{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:LF4LIMKRG47X3VRHS42J4WTQWT","short_pith_number":"pith:LF4LIMKR","schema_version":"1.0","canonical_sha256":"5978b43151373f7dd62797349e5a70b4ef5f0271e8f18f1a033e7092c44cd497","source":{"kind":"arxiv","id":"2506.01434","version":2},"attestation_state":"computed","paper":{"title":"General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Jiabin Yin, Xingjian Zhou","submitted_at":"2025-06-02T08:50:23Z","abstract_excerpt":"In this paper, we deal with an overdetermined problem for the $k$-Hessian equation ($1\\leq k<\\frac n2$) in the exterior domain and prove the corresponding ball characterizations. Since that Weinberger type approach seems to fail to solve the problem, we give a new perspective to solve exterior overdetermined problem by combining two integral identities and geometric inequalities inspired by Brandolini-Nitsch-Salani's results \\cite{BNS}. Meanwhile, we establish general monotone formulas to derive geometric inequalities related to $k$-admissible solution $u$ in $\\mathbb R^n\\setminus\\Omega$, wher"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.01434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T08:50:23Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"eec53bc496839a9b3d54033879cb6aca491a655324c4837b6e84c30693792986","abstract_canon_sha256":"1bc43f19863f41cb89dbf3c7aa3a40b39a5422ec40c297dcae9946499d57dfe7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:41:42.533846Z","signature_b64":"lxwcX7fO3cxFsD8sEOZIZu5VXo1CLIuBU+gtH+X7bmHm5bLGGhJM7c/gbr+xZvlMERl/6jh6pAjZanLM2DVqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5978b43151373f7dd62797349e5a70b4ef5f0271e8f18f1a033e7092c44cd497","last_reissued_at":"2026-07-05T11:41:42.533212Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:41:42.533212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Jiabin Yin, Xingjian Zhou","submitted_at":"2025-06-02T08:50:23Z","abstract_excerpt":"In this paper, we deal with an overdetermined problem for the $k$-Hessian equation ($1\\leq k<\\frac n2$) in the exterior domain and prove the corresponding ball characterizations. Since that Weinberger type approach seems to fail to solve the problem, we give a new perspective to solve exterior overdetermined problem by combining two integral identities and geometric inequalities inspired by Brandolini-Nitsch-Salani's results \\cite{BNS}. Meanwhile, we establish general monotone formulas to derive geometric inequalities related to $k$-admissible solution $u$ in $\\mathbb R^n\\setminus\\Omega$, wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01434","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.01434/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.01434","created_at":"2026-07-05T11:41:42.533284+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.01434v2","created_at":"2026-07-05T11:41:42.533284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01434","created_at":"2026-07-05T11:41:42.533284+00:00"},{"alias_kind":"pith_short_12","alias_value":"LF4LIMKRG47X","created_at":"2026-07-05T11:41:42.533284+00:00"},{"alias_kind":"pith_short_16","alias_value":"LF4LIMKRG47X3VRH","created_at":"2026-07-05T11:41:42.533284+00:00"},{"alias_kind":"pith_short_8","alias_value":"LF4LIMKR","created_at":"2026-07-05T11:41:42.533284+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT","json":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT.json","graph_json":"https://pith.science/api/pith-number/LF4LIMKRG47X3VRHS42J4WTQWT/graph.json","events_json":"https://pith.science/api/pith-number/LF4LIMKRG47X3VRHS42J4WTQWT/events.json","paper":"https://pith.science/paper/LF4LIMKR"},"agent_actions":{"view_html":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT","download_json":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT.json","view_paper":"https://pith.science/paper/LF4LIMKR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.01434&json=true","fetch_graph":"https://pith.science/api/pith-number/LF4LIMKRG47X3VRHS42J4WTQWT/graph.json","fetch_events":"https://pith.science/api/pith-number/LF4LIMKRG47X3VRHS42J4WTQWT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/action/storage_attestation","attest_author":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/action/author_attestation","sign_citation":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/action/citation_signature","submit_replication":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/action/replication_record"}},"created_at":"2026-07-05T11:41:42.533284+00:00","updated_at":"2026-07-05T11:41:42.533284+00:00"}