{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FBCGYJM2OGZI3MASTQ6Y54YZ3K","short_pith_number":"pith:FBCGYJM2","schema_version":"1.0","canonical_sha256":"28446c259a71b28db0129c3d8ef319da9e20751b49cb56e2e367b7c84e46ed1f","source":{"kind":"arxiv","id":"1503.07014","version":2},"attestation_state":"computed","paper":{"title":"Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Manuel Ritor\\'e","submitted_at":"2015-03-24T12:34:34Z","abstract_excerpt":"Let $M$ be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of $M$ is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatures."},"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":"1503.07014","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-03-24T12:34:34Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"0eabe0406762d527dae90b43639dec6c85739814056ba8b229ca39a4c9c79e37","abstract_canon_sha256":"4a47052dc36c336293c12ede5bf65c481d72507474676b763b99d6b814e901e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:35.063477Z","signature_b64":"svcoipK2iONpHOKps51TIcv/xuKylzyDjpxXWv0OFRQyAkMvE8zu2mauedCBbvZ8jhIJJ0HgeeJIZXsTkJ+wCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28446c259a71b28db0129c3d8ef319da9e20751b49cb56e2e367b7c84e46ed1f","last_reissued_at":"2026-05-18T00:49:35.062805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:35.062805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Manuel Ritor\\'e","submitted_at":"2015-03-24T12:34:34Z","abstract_excerpt":"Let $M$ be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of $M$ is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07014","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":"1503.07014","created_at":"2026-05-18T00:49:35.062911+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.07014v2","created_at":"2026-05-18T00:49:35.062911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07014","created_at":"2026-05-18T00:49:35.062911+00:00"},{"alias_kind":"pith_short_12","alias_value":"FBCGYJM2OGZI","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FBCGYJM2OGZI3MAS","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FBCGYJM2","created_at":"2026-05-18T12:29:19.899920+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/FBCGYJM2OGZI3MASTQ6Y54YZ3K","json":"https://pith.science/pith/FBCGYJM2OGZI3MASTQ6Y54YZ3K.json","graph_json":"https://pith.science/api/pith-number/FBCGYJM2OGZI3MASTQ6Y54YZ3K/graph.json","events_json":"https://pith.science/api/pith-number/FBCGYJM2OGZI3MASTQ6Y54YZ3K/events.json","paper":"https://pith.science/paper/FBCGYJM2"},"agent_actions":{"view_html":"https://pith.science/pith/FBCGYJM2OGZI3MASTQ6Y54YZ3K","download_json":"https://pith.science/pith/FBCGYJM2OGZI3MASTQ6Y54YZ3K.json","view_paper":"https://pith.science/paper/FBCGYJM2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.07014&json=true","fetch_graph":"https://pith.science/api/pith-number/FBCGYJM2OGZI3MASTQ6Y54YZ3K/graph.json","fetch_events":"https://pith.science/api/pith-number/FBCGYJM2OGZI3MASTQ6Y54YZ3K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FBCGYJM2OGZI3MASTQ6Y54YZ3K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FBCGYJM2OGZI3MASTQ6Y54YZ3K/action/storage_attestation","attest_author":"https://pith.science/pith/FBCGYJM2OGZI3MASTQ6Y54YZ3K/action/author_attestation","sign_citation":"https://pith.science/pith/FBCGYJM2OGZI3MASTQ6Y54YZ3K/action/citation_signature","submit_replication":"https://pith.science/pith/FBCGYJM2OGZI3MASTQ6Y54YZ3K/action/replication_record"}},"created_at":"2026-05-18T00:49:35.062911+00:00","updated_at":"2026-05-18T00:49:35.062911+00:00"}