{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DG2JYXENBJMXWVR7GIJ2XJ5LWT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dcc2068ad6e86cdfb88cf309be5b53c553dadbf82bb73db30eec50d05b95424b","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-08T17:09:57Z","title_canon_sha256":"1ef95db4da1f6f6b2afdb4f6db8c01887a3736b46496000a24a73cdd22f9449c"},"schema_version":"1.0","source":{"id":"1304.2271","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2271","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2271v2","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2271","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"DG2JYXENBJMX","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DG2JYXENBJMXWVR7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DG2JYXEN","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:18031b0ca006b1053e0ae45fb9e8c04db02e92b0d05af0b310b152934868a1d3","target":"graph","created_at":"2026-05-18T03:28:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we prove a Sobolev and isoperimetric inequalities for submanifold in weighted manifold. Our results generalize the Hoffman-Spruck's inequalities.","authors_text":"Heudson Mirandola, Marcio Batista","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-08T17:09:57Z","title":"Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2271","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d226c9504e3dcef4a8b453af0861f94bf4d8b6a0e0a2d9c90616128d03544eb2","target":"record","created_at":"2026-05-18T03:28:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dcc2068ad6e86cdfb88cf309be5b53c553dadbf82bb73db30eec50d05b95424b","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-08T17:09:57Z","title_canon_sha256":"1ef95db4da1f6f6b2afdb4f6db8c01887a3736b46496000a24a73cdd22f9449c"},"schema_version":"1.0","source":{"id":"1304.2271","kind":"arxiv","version":2}},"canonical_sha256":"19b49c5c8d0a597b563f3213aba7abb4fbc23fb052efa344fa614a942cf7ccec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19b49c5c8d0a597b563f3213aba7abb4fbc23fb052efa344fa614a942cf7ccec","first_computed_at":"2026-05-18T03:28:16.885339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:16.885339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"320PKlbzisuSGKsCDjE21DOEwoCNMRbG2YAgp/dPoD/RRgBzfUPaKSGuUwV767noewyyG4u011/Pz6rXIGtyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:16.885998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2271","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d226c9504e3dcef4a8b453af0861f94bf4d8b6a0e0a2d9c90616128d03544eb2","sha256:18031b0ca006b1053e0ae45fb9e8c04db02e92b0d05af0b310b152934868a1d3"],"state_sha256":"b76c256af7bed2e590ef25bb714aa9fffba17768fd4cb62037fd00bf677ec3fb"}