{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:U54BYD63JJRV2KCIPGOGJNOTZB","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":"91e07abc32b8684a4280c9ece702430182cf6d1e6c45ad27a75b2090699be395","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-31T17:34:06Z","title_canon_sha256":"a63d30ecfc676f55e47cfd93bee0af928fba28564c4e139265681ac03498e639"},"schema_version":"1.0","source":{"id":"1003.6104","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.6104","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1003.6104v2","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.6104","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"U54BYD63JJRV","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U54BYD63JJRV2KCI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U54BYD63","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:c993bf61c9be3014ee7181895628d73217f4d0c6b9b4ec5c460817f6643981af","target":"graph","created_at":"2026-05-18T02:58:02Z","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 give formulas for the numbers of type II and type IV hyperbolic components in the space of quadratic rational maps, for all fixed periods of attractive cycles.","authors_text":"Jan Kiwi, Mary Rees","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-31T17:34:06Z","title":"Counting Hyperbolic Components"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.6104","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":"sha256:74049c23723df6fbeaa87354b6e6218d10c9ea0004abd999898264c4aef28fd4","target":"record","created_at":"2026-05-18T02:58:02Z","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":"91e07abc32b8684a4280c9ece702430182cf6d1e6c45ad27a75b2090699be395","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-31T17:34:06Z","title_canon_sha256":"a63d30ecfc676f55e47cfd93bee0af928fba28564c4e139265681ac03498e639"},"schema_version":"1.0","source":{"id":"1003.6104","kind":"arxiv","version":2}},"canonical_sha256":"a7781c0fdb4a635d2848799c64b5d3c84ad1506a18cb824a4428260794e2a007","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7781c0fdb4a635d2848799c64b5d3c84ad1506a18cb824a4428260794e2a007","first_computed_at":"2026-05-18T02:58:02.302017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:02.302017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TeOVODZkRl9knTYGeUVhzjeEg/iDW/mkeGKHOnvKJ5Da4JhAPqzAPMVtGfd3+CChXDqjGvan6ILkiEIwmucNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:02.302516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.6104","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74049c23723df6fbeaa87354b6e6218d10c9ea0004abd999898264c4aef28fd4","sha256:c993bf61c9be3014ee7181895628d73217f4d0c6b9b4ec5c460817f6643981af"],"state_sha256":"a0ef23b500042e340271c0479834225f3ab4b64e0ef618501d1c8d16a1a50b33"}