{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:L4KVOZZJW2FLJBN2IQZFTGGA6Z","short_pith_number":"pith:L4KVOZZJ","schema_version":"1.0","canonical_sha256":"5f15576729b68ab485ba44325998c0f64e5fb2cf558918fa1b810f1f5a15c9bb","source":{"kind":"arxiv","id":"2505.10177","version":1},"attestation_state":"computed","paper":{"title":"Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MG","math.PR"],"primary_cat":"math.AP","authors_text":"Fabrice Baudoin, Li Chen, Meng Yang","submitted_at":"2025-05-15T11:08:58Z","abstract_excerpt":"We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform volume growth condition. Using the intrinsic geodesic structure, we define weak gradients and develop from it a coherent theory of Sobolev and BV spaces. We provide two main characterizations: one via Korevaar-Schoen-type energy functionals and another via the heat kernel associated with the natural Dirichlet form. Applications include interpolation results for Besov-Lipschitz spaces, critical exponents computations, a"},"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":"2505.10177","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-15T11:08:58Z","cross_cats_sorted":["math.FA","math.MG","math.PR"],"title_canon_sha256":"88e27cbde4de7cfcd36c70d9249adea2ec534ebf518d68ddc05870575937c686","abstract_canon_sha256":"821e53ef0a56534f50c0f8bc4631bb2d572941f87498d4a6e3965726b1b95ed5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:03:34.515012Z","signature_b64":"nFQKLj2pKjH+SFj7mvvQ3Lzfz7m2U5nN9MxciDgUw2bCCt8VfJ5N0dfrlFn1rYLNgxjNmu93zXAhQgOYaTbYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f15576729b68ab485ba44325998c0f64e5fb2cf558918fa1b810f1f5a15c9bb","last_reissued_at":"2026-07-05T11:03:34.514532Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:03:34.514532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MG","math.PR"],"primary_cat":"math.AP","authors_text":"Fabrice Baudoin, Li Chen, Meng Yang","submitted_at":"2025-05-15T11:08:58Z","abstract_excerpt":"We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform volume growth condition. Using the intrinsic geodesic structure, we define weak gradients and develop from it a coherent theory of Sobolev and BV spaces. We provide two main characterizations: one via Korevaar-Schoen-type energy functionals and another via the heat kernel associated with the natural Dirichlet form. Applications include interpolation results for Besov-Lipschitz spaces, critical exponents computations, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10177","kind":"arxiv","version":1},"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/2505.10177/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":"2505.10177","created_at":"2026-07-05T11:03:34.514590+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.10177v1","created_at":"2026-07-05T11:03:34.514590+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10177","created_at":"2026-07-05T11:03:34.514590+00:00"},{"alias_kind":"pith_short_12","alias_value":"L4KVOZZJW2FL","created_at":"2026-07-05T11:03:34.514590+00:00"},{"alias_kind":"pith_short_16","alias_value":"L4KVOZZJW2FLJBN2","created_at":"2026-07-05T11:03:34.514590+00:00"},{"alias_kind":"pith_short_8","alias_value":"L4KVOZZJ","created_at":"2026-07-05T11:03:34.514590+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.30927","citing_title":"Sobolev spaces on snowtrees","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z","json":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z.json","graph_json":"https://pith.science/api/pith-number/L4KVOZZJW2FLJBN2IQZFTGGA6Z/graph.json","events_json":"https://pith.science/api/pith-number/L4KVOZZJW2FLJBN2IQZFTGGA6Z/events.json","paper":"https://pith.science/paper/L4KVOZZJ"},"agent_actions":{"view_html":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z","download_json":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z.json","view_paper":"https://pith.science/paper/L4KVOZZJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.10177&json=true","fetch_graph":"https://pith.science/api/pith-number/L4KVOZZJW2FLJBN2IQZFTGGA6Z/graph.json","fetch_events":"https://pith.science/api/pith-number/L4KVOZZJW2FLJBN2IQZFTGGA6Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z/action/storage_attestation","attest_author":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z/action/author_attestation","sign_citation":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z/action/citation_signature","submit_replication":"https://pith.science/pith/L4KVOZZJW2FLJBN2IQZFTGGA6Z/action/replication_record"}},"created_at":"2026-07-05T11:03:34.514590+00:00","updated_at":"2026-07-05T11:03:34.514590+00:00"}