{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FAAQ24T5HXFNXV7H6XN6TYG2WU","short_pith_number":"pith:FAAQ24T5","schema_version":"1.0","canonical_sha256":"28010d727d3dcadbd7e7f5dbe9e0dab52f8e4b4bd4030658a3fc1aa87e5f7991","source":{"kind":"arxiv","id":"1411.5801","version":1},"attestation_state":"computed","paper":{"title":"Transitional geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.HO"],"primary_cat":"math.GT","authors_text":"Athanase Papadopoulos (IRMA, GSU), Norbert A'Campo","submitted_at":"2014-11-21T09:01:46Z","abstract_excerpt":"We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric entities like points, lines, dis-tances, triangles, angles, area, curvature, etc. as well as trigonometric formulae and other properties transit in a continuous manner from one geometry to another. AMS classification: 01-99 ; 53-02 ; 53-03 ; 53A35."},"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":"1411.5801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-21T09:01:46Z","cross_cats_sorted":["math.HO"],"title_canon_sha256":"f862dd25d58dc65757e81204783a7409b01e1a023d9d5c56ee04f5c38cba663b","abstract_canon_sha256":"71529cb376df1dcc0f5f095e4291cbdb58fb4ff7aac4a6157b7f93ad6077d642"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:02.191563Z","signature_b64":"uDpwjh8nI5P5P1wsRx3OqWoMYH5Zlc05ayUEq90jIIyY9r/p1neGCRmIj7tP53VFj9mIP3tOnkBwa+hnedqNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28010d727d3dcadbd7e7f5dbe9e0dab52f8e4b4bd4030658a3fc1aa87e5f7991","last_reissued_at":"2026-05-18T02:33:02.191033Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:02.191033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transitional geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.HO"],"primary_cat":"math.GT","authors_text":"Athanase Papadopoulos (IRMA, GSU), Norbert A'Campo","submitted_at":"2014-11-21T09:01:46Z","abstract_excerpt":"We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric entities like points, lines, dis-tances, triangles, angles, area, curvature, etc. as well as trigonometric formulae and other properties transit in a continuous manner from one geometry to another. AMS classification: 01-99 ; 53-02 ; 53-03 ; 53A35."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5801","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":"1411.5801","created_at":"2026-05-18T02:33:02.191113+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.5801v1","created_at":"2026-05-18T02:33:02.191113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5801","created_at":"2026-05-18T02:33:02.191113+00:00"},{"alias_kind":"pith_short_12","alias_value":"FAAQ24T5HXFN","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FAAQ24T5HXFNXV7H","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FAAQ24T5","created_at":"2026-05-18T12:28:28.263976+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/FAAQ24T5HXFNXV7H6XN6TYG2WU","json":"https://pith.science/pith/FAAQ24T5HXFNXV7H6XN6TYG2WU.json","graph_json":"https://pith.science/api/pith-number/FAAQ24T5HXFNXV7H6XN6TYG2WU/graph.json","events_json":"https://pith.science/api/pith-number/FAAQ24T5HXFNXV7H6XN6TYG2WU/events.json","paper":"https://pith.science/paper/FAAQ24T5"},"agent_actions":{"view_html":"https://pith.science/pith/FAAQ24T5HXFNXV7H6XN6TYG2WU","download_json":"https://pith.science/pith/FAAQ24T5HXFNXV7H6XN6TYG2WU.json","view_paper":"https://pith.science/paper/FAAQ24T5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.5801&json=true","fetch_graph":"https://pith.science/api/pith-number/FAAQ24T5HXFNXV7H6XN6TYG2WU/graph.json","fetch_events":"https://pith.science/api/pith-number/FAAQ24T5HXFNXV7H6XN6TYG2WU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FAAQ24T5HXFNXV7H6XN6TYG2WU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FAAQ24T5HXFNXV7H6XN6TYG2WU/action/storage_attestation","attest_author":"https://pith.science/pith/FAAQ24T5HXFNXV7H6XN6TYG2WU/action/author_attestation","sign_citation":"https://pith.science/pith/FAAQ24T5HXFNXV7H6XN6TYG2WU/action/citation_signature","submit_replication":"https://pith.science/pith/FAAQ24T5HXFNXV7H6XN6TYG2WU/action/replication_record"}},"created_at":"2026-05-18T02:33:02.191113+00:00","updated_at":"2026-05-18T02:33:02.191113+00:00"}