{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ASGMMGG7PBPPJWTEGHUGXBCXAU","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":"f9a7f953c7c5bc3515445d32cf7aba3b718d125ecbab098885296fed7a0d8fa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-04T20:18:32Z","title_canon_sha256":"31a2046018a870d30e1a556951648064c51a421308346cd68b54eb13fb59ade3"},"schema_version":"1.0","source":{"id":"1205.1067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1067","created_at":"2026-05-18T03:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1067v1","created_at":"2026-05-18T03:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1067","created_at":"2026-05-18T03:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"ASGMMGG7PBPP","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ASGMMGG7PBPPJWTE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ASGMMGG7","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:adcc7d3173774d21a3a8bdd7143ff00b1df3fc5dd2ac5597f3885b66492a3320","target":"graph","created_at":"2026-05-18T03:56:12Z","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 extend a factorization due to Krein to arbitrary analytic functions from the upper half-plane to itself. The factorization represents every such function as a product of fractional linear factors times a function which, generally, has fewer zeros and singularities than the original one. The result is used to construct functions with given zeros and poles on the real line.","authors_text":"Dan Timotin, Hari Bercovici","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-04T20:18:32Z","title":"Factorizations of analytic self-maps of the upper half-plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1067","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":"sha256:928ece1fe8a7145d1408b53c3edeee5e5066742942257ef58c02978992028588","target":"record","created_at":"2026-05-18T03:56:12Z","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":"f9a7f953c7c5bc3515445d32cf7aba3b718d125ecbab098885296fed7a0d8fa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-04T20:18:32Z","title_canon_sha256":"31a2046018a870d30e1a556951648064c51a421308346cd68b54eb13fb59ade3"},"schema_version":"1.0","source":{"id":"1205.1067","kind":"arxiv","version":1}},"canonical_sha256":"048cc618df785ef4da6431e86b8457052cccacd96c6ac29438bd228dbeb0c8bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"048cc618df785ef4da6431e86b8457052cccacd96c6ac29438bd228dbeb0c8bf","first_computed_at":"2026-05-18T03:56:12.222394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:12.222394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cARaDUqhn/6TSwrg3nLUT9lEcFFu6xFJPH6JcwcJ8mf5q/nr4CJSZCir3soqDnLOM4hZ3bq2hcKm0AeGBfhDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:12.222997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:928ece1fe8a7145d1408b53c3edeee5e5066742942257ef58c02978992028588","sha256:adcc7d3173774d21a3a8bdd7143ff00b1df3fc5dd2ac5597f3885b66492a3320"],"state_sha256":"9ea38d85f695a9fa75f41b27abf721ca54882a093c1390cee7e7e9f46cd08542"}