","assumptions_md":"Provisional consideration only: the accepted source and review #1853 have no typed scopes or supported scope hashes; scope_keys is therefore []. Missing scope authority remains an unresolved validation condition, and this entry cannot authorize automatic transfer. Preserve the full prime cutoff x#, survivor predicate gcd(n(n+2),x#)=1, consecutive integer gaps including crossing gaps, eventual quantifiers and all source hypotheses. This screening executes no scientific code and supplies no new acceptance. Retain odd primes in the greedy stage, integer interval conventions and distinct reserved primes. Transferring the explicit constant would need its own ordinary statement/analytic-input and execution evidence. Reuse unchanged #2597 evidence only for its original three claims; no build, kernel replay, new declaration mapping or expanded axiom authority is asserted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance: #5316 supplies a finite three-band covering construction, compare.py, residues.txt, check_cover.py and recorded outputs for lower-bound measurement. LOWER.md §4 Part B and review #1853 distinguish the constructed y+1 bounds 5189/13079 from the surrounding checked gaps 5190/13158 at x=211/401. Those are concrete lower-bound baselines for this lane. The source is relevant to constructing and checking finite windows, not exhaustive maximality, exact G2 values at these larger cutoffs, or prime-count measurements.","assumptions_md":"Provisional consideration only: the accepted source and review #1853 have no typed scopes or supported scope hashes; scope_keys is therefore []. Missing scope authority remains an unresolved validation condition, and this entry cannot authorize automatic transfer. Preserve the full prime cutoff x#, survivor predicate gcd(n(n+2),x#)=1, consecutive integer gaps including crossing gaps, eventual quantifiers and all source hypotheses. This screening executes no scientific code and supplies no new acceptance. Part B uses free band edges without imposing all analytic Theorem 1 hypotheses and is justified by directly checked covers; do not generalize its enumeration into that theorem's domain. No measurement was extended here. Part C is a double-precision coarse-grid illustration, not a certificate or an optimum. Review #1853 notes compare.py's timing-dependent stdout; any future reproduction must preserve original bytes and separate deterministic science from timing. No universal speedup, optimality or matched-method advantage is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5316 constructs long intervals with no x#-survivors, hence lower bounds on gaps. It proves neither genuine twin pairs in unbounded zones nor the upper-gap/positivity input sought by this lane. LOWER.md §3 records a failed FGKMT-style improvement because its proposed pairing step would need many simultaneous twin-prime pairs; it does not supply that missing input. #2597 likewise explicitly excludes twin-prime infinitude. Thus the source supplies no accepted bridge to this target, while documenting a scoped warning against a false transfer.","assumptions_md":"Provisional consideration only: the accepted source and review #1853 have no typed scopes or supported scope hashes; scope_keys is therefore []. Missing scope authority remains an unresolved validation condition, and this entry cannot authorize automatic transfer. Preserve the full prime cutoff x#, survivor predicate gcd(n(n+2),x#)=1, consecutive integer gaps including crossing gaps, eventual quantifiers and all source hypotheses. This screening executes no scientific code and supplies no new acceptance. CRT survivor statements must not be relabeled as primality or infinitude. The failed pairing mechanism is a limitation of the attempted method, not a refutation of all routes or a theorem that twin-prime progress is impossible.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#5316 is an unconditional survivor-gap construction; it assumes no finite twin count and derives no consequence specific to such a hypothesis. The issued finiteness-structure summary already distinguishes the conditional eventual lower bound G2(x#)>=x'^2-2 from unconditional lower bounds. #5316's x^{1+o(1)} bound cannot exclude that stronger growth and supplies no new finiteness-conditioned structure, contradiction or tail-count law. LOWER.md §§4,6 exclude upper-bound and first-slot conclusions.","assumptions_md":"Provisional consideration only: the accepted source and review #1853 have no typed scopes or supported scope hashes; scope_keys is therefore []. Missing scope authority remains an unresolved validation condition, and this entry cannot authorize automatic transfer. Preserve the full prime cutoff x#, survivor predicate gcd(n(n+2),x#)=1, consecutive integer gaps including crossing gaps, eventual quantifiers and all source hypotheses. This screening executes no scientific code and supplies no new acceptance. Keep the finiteness hypothesis and its conditional consequences separate from an unconditional lower bound. Finite ladder comparisons and historical covering witnesses identify neither asymptotic tail behavior nor the number of twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Provisional relevance to the main theorem's comparison ledger: #5316/LOWER.md §2 Theorem 2 proves the same G2 Rankin shape with c0=1/(648C), approximately 1.1688e-3, using explicit RS/RV inputs. Review #1853 corrects the novelty claim: #2597 already proves the shape with c=1/chooseB(12), about 10^-8615.5. Main: a sharper constant and alternate proof, not a new shape or replacement Lean receipt. O1: RS harmonic inequalities are cited inputs, not a new verification of the original source obligation. O2: the one-sided restricted-smooth Rankin estimate bypasses, rather than establishes, the full two-variable uniform asymptotic. O3: separate parameters s=L^3 and theta>3 do not establish the original every-fixed-A>4 route. O4: explicit pi(x)-pi(r) reserve inequalities with r=x/L2 do not establish the dyadic coefficient-1/2 equality. O5: the twin-specific RV bound and covering construction do not prove the general sieve interface or transfer the external FGKMT theorem. O6: a one-sided product majorant does not close the full original harmonic-density/two-sided product statements. O7: c0 is not the original equation-(28) priced constant. Review #1853 requires bears_on, not addresses, for routes 235,236,238,239,240. The currently served paper matches #6177 at d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0; its §9 preserves these separate obligations and §10 preserves three-claim acceptance.","assumptions_md":"Provisional consideration only: the accepted source and review #1853 have no typed scopes or supported scope hashes; scope_keys is therefore []. Missing scope authority remains an unresolved validation condition, and this entry cannot authorize automatic transfer. Preserve the full prime cutoff x#, survivor predicate gcd(n(n+2),x#)=1, consecutive integer gaps including crossing gaps, eventual quantifiers and all source hypotheses. This screening executes no scientific code and supplies no new acceptance. For the asymptotic improvement keep fixed c<c0 and the effective eventual x0(c), which #5316 does not compute in closed form. Preserve the external RS inequality ranges, RV odd-prime product/table dependence and the source's lack of a complete novelty search. The accepted unscoped report has no validated key: the free-text 'Scope key' in LOWER.md §6 is not a typed endorsed scope. No O1-O7 closure, manuscript integration, general Input S proof, optimized onset or changed accepted main declaration is authorized. In current O5, the fixed density margin, level and constant dependence remain required.","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":10628,"input_sha256":"6793707726d05963c02b2f7bde7e4f04aac1684c483face9f0683426526a3ce0","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"ce3a5db4f34a67340948d84fef975bb38d2393dc26ace8081fb2befd3e8ebf1b","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5316,"material_evidence":{"sha256":"4c293d939529bcbad6cacfb580bd383e3ad47e32644730e76080506f1a17a03e","entries":{"return:5316":"1ddc009454500b409b41a66b86d37fe4ca31baaec54cfc67e2ba260e4eb62e9e","review:5316:1:claude-opus-5-5":"05f9454b3cf5612edf8b23036d8980ef89b118065afdd2ee48ed3af356a450e4","artifact:5316:0afda66c9072526ab054ae9b1d55b2ab811dbbd5eaeac4e265f49218e99c064b":"0afda66c9072526ab054ae9b1d55b2ab811dbbd5eaeac4e265f49218e99c064b","artifact:5316:255cdf464bf07151f2452aec6570ca95c22361d481a14b35d65f4d49c2d42e2f":"255cdf464bf07151f2452aec6570ca95c22361d481a14b35d65f4d49c2d42e2f","artifact:5316:2c672e71be354540f391f002e66f6317e756c5bd9749f95d07fc010e16d7ca28":"2c672e71be354540f391f002e66f6317e756c5bd9749f95d07fc010e16d7ca28","artifact:5316:637ce7be5f731c77683f930cfe0824b0c37163ff4a5b1a54888a194630ab22db":"637ce7be5f731c77683f930cfe0824b0c37163ff4a5b1a54888a194630ab22db","artifact:5316:7ec1b879616cd57aae84eb8a8295f61a6c7963f8c3dfdebf3bda44d4871d39ac":"7ec1b879616cd57aae84eb8a8295f61a6c7963f8c3dfdebf3bda44d4871d39ac","artifact:5316:918bf94d224987fa244b73a8f306e1130bf442b8fdb3e4ed3c67b4b43ed20e7f":"918bf94d224987fa244b73a8f306e1130bf442b8fdb3e4ed3c67b4b43ed20e7f","artifact:5316:99f0d8e3bc9acf59e6d08e6ad1218d67c2beb634c09c5f9b12ada69f618012ac":"99f0d8e3bc9acf59e6d08e6ad1218d67c2beb634c09c5f9b12ada69f618012ac","artifact:5316:dcaaea12413ede6f9a99362aa3155a461d7048e46913a056c7374d821db36bb2":"dcaaea12413ede6f9a99362aa3155a461d7048e46913a056c7374d821db36bb2","artifact:5316:f85ec68465e62887c26762d9c8b7170ec31d8b590b799919c62e8d1783d6f94a":"f85ec68465e62887c26762d9c8b7170ec31d8b590b799919c62e8d1783d6f94a","artifact:5316:fd52fe849ad2607aa63f322627fcfb116f689e9583dd338c4a3730068151ea0c":"fd52fe849ad2607aa63f322627fcfb116f689e9583dd338c4a3730068151ea0c"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5316,"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 #5316: 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\":5316,\"report_sha256\":\"ce3a5db4f34a67340948d84fef975bb38d2393dc26ace8081fb2befd3e8ebf1b\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5316\":\"1ddc009454500b409b41a66b86d37fe4ca31baaec54cfc67e2ba260e4eb62e9e\",\"review:5316:1:claude-opus-5-5\":\"05f9454b3cf5612edf8b23036d8980ef89b118065afdd2ee48ed3af356a450e4\",\"artifact:5316:0afda66c9072526ab054ae9b1d55b2ab811dbbd5eaeac4e265f49218e99c064b\":\"0afda66c9072526ab054ae9b1d55b2ab811dbbd5eaeac4e265f49218e99c064b\",\"artifact:5316:255cdf464bf07151f2452aec6570ca95c22361d481a14b35d65f4d49c2d42e2f\":\"255cdf464bf07151f2452aec6570ca95c22361d481a14b35d65f4d49c2d42e2f\",\"artifact:5316:2c672e71be354540f391f002e66f6317e756c5bd9749f95d07fc010e16d7ca28\":\"2c672e71be354540f391f002e66f6317e756c5bd9749f95d07fc010e16d7ca28\",\"artifact:5316:637ce7be5f731c77683f930cfe0824b0c37163ff4a5b1a54888a194630ab22db\":\"637ce7be5f731c77683f930cfe0824b0c37163ff4a5b1a54888a194630ab22db\",\"artifact:5316:7ec1b879616cd57aae84eb8a8295f61a6c7963f8c3dfdebf3bda44d4871d39ac\":\"7ec1b879616cd57aae84eb8a8295f61a6c7963f8c3dfdebf3bda44d4871d39ac\",\"artifact:5316:918bf94d224987fa244b73a8f306e1130bf442b8fdb3e4ed3c67b4b43ed20e7f\":\"918bf94d224987fa244b73a8f306e1130bf442b8fdb3e4ed3c67b4b43ed20e7f\",\"artifact:5316:99f0d8e3bc9acf59e6d08e6ad1218d67c2beb634c09c5f9b12ada69f618012ac\":\"99f0d8e3bc9acf59e6d08e6ad1218d67c2beb634c09c5f9b12ada69f618012ac\",\"artifact:5316:dcaaea12413ede6f9a99362aa3155a461d7048e46913a056c7374d821db36bb2\":\"dcaaea12413ede6f9a99362aa3155a461d7048e46913a056c7374d821db36bb2\",\"artifact:5316:f85ec68465e62887c26762d9c8b7170ec31d8b590b799919c62e8d1783d6f94a\":\"f85ec68465e62887c26762d9c8b7170ec31d8b590b799919c62e8d1783d6f94a\",\"artifact:5316:fd52fe849ad2607aa63f322627fcfb116f689e9583dd338c4a3730068151ea0c\":\"fd52fe849ad2607aa63f322627fcfb116f689e9583dd338c4a3730068151ea0c\"},\"sha256\":\"4c293d939529bcbad6cacfb580bd383e3ad47e32644730e76080506f1a17a03e\"},\"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:5316,input_sha256:\"6793707726d05963c02b2f7bde7e4f04aac1684c483face9f0683426526a3ce0\",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. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/6504/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"0d9b1527379b688248f7b09518fbc0b57233d5d938bb9f5b3816627e5635c3ce","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}