{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6HPR3PFZY2MM42N2J6MUMSTLZZ","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":"9ff571316fc9018493fec88c5af0fd6c17dae01a8dad849d1c97a552d6e88952","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-07-23T10:09:25Z","title_canon_sha256":"984c9cbeeb7e9fc7f30eada921b143d39b43191bf0e05743236c665a692344ce"},"schema_version":"1.0","source":{"id":"1407.6155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6155","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6155v1","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6155","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"6HPR3PFZY2MM","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6HPR3PFZY2MM42N2","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6HPR3PFZ","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:a988d973fbbc6df55be4031762a4e0ed98d81e944d63aab196251d561164a334","target":"graph","created_at":"2026-05-18T02:46:58Z","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 introduce and study $\\alpha$-embedded sets and apply them to generalize the Kuratowski Extension Theorem.","authors_text":"Olena Karlova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-07-23T10:09:25Z","title":"On $\\alpha$-embedded sets and extension of mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6155","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:e32e17d15fa149118d40b15c5ee2e79bdc0c5e1b89365a1838c219ca9d309ff3","target":"record","created_at":"2026-05-18T02:46:58Z","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":"9ff571316fc9018493fec88c5af0fd6c17dae01a8dad849d1c97a552d6e88952","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-07-23T10:09:25Z","title_canon_sha256":"984c9cbeeb7e9fc7f30eada921b143d39b43191bf0e05743236c665a692344ce"},"schema_version":"1.0","source":{"id":"1407.6155","kind":"arxiv","version":1}},"canonical_sha256":"f1df1dbcb9c698ce69ba4f99464a6bce5941dac53f9b4272cabe3f3e1c77502f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1df1dbcb9c698ce69ba4f99464a6bce5941dac53f9b4272cabe3f3e1c77502f","first_computed_at":"2026-05-18T02:46:58.829980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:58.829980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"18zrXAXGwq+lhUGIjBbMX7cMr0Ed80lQ9HRDTaUhxq0SLFQNNc3B3GT/HT/tJaGY4iL4cOfahq/oZNWYr6p5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:58.830636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e32e17d15fa149118d40b15c5ee2e79bdc0c5e1b89365a1838c219ca9d309ff3","sha256:a988d973fbbc6df55be4031762a4e0ed98d81e944d63aab196251d561164a334"],"state_sha256":"eb2376220e5af85f868fff8694d9854680377671b2df9f41d884296c42456e41"}