{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ILJ6MXICFF3L77PDRW57S2CE4Z","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":"07ffa35a05ff6d6eabf3910481d61dea1908e9dbfc257e4e740ffecef4dfe895","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-28T16:39:26Z","title_canon_sha256":"e6e2ccac38610ec4415201a50f861cdf5735fcc82d6ca0b4faf3045b36a9864b"},"schema_version":"1.0","source":{"id":"1302.7249","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7249","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7249v7","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7249","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"ILJ6MXICFF3L","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ILJ6MXICFF3L77PD","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ILJ6MXIC","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:de90350106e462aeb61c7274569506bd90fc8435cfcf31aa0e73e5af2a83e45b","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 dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroup case. We also investigate the dynamics of conjugate semigroups, Abelian transcendental semigroups and wandering and Baker domains of transcendental semigroups.","authors_text":"Dinesh Kumar, Sanjay Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-28T16:39:26Z","title":"The dynamics of semigroups of transcendental entire functions I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7249","kind":"arxiv","version":7},"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":"sha256:13d260a5c98708e5848fb55661805611f89c367607f4caf764965e92822f0945","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":"07ffa35a05ff6d6eabf3910481d61dea1908e9dbfc257e4e740ffecef4dfe895","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-28T16:39:26Z","title_canon_sha256":"e6e2ccac38610ec4415201a50f861cdf5735fcc82d6ca0b4faf3045b36a9864b"},"schema_version":"1.0","source":{"id":"1302.7249","kind":"arxiv","version":7}},"canonical_sha256":"42d3e65d022976bffde38dbbf96844e6682316bd644993d0f896ea6f62db8a3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42d3e65d022976bffde38dbbf96844e6682316bd644993d0f896ea6f62db8a3e","first_computed_at":"2026-05-18T02:51:42.457687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.457687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jy0HgH9tPr/Iclqb3mjRwcVNTMWYDab6Pp7BDATBvPNYiDmHYk5zo/RaG9ktB9JVWIQxDha2huSWHj1VWEq0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.458156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.7249","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13d260a5c98708e5848fb55661805611f89c367607f4caf764965e92822f0945","sha256:de90350106e462aeb61c7274569506bd90fc8435cfcf31aa0e73e5af2a83e45b"],"state_sha256":"389c443fc9e24390c2d5e422b7bf923b7ce659021775c004477bc3ffa9f6a8e5"}