{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ELUHLUVACVS275I4TKJI6SH3K4","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":"e31dda396d5f31f31160e4823b4c20944fe4191c2e35b11e2a12a751fcba2478","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-30T03:09:59Z","title_canon_sha256":"4b4ecbac92c474f4d5898d2135838bbd43914419b4551fad79b88e2e6f744cad"},"schema_version":"1.0","source":{"id":"1804.11033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11033","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11033v1","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11033","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"ELUHLUVACVS2","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ELUHLUVACVS275I4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ELUHLUVA","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:e12b6301603460b15b8beeae95697fe544a9851b81beac3e84f53f7d8c1b269b","target":"graph","created_at":"2026-05-18T00:17:14Z","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":"For a finite planar graph, it associates with some metric spaces, called (regular) spherical polyhedral surfaces, by replacing faces with regular spherical polygons in the unit sphere and gluing them edge-to-edge. We consider the class of planar graphs which admit spherical polyhedral surfaces with the curvature bounded below by 1 in the sense of Alexandrov, i.e. the total angle at each vertex is at most $2\\pi$. We classify all spherical tilings with regular spherical polygons, i.e. total angles at vertices are exactly $2\\pi$. We prove that for any graph in this class which does not admit a sp","authors_text":"Bobo Hua, Yanhui Su, Yohji Akama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-30T03:09:59Z","title":"Areas of spherical polyhedral surfaces with regular faces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11033","kind":"arxiv","version":1},"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":"sha256:5d0aab431ae422f8caa5fedff950aca50f75a61acbb55447568113bea886f755","target":"record","created_at":"2026-05-18T00:17:14Z","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":"e31dda396d5f31f31160e4823b4c20944fe4191c2e35b11e2a12a751fcba2478","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-30T03:09:59Z","title_canon_sha256":"4b4ecbac92c474f4d5898d2135838bbd43914419b4551fad79b88e2e6f744cad"},"schema_version":"1.0","source":{"id":"1804.11033","kind":"arxiv","version":1}},"canonical_sha256":"22e875d2a01565aff51c9a928f48fb5733f08fed9c0d5639714e6f965d6d261a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22e875d2a01565aff51c9a928f48fb5733f08fed9c0d5639714e6f965d6d261a","first_computed_at":"2026-05-18T00:17:14.834556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:14.834556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sOHohhSsuKZd0/IQxbXWi88izVjuac2tWFFJsvm9V1V0bfCREN4beynIorCsjlVxM4prRWYkqHASlztJxF0eBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:14.835953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.11033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d0aab431ae422f8caa5fedff950aca50f75a61acbb55447568113bea886f755","sha256:e12b6301603460b15b8beeae95697fe544a9851b81beac3e84f53f7d8c1b269b"],"state_sha256":"06588cf3ec547a602b95e5d7fcc05d74c4f40a59bd6c747df83af21d007f016f"}