{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KZLO6GH3Z3F3OHUU37CFTPBXIV","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":"0b5d23479aed6ca84f16b7d55b5049597cc95dffc03ef60b6e995319752dc465","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-05-13T02:58:03Z","title_canon_sha256":"bb44e1049501e889c61536d8a67d0519b5142449cf526fca7068c719ed6a0d78"},"schema_version":"1.0","source":{"id":"1005.2252","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2252","created_at":"2026-05-18T04:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2252v2","created_at":"2026-05-18T04:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2252","created_at":"2026-05-18T04:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"KZLO6GH3Z3F3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KZLO6GH3Z3F3OHUU","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KZLO6GH3","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:b2366a6d31ef0249faab8817ab573d5dc14ee8457c8a020b9be294dc3d8f7691","target":"graph","created_at":"2026-05-18T04:32:00Z","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 polynomial maps of the form f(z,w) = (p(z),q(z,w)) that extend as holomorphic maps of CP^2. Mattias Jonsson introduces in (Math. Ann., 1999) a notion of connectedness for such polynomial skew products that is analogous to connectivity for the Julia set of a polynomial map in one-variable. We prove the following dichotomy: if f is an Axiom-A polynomial skew product, and f is connected, then every Fatou component of f is homeomorphic to an open ball; otherwise, some Fatou component of f has infinitely generated first homology.","authors_text":"Roland K.W. Roeder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-05-13T02:58:03Z","title":"A dichotomy for Fatou components of polynomial skew products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2252","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:f8c6819292b9314124f81f2493c1b0198db7b72300d538eda2add7c8cce97fc4","target":"record","created_at":"2026-05-18T04:32:00Z","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":"0b5d23479aed6ca84f16b7d55b5049597cc95dffc03ef60b6e995319752dc465","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-05-13T02:58:03Z","title_canon_sha256":"bb44e1049501e889c61536d8a67d0519b5142449cf526fca7068c719ed6a0d78"},"schema_version":"1.0","source":{"id":"1005.2252","kind":"arxiv","version":2}},"canonical_sha256":"5656ef18fbcecbb71e94dfc459bc37454791b7332e092a9b464c543c7106bb5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5656ef18fbcecbb71e94dfc459bc37454791b7332e092a9b464c543c7106bb5b","first_computed_at":"2026-05-18T04:32:00.688992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:00.688992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NPMDyQSfGaIzPIfvoyXJy0WIhcr/j658Y+Fz9fhNYsPNC/LHJ0hqaruL+51nec6I7uIT7reHsmmgehxUHe7xCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:00.689454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2252","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8c6819292b9314124f81f2493c1b0198db7b72300d538eda2add7c8cce97fc4","sha256:b2366a6d31ef0249faab8817ab573d5dc14ee8457c8a020b9be294dc3d8f7691"],"state_sha256":"8898355ed647d180c59c87277413d026e191d91656bb9e30dcd644ccf0eb1b52"}