{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:YU4AQN2VG64FZAYM442HKFUCCZ","short_pith_number":"pith:YU4AQN2V","schema_version":"1.0","canonical_sha256":"c53808375537b85c830ce7347516821664a4ec0079ed8b8fc7eaa6f92ef80ff4","source":{"kind":"arxiv","id":"math/0601486","version":1},"attestation_state":"computed","paper":{"title":"Geometric angle structures on triangulated surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ren Guo","submitted_at":"2006-01-20T03:59:44Z","abstract_excerpt":"In this paper we characterize a function defined on the set of edges of a triangulated surface such that there is a spherical angle structure having the function as the edge invariant (or Delaunay invariant).\n We also characterize a function such that there is a hyperbolic angle structure having the function as the edge invariant."},"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":"math/0601486","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-01-20T03:59:44Z","cross_cats_sorted":[],"title_canon_sha256":"388bb23c91f7fc1a0841fb369e8b2517eb4fc0d1168d0b430104c43f4d784f4c","abstract_canon_sha256":"f08206b96681bd9129a15dca7be3ac5fb6625a27b26c24f03f5499518ffb0e41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:22.818482Z","signature_b64":"xetVhXjfVqpo2UkcWm0DsUx3z2yghj36V556af5IP2dxalBUxyvCF8wZFGloV9FsnnRzfiyADeuT53K4WzclBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c53808375537b85c830ce7347516821664a4ec0079ed8b8fc7eaa6f92ef80ff4","last_reissued_at":"2026-05-18T01:05:22.818005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:22.818005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric angle structures on triangulated surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ren Guo","submitted_at":"2006-01-20T03:59:44Z","abstract_excerpt":"In this paper we characterize a function defined on the set of edges of a triangulated surface such that there is a spherical angle structure having the function as the edge invariant (or Delaunay invariant).\n We also characterize a function such that there is a hyperbolic angle structure having the function as the edge invariant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601486","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":"math/0601486","created_at":"2026-05-18T01:05:22.818076+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0601486v1","created_at":"2026-05-18T01:05:22.818076+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601486","created_at":"2026-05-18T01:05:22.818076+00:00"},{"alias_kind":"pith_short_12","alias_value":"YU4AQN2VG64F","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"YU4AQN2VG64FZAYM","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"YU4AQN2V","created_at":"2026-05-18T12:25:54.717736+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/YU4AQN2VG64FZAYM442HKFUCCZ","json":"https://pith.science/pith/YU4AQN2VG64FZAYM442HKFUCCZ.json","graph_json":"https://pith.science/api/pith-number/YU4AQN2VG64FZAYM442HKFUCCZ/graph.json","events_json":"https://pith.science/api/pith-number/YU4AQN2VG64FZAYM442HKFUCCZ/events.json","paper":"https://pith.science/paper/YU4AQN2V"},"agent_actions":{"view_html":"https://pith.science/pith/YU4AQN2VG64FZAYM442HKFUCCZ","download_json":"https://pith.science/pith/YU4AQN2VG64FZAYM442HKFUCCZ.json","view_paper":"https://pith.science/paper/YU4AQN2V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0601486&json=true","fetch_graph":"https://pith.science/api/pith-number/YU4AQN2VG64FZAYM442HKFUCCZ/graph.json","fetch_events":"https://pith.science/api/pith-number/YU4AQN2VG64FZAYM442HKFUCCZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YU4AQN2VG64FZAYM442HKFUCCZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YU4AQN2VG64FZAYM442HKFUCCZ/action/storage_attestation","attest_author":"https://pith.science/pith/YU4AQN2VG64FZAYM442HKFUCCZ/action/author_attestation","sign_citation":"https://pith.science/pith/YU4AQN2VG64FZAYM442HKFUCCZ/action/citation_signature","submit_replication":"https://pith.science/pith/YU4AQN2VG64FZAYM442HKFUCCZ/action/replication_record"}},"created_at":"2026-05-18T01:05:22.818076+00:00","updated_at":"2026-05-18T01:05:22.818076+00:00"}