{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:5LQCXZX4BV35BGOAN27M4RTQ4J","short_pith_number":"pith:5LQCXZX4","schema_version":"1.0","canonical_sha256":"eae02be6fc0d77d099c06ebece4670e258622fd4d970c8a7aa10877c468f4625","source":{"kind":"arxiv","id":"1008.3318","version":3},"attestation_state":"computed","paper":{"title":"Curvature bounded below: a definition a la Berg--Nikolaev","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Anton Petrunin, Nina Lebedeva","submitted_at":"2010-08-19T14:58:55Z","abstract_excerpt":"We give a new characterization of spaces with nonnegative curvature in the sense of Alexandrov."},"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":"1008.3318","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.MG","submitted_at":"2010-08-19T14:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"5f24cb5c9509978316b283bbb5322bc5aa29e8490957b11fe8c576ea26b20c67","abstract_canon_sha256":"f2f60b79786b9ec1626034c4c7b8a78d987c5f36317b4acda18e46a721392791"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:24.204743Z","signature_b64":"9hm85B7MlQLRd4mQRHRiX0nGw1yszT+MT9ud+yqppyWGOBxxLs7RECsxmVaqB3zYlzx0GvnJWxoU23D25etVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eae02be6fc0d77d099c06ebece4670e258622fd4d970c8a7aa10877c468f4625","last_reissued_at":"2026-05-18T00:11:24.204119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:24.204119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Curvature bounded below: a definition a la Berg--Nikolaev","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Anton Petrunin, Nina Lebedeva","submitted_at":"2010-08-19T14:58:55Z","abstract_excerpt":"We give a new characterization of spaces with nonnegative curvature in the sense of Alexandrov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3318","kind":"arxiv","version":3},"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":"1008.3318","created_at":"2026-05-18T00:11:24.204237+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3318v3","created_at":"2026-05-18T00:11:24.204237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3318","created_at":"2026-05-18T00:11:24.204237+00:00"},{"alias_kind":"pith_short_12","alias_value":"5LQCXZX4BV35","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"5LQCXZX4BV35BGOA","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"5LQCXZX4","created_at":"2026-05-18T12:26:04.259169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.09459","citing_title":"Nonlinear Lebesgue spaces: Curves and geometry","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J","json":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J.json","graph_json":"https://pith.science/api/pith-number/5LQCXZX4BV35BGOAN27M4RTQ4J/graph.json","events_json":"https://pith.science/api/pith-number/5LQCXZX4BV35BGOAN27M4RTQ4J/events.json","paper":"https://pith.science/paper/5LQCXZX4"},"agent_actions":{"view_html":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J","download_json":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J.json","view_paper":"https://pith.science/paper/5LQCXZX4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3318&json=true","fetch_graph":"https://pith.science/api/pith-number/5LQCXZX4BV35BGOAN27M4RTQ4J/graph.json","fetch_events":"https://pith.science/api/pith-number/5LQCXZX4BV35BGOAN27M4RTQ4J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J/action/storage_attestation","attest_author":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J/action/author_attestation","sign_citation":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J/action/citation_signature","submit_replication":"https://pith.science/pith/5LQCXZX4BV35BGOAN27M4RTQ4J/action/replication_record"}},"created_at":"2026-05-18T00:11:24.204237+00:00","updated_at":"2026-05-18T00:11:24.204237+00:00"}