{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7WPP2KCMRTQJTWGVVX3326NV7Z","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":"d896c69789311cb9b6d64437b5851c732e3f59a27f1e88167cd7933d9612a9f9","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-08-10T12:17:14Z","title_canon_sha256":"3809dbc3cbd78fd4343f6de49080beb516d720214c0c55ddc30f583cf5057ad6"},"schema_version":"1.0","source":{"id":"0908.1307","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1307","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1307v3","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1307","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"pith_short_12","alias_value":"7WPP2KCMRTQJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7WPP2KCMRTQJTWGV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7WPP2KCM","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:edb82b02308e4e7f27f99f5f74fbacb45207aae48f18c6e6be8898d8564ed6c7","target":"graph","created_at":"2026-05-18T03:55:22Z","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":"We give an effective estimate for the totally ramified value number of the hyperbolic Gauss maps of complete flat fronts in the hyperbolic three-space. As a corollary, we give the upper bound of the number of exceptional values of them for some topological cases. Moreover, we obtain some new examples for this class.","authors_text":"Yu Kawakami","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-08-10T12:17:14Z","title":"Value distribution of the hyperbolic Gauss maps for flat fronts in hyperbolic three-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1307","kind":"arxiv","version":3},"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:ca0d10eed1bee34972a71d0b50882ff37d96c61f7db43c9a185f3dbb8363a9f2","target":"record","created_at":"2026-05-18T03:55:22Z","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":"d896c69789311cb9b6d64437b5851c732e3f59a27f1e88167cd7933d9612a9f9","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-08-10T12:17:14Z","title_canon_sha256":"3809dbc3cbd78fd4343f6de49080beb516d720214c0c55ddc30f583cf5057ad6"},"schema_version":"1.0","source":{"id":"0908.1307","kind":"arxiv","version":3}},"canonical_sha256":"fd9efd284c8ce099d8d5adf7bd79b5fe545e11964c0cce2e95156095b74f5376","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd9efd284c8ce099d8d5adf7bd79b5fe545e11964c0cce2e95156095b74f5376","first_computed_at":"2026-05-18T03:55:22.160713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:22.160713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9yQs3VPGhdLBYs3qd11NjWhYlfEjtQrxvotsAbvfD9gswl7hQbqzn1IOlUKuT5bCdjinnVnFr6Ae8DbT9FF5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:22.161462Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1307","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca0d10eed1bee34972a71d0b50882ff37d96c61f7db43c9a185f3dbb8363a9f2","sha256:edb82b02308e4e7f27f99f5f74fbacb45207aae48f18c6e6be8898d8564ed6c7"],"state_sha256":"10b6177c555b3af303f1b045dfe06508b280afc386f47fd10e71be4dde3b4c4e"}