{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QOVT3PBS43C3V4B34OJNMVXS43","short_pith_number":"pith:QOVT3PBS","schema_version":"1.0","canonical_sha256":"83ab3dbc32e6c5baf03be392d656f2e6dcaa613cd8a446f975e43e543d7759e9","source":{"kind":"arxiv","id":"1702.01449","version":1},"attestation_state":"computed","paper":{"title":"Concepts of curvatures in normed planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Emad Shonoda, Horst Martini, Vitor Balestro","submitted_at":"2017-02-05T20:17:57Z","abstract_excerpt":"The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a comprehensive overview on geometric properties of and relations between all introduced curvature concepts, we try to fill this gap. Certainly, this yields a basis for further research and also for possible extensions of the whole existing framework. In addition, we derive various new results referring in full broadness to the variety of known curvature types in normed p"},"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":"1702.01449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-05T20:17:57Z","cross_cats_sorted":[],"title_canon_sha256":"7c5043c7cc0b621d7de46cd466f117078d7530e3ae9a23ef758c0baff538ede0","abstract_canon_sha256":"50774bce13d7a360dc3be55328459aa275f3e94f95ad6a3fbce0e72419f7bd32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:23.368381Z","signature_b64":"WZgLmPHqsaOYvnUo425D4gWXtv31yZ4ypWP20kz/+z8nmZDsV7/VckMQx7M8uj8/ZI+GkHKZPHKoTs6xrVJRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83ab3dbc32e6c5baf03be392d656f2e6dcaa613cd8a446f975e43e543d7759e9","last_reissued_at":"2026-05-18T00:51:23.367921Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:23.367921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concepts of curvatures in normed planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Emad Shonoda, Horst Martini, Vitor Balestro","submitted_at":"2017-02-05T20:17:57Z","abstract_excerpt":"The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a comprehensive overview on geometric properties of and relations between all introduced curvature concepts, we try to fill this gap. Certainly, this yields a basis for further research and also for possible extensions of the whole existing framework. In addition, we derive various new results referring in full broadness to the variety of known curvature types in normed p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01449","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":""},"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":"1702.01449","created_at":"2026-05-18T00:51:23.367982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.01449v1","created_at":"2026-05-18T00:51:23.367982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01449","created_at":"2026-05-18T00:51:23.367982+00:00"},{"alias_kind":"pith_short_12","alias_value":"QOVT3PBS43C3","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QOVT3PBS43C3V4B3","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QOVT3PBS","created_at":"2026-05-18T12:31:39.905425+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/QOVT3PBS43C3V4B34OJNMVXS43","json":"https://pith.science/pith/QOVT3PBS43C3V4B34OJNMVXS43.json","graph_json":"https://pith.science/api/pith-number/QOVT3PBS43C3V4B34OJNMVXS43/graph.json","events_json":"https://pith.science/api/pith-number/QOVT3PBS43C3V4B34OJNMVXS43/events.json","paper":"https://pith.science/paper/QOVT3PBS"},"agent_actions":{"view_html":"https://pith.science/pith/QOVT3PBS43C3V4B34OJNMVXS43","download_json":"https://pith.science/pith/QOVT3PBS43C3V4B34OJNMVXS43.json","view_paper":"https://pith.science/paper/QOVT3PBS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.01449&json=true","fetch_graph":"https://pith.science/api/pith-number/QOVT3PBS43C3V4B34OJNMVXS43/graph.json","fetch_events":"https://pith.science/api/pith-number/QOVT3PBS43C3V4B34OJNMVXS43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QOVT3PBS43C3V4B34OJNMVXS43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QOVT3PBS43C3V4B34OJNMVXS43/action/storage_attestation","attest_author":"https://pith.science/pith/QOVT3PBS43C3V4B34OJNMVXS43/action/author_attestation","sign_citation":"https://pith.science/pith/QOVT3PBS43C3V4B34OJNMVXS43/action/citation_signature","submit_replication":"https://pith.science/pith/QOVT3PBS43C3V4B34OJNMVXS43/action/replication_record"}},"created_at":"2026-05-18T00:51:23.367982+00:00","updated_at":"2026-05-18T00:51:23.367982+00:00"}