{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V5Z4VGXFNIEWVDNIKQDPKIXG2J","short_pith_number":"pith:V5Z4VGXF","canonical_record":{"source":{"id":"1103.2905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-15T13:44:38Z","cross_cats_sorted":[],"title_canon_sha256":"a1eaf0a99bbee7cd5e82a61e8627f10d5f24e09eb5df82c4e61d1c16e485b712","abstract_canon_sha256":"9c2968c62c22db696afe3b580001163ecbfe2e4b712593ba91bcd254dd129958"},"schema_version":"1.0"},"canonical_sha256":"af73ca9ae56a096a8da85406f522e6d25ea4d827390d9deb001128eeb9a209c8","source":{"kind":"arxiv","id":"1103.2905","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2905","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2905v1","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2905","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"V5Z4VGXFNIEW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V5Z4VGXFNIEWVDNI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V5Z4VGXF","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V5Z4VGXFNIEWVDNIKQDPKIXG2J","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-15T13:44:38Z","cross_cats_sorted":[],"title_canon_sha256":"a1eaf0a99bbee7cd5e82a61e8627f10d5f24e09eb5df82c4e61d1c16e485b712","abstract_canon_sha256":"9c2968c62c22db696afe3b580001163ecbfe2e4b712593ba91bcd254dd129958"},"schema_version":"1.0"},"canonical_sha256":"af73ca9ae56a096a8da85406f522e6d25ea4d827390d9deb001128eeb9a209c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:19.061909Z","signature_b64":"YTREdWcvvLq1se+fXKg0pSxyp7XYaEtUbBje+b0iyGypo0/e3RP14okeFIlCNlebTCc89QXmHT5kV6oQrBFZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af73ca9ae56a096a8da85406f522e6d25ea4d827390d9deb001128eeb9a209c8","last_reissued_at":"2026-05-18T02:22:19.061222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:19.061222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2905","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSwA3J/2Qd4wONWZeAmr0sFaZ9TZc+5BKpNlt+ZqV0Y9LHW/eqs0geP1RTS25rHtQnOF1jnpN98iA4ODS3cPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:31:30.317420Z"},"content_sha256":"822336756a1599375596e858394ceb0a9d017a041a2b28f456cd05b5abb7b404","schema_version":"1.0","event_id":"sha256:822336756a1599375596e858394ceb0a9d017a041a2b28f456cd05b5abb7b404"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V5Z4VGXFNIEWVDNIKQDPKIXG2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the natural extension of a map with a Siegel or Cremer point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Cabrera, Tomoki Kawahira","submitted_at":"2011-03-15T13:44:38Z","abstract_excerpt":"In this note we show that the regular part of the natural extension (in the sense of Lyubich and Minsky) of quadratic map $f(z) = e^{2 \\pi i \\theta}z + z^2$ with irrational $\\theta$ of bounded type has only parabolic leaves except the invariant lift of the Siegel disk.\n  We also show that though the natural extension of a rational function with a Cremer fixed point has a continuum of irregular points, it can not supply enough singularity to apply the Gross star theorem to find hyperbolic leaves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2905","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqwW7/joIytjm+ScaZwM0iEBTy0ergydv4W6dc0YP/RlTNRVfRsBVvb2ZclWZuqi3txcWDsCR+uHoKU3IItpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:31:30.317759Z"},"content_sha256":"308e8ff3c98c293cedbbf409feb977357e8a02f6da359593bb91477033c7de9a","schema_version":"1.0","event_id":"sha256:308e8ff3c98c293cedbbf409feb977357e8a02f6da359593bb91477033c7de9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V5Z4VGXFNIEWVDNIKQDPKIXG2J/bundle.json","state_url":"https://pith.science/pith/V5Z4VGXFNIEWVDNIKQDPKIXG2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V5Z4VGXFNIEWVDNIKQDPKIXG2J/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T17:31:30Z","links":{"resolver":"https://pith.science/pith/V5Z4VGXFNIEWVDNIKQDPKIXG2J","bundle":"https://pith.science/pith/V5Z4VGXFNIEWVDNIKQDPKIXG2J/bundle.json","state":"https://pith.science/pith/V5Z4VGXFNIEWVDNIKQDPKIXG2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V5Z4VGXFNIEWVDNIKQDPKIXG2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V5Z4VGXFNIEWVDNIKQDPKIXG2J","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":"9c2968c62c22db696afe3b580001163ecbfe2e4b712593ba91bcd254dd129958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-15T13:44:38Z","title_canon_sha256":"a1eaf0a99bbee7cd5e82a61e8627f10d5f24e09eb5df82c4e61d1c16e485b712"},"schema_version":"1.0","source":{"id":"1103.2905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2905","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2905v1","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2905","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"V5Z4VGXFNIEW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V5Z4VGXFNIEWVDNI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V5Z4VGXF","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:308e8ff3c98c293cedbbf409feb977357e8a02f6da359593bb91477033c7de9a","target":"graph","created_at":"2026-05-18T02:22:19Z","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":"In this note we show that the regular part of the natural extension (in the sense of Lyubich and Minsky) of quadratic map $f(z) = e^{2 \\pi i \\theta}z + z^2$ with irrational $\\theta$ of bounded type has only parabolic leaves except the invariant lift of the Siegel disk.\n  We also show that though the natural extension of a rational function with a Cremer fixed point has a continuum of irregular points, it can not supply enough singularity to apply the Gross star theorem to find hyperbolic leaves.","authors_text":"Carlos Cabrera, Tomoki Kawahira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-15T13:44:38Z","title":"On the natural extension of a map with a Siegel or Cremer point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2905","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":"sha256:822336756a1599375596e858394ceb0a9d017a041a2b28f456cd05b5abb7b404","target":"record","created_at":"2026-05-18T02:22:19Z","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":"9c2968c62c22db696afe3b580001163ecbfe2e4b712593ba91bcd254dd129958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-15T13:44:38Z","title_canon_sha256":"a1eaf0a99bbee7cd5e82a61e8627f10d5f24e09eb5df82c4e61d1c16e485b712"},"schema_version":"1.0","source":{"id":"1103.2905","kind":"arxiv","version":1}},"canonical_sha256":"af73ca9ae56a096a8da85406f522e6d25ea4d827390d9deb001128eeb9a209c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af73ca9ae56a096a8da85406f522e6d25ea4d827390d9deb001128eeb9a209c8","first_computed_at":"2026-05-18T02:22:19.061222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:19.061222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YTREdWcvvLq1se+fXKg0pSxyp7XYaEtUbBje+b0iyGypo0/e3RP14okeFIlCNlebTCc89QXmHT5kV6oQrBFZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:19.061909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:822336756a1599375596e858394ceb0a9d017a041a2b28f456cd05b5abb7b404","sha256:308e8ff3c98c293cedbbf409feb977357e8a02f6da359593bb91477033c7de9a"],"state_sha256":"84abfb6f48506482a525c6751acce1bb5011cf0aeaab4a809c91816fd34b68fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D1U3N+sKgKfgWrzRtsQKqNbW8Is7ZwZ6EAnizL6jQGPhhPQ38jWrtiI7mcLcK7Bg5zwiZ/DJ6+01qlwXdPg2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:31:30.319600Z","bundle_sha256":"e4be66ec70389694682b520ab3fff9db803fd4cff14cbdeb4c3a3b5485a0e5d3"}}