{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ADJ26DA2D6WORZ4JMBV5YFSVJI","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":"77d9bfb07ad087b4d856fc0bfe272d683aab80e7208b28aa5971fd87389ffb0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-22T17:13:07Z","title_canon_sha256":"839e92d39d7dd0aecaa4a396ae80a146423516e7d7e4b3a69bc7cb7110ae6d3e"},"schema_version":"1.0","source":{"id":"1307.5785","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5785","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5785v2","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5785","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"ADJ26DA2D6WO","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ADJ26DA2D6WORZ4J","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ADJ26DA2","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:5a86163940bd545d41e717d308dc66b2d8ed070d582f09592e6af3aa16efb204","target":"graph","created_at":"2026-05-18T02:51:42Z","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 consider the dynamical properties of transcendental entire functions and their compositions. We give several conditions under which Fatou set of a transcendental entire function $f$ coincide with that of $f\\circ g,$ where $g$ is another transcendental entire function. We also prove some result giving relationship between singular values of transcendental entire functions and their compositions.","authors_text":"Dinesh Kumar, Sanjay Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-22T17:13:07Z","title":"On dynamics of composite entire functions and singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5785","kind":"arxiv","version":2},"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":"sha256:5ecaba903edf5089b766a3d68767c5fdf36e2151e74f7b073fbef603de834822","target":"record","created_at":"2026-05-18T02:51:42Z","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":"77d9bfb07ad087b4d856fc0bfe272d683aab80e7208b28aa5971fd87389ffb0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-22T17:13:07Z","title_canon_sha256":"839e92d39d7dd0aecaa4a396ae80a146423516e7d7e4b3a69bc7cb7110ae6d3e"},"schema_version":"1.0","source":{"id":"1307.5785","kind":"arxiv","version":2}},"canonical_sha256":"00d3af0c1a1face8e789606bdc16554a389ab90830979c1be0a27787e6ced45e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00d3af0c1a1face8e789606bdc16554a389ab90830979c1be0a27787e6ced45e","first_computed_at":"2026-05-18T02:51:42.231967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.231967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BvzAvGtaQAhavefQwm+A6gI+J39IOMotiKhv6RnTIRyAvlegwZ8eKX+E52FrSh83F6PUR1P82k1Dc0iQEMHrAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.232503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5785","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ecaba903edf5089b766a3d68767c5fdf36e2151e74f7b073fbef603de834822","sha256:5a86163940bd545d41e717d308dc66b2d8ed070d582f09592e6af3aa16efb204"],"state_sha256":"8bd9a3c21ad0c33778ef4181fd21a116d9805b464a57950e016de87d1e6305ef"}