{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CJAKH54UV4BYPRGJVSPWAW3KEM","short_pith_number":"pith:CJAKH54U","schema_version":"1.0","canonical_sha256":"1240a3f794af0387c4c9ac9f605b6a230e653e1d06fc1f206d857e12e7b2237a","source":{"kind":"arxiv","id":"1005.2343","version":2},"attestation_state":"computed","paper":{"title":"Stokes' theorem, volume growth and parabolicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniele Valtorta, Giona Veronelli","submitted_at":"2010-05-13T15:16:07Z","abstract_excerpt":"We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced."},"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":"1005.2343","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-05-13T15:16:07Z","cross_cats_sorted":[],"title_canon_sha256":"4d064cc55594657a90408b7950330d8a70447346afe668703f006e25116c648e","abstract_canon_sha256":"2a7d44df7f70d2abd9dafd2da3a521a4ea80a92fe5077975a652ff2c4e0aa732"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:34.540111Z","signature_b64":"RrFT4o+nMHAFw/eYQvznfLx+G0XCn88kBJIPXxEqe5y8VW7kQGGTcV78EPMLujQrnZeeG52Rp3rTr8bLQOdPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1240a3f794af0387c4c9ac9f605b6a230e653e1d06fc1f206d857e12e7b2237a","last_reissued_at":"2026-05-18T03:48:34.539619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:34.539619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stokes' theorem, volume growth and parabolicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniele Valtorta, Giona Veronelli","submitted_at":"2010-05-13T15:16:07Z","abstract_excerpt":"We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2343","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":""},"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":"1005.2343","created_at":"2026-05-18T03:48:34.539681+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.2343v2","created_at":"2026-05-18T03:48:34.539681+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2343","created_at":"2026-05-18T03:48:34.539681+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJAKH54UV4BY","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJAKH54UV4BYPRGJ","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJAKH54U","created_at":"2026-05-18T12:26:06.534383+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/CJAKH54UV4BYPRGJVSPWAW3KEM","json":"https://pith.science/pith/CJAKH54UV4BYPRGJVSPWAW3KEM.json","graph_json":"https://pith.science/api/pith-number/CJAKH54UV4BYPRGJVSPWAW3KEM/graph.json","events_json":"https://pith.science/api/pith-number/CJAKH54UV4BYPRGJVSPWAW3KEM/events.json","paper":"https://pith.science/paper/CJAKH54U"},"agent_actions":{"view_html":"https://pith.science/pith/CJAKH54UV4BYPRGJVSPWAW3KEM","download_json":"https://pith.science/pith/CJAKH54UV4BYPRGJVSPWAW3KEM.json","view_paper":"https://pith.science/paper/CJAKH54U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.2343&json=true","fetch_graph":"https://pith.science/api/pith-number/CJAKH54UV4BYPRGJVSPWAW3KEM/graph.json","fetch_events":"https://pith.science/api/pith-number/CJAKH54UV4BYPRGJVSPWAW3KEM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJAKH54UV4BYPRGJVSPWAW3KEM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJAKH54UV4BYPRGJVSPWAW3KEM/action/storage_attestation","attest_author":"https://pith.science/pith/CJAKH54UV4BYPRGJVSPWAW3KEM/action/author_attestation","sign_citation":"https://pith.science/pith/CJAKH54UV4BYPRGJVSPWAW3KEM/action/citation_signature","submit_replication":"https://pith.science/pith/CJAKH54UV4BYPRGJVSPWAW3KEM/action/replication_record"}},"created_at":"2026-05-18T03:48:34.539681+00:00","updated_at":"2026-05-18T03:48:34.539681+00:00"}