{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XEEGKJART6T3MDZN7DFGSPMBH7","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":"9e8f0ccc7b7bbf8f3f807793cb08d5b37697fdade79fa7b6079c0b8d7f1f358b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-09T11:51:10Z","title_canon_sha256":"3d92484c8af8666682cafcae8cf346d0fa96b294dc3397272e8256d85bc4378c"},"schema_version":"1.0","source":{"id":"1103.1764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1764","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1764v1","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1764","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"XEEGKJART6T3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XEEGKJART6T3MDZN","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XEEGKJAR","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:26e6476a775d4ed49d9d81b04e806cb52b4c8b3194120c9ed1304afb71e02d90","target":"graph","created_at":"2026-05-18T01:09:25Z","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 proved in another paper that every connected graph can be realized as the cut locus of some point on some riemannian surface. Here we give upper bounds on the number of such realizations.","authors_text":"Costin V\\^ilcu, Jin-ichi Itoh","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-09T11:51:10Z","title":"On the number of cut locus structures on graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1764","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:ee77d2ff6210e8a058ec2048dfb5d935ecb2263cfbcebdc19c2c65d5b387ab02","target":"record","created_at":"2026-05-18T01:09:25Z","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":"9e8f0ccc7b7bbf8f3f807793cb08d5b37697fdade79fa7b6079c0b8d7f1f358b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-09T11:51:10Z","title_canon_sha256":"3d92484c8af8666682cafcae8cf346d0fa96b294dc3397272e8256d85bc4378c"},"schema_version":"1.0","source":{"id":"1103.1764","kind":"arxiv","version":1}},"canonical_sha256":"b9086524119fa7b60f2df8ca693d813ff41eda38b37fb5b67241ebeb419f6798","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9086524119fa7b60f2df8ca693d813ff41eda38b37fb5b67241ebeb419f6798","first_computed_at":"2026-05-18T01:09:25.662559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:25.662559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tqgb7nZgCaLkkH/F2S5KSOWwNtWuQJ7dAp6E9z9nO+9IuU91fRLOrJco7ELA5RfaHNksA21d9RUsTHK+q57aAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:25.663068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee77d2ff6210e8a058ec2048dfb5d935ecb2263cfbcebdc19c2c65d5b387ab02","sha256:26e6476a775d4ed49d9d81b04e806cb52b4c8b3194120c9ed1304afb71e02d90"],"state_sha256":"da0e2bb970800f9cb965d2f767325751074bcb0d33886d631ae6850995ffff0c"}