{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KJQLV663PYTKQZSAXV32Z7RVVI","short_pith_number":"pith:KJQLV663","canonical_record":{"source":{"id":"1112.4780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-20T17:32:00Z","cross_cats_sorted":[],"title_canon_sha256":"9d259a0c15650586d74f52fcdc88d81b3c0e18283873c611d79af09b17a973a8","abstract_canon_sha256":"f6cd47a8851631c13ae0a773e827be8220a672a069bfae6eadda3e251bc51a4b"},"schema_version":"1.0"},"canonical_sha256":"5260bafbdb7e26a86640bd77acfe35aa06235564868a12163a1b515134a9e4de","source":{"kind":"arxiv","id":"1112.4780","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4780","created_at":"2026-05-18T04:05:58Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4780v1","created_at":"2026-05-18T04:05:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4780","created_at":"2026-05-18T04:05:58Z"},{"alias_kind":"pith_short_12","alias_value":"KJQLV663PYTK","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KJQLV663PYTKQZSA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KJQLV663","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KJQLV663PYTKQZSAXV32Z7RVVI","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-20T17:32:00Z","cross_cats_sorted":[],"title_canon_sha256":"9d259a0c15650586d74f52fcdc88d81b3c0e18283873c611d79af09b17a973a8","abstract_canon_sha256":"f6cd47a8851631c13ae0a773e827be8220a672a069bfae6eadda3e251bc51a4b"},"schema_version":"1.0"},"canonical_sha256":"5260bafbdb7e26a86640bd77acfe35aa06235564868a12163a1b515134a9e4de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:58.075872Z","signature_b64":"z2NHOzRWciHJM9N9gwJ4KhzX0hq6TvsFCQI1WfGHdQMFR7jaiRGbSVAICe7lfnea0K8OvXQL8YAAeZI4KBPyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5260bafbdb7e26a86640bd77acfe35aa06235564868a12163a1b515134a9e4de","last_reissued_at":"2026-05-18T04:05:58.075251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:58.075251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4780","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":"2026-05-18T04:05:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D4sNKpiuLkdJ+FI9DcyPEsL3usPwZ5tZInE2aNZ6wqy3i+x7gvndSctJ1iwwnSIqUf4OwwwF1AEQQjQr9p6FBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:32:33.269944Z"},"content_sha256":"bc64a92a2961adf37f7ba0e98dbdb0b2ae324e4d1ceeddc5dd4b36f950ee137f","schema_version":"1.0","event_id":"sha256:bc64a92a2961adf37f7ba0e98dbdb0b2ae324e4d1ceeddc5dd4b36f950ee137f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KJQLV663PYTKQZSAXV32Z7RVVI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matings with laminations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dzmitry Dudko","submitted_at":"2011-12-20T17:32:00Z","abstract_excerpt":"We give a topological description of the space of quadratic rational maps with superattractive two-cycles: its \"non-escape locus\" M2 (the analog of the Mandelbrot set M) is locally connected, it is the continuous image of M under a canonical map, and it can be described as M (minus the 1/2-limb), mated with the lamination of the basilica. The latter statement is a refined version of a conjecture of Ben Wittner, which in its original version requires local connectivity of M to even be stated. Our methods of mating with a lamination also apply to dynamical matings of certain non-locally connecte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4780","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":"2026-05-18T04:05:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j4VusaNzfIDmbhQ7uwwK3J6uHKd47CdYSrp4mfmS7EQLoJEorOoqqpaXXU1W92wU3DaxzEyyaNfjguP3S7e7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:32:33.270553Z"},"content_sha256":"8529608476b2659fb0e0049ed22b4d0317efae9e557c765c6f89478fcf691060","schema_version":"1.0","event_id":"sha256:8529608476b2659fb0e0049ed22b4d0317efae9e557c765c6f89478fcf691060"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJQLV663PYTKQZSAXV32Z7RVVI/bundle.json","state_url":"https://pith.science/pith/KJQLV663PYTKQZSAXV32Z7RVVI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJQLV663PYTKQZSAXV32Z7RVVI/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":"2026-06-02T14:32:33Z","links":{"resolver":"https://pith.science/pith/KJQLV663PYTKQZSAXV32Z7RVVI","bundle":"https://pith.science/pith/KJQLV663PYTKQZSAXV32Z7RVVI/bundle.json","state":"https://pith.science/pith/KJQLV663PYTKQZSAXV32Z7RVVI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJQLV663PYTKQZSAXV32Z7RVVI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KJQLV663PYTKQZSAXV32Z7RVVI","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":"f6cd47a8851631c13ae0a773e827be8220a672a069bfae6eadda3e251bc51a4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-20T17:32:00Z","title_canon_sha256":"9d259a0c15650586d74f52fcdc88d81b3c0e18283873c611d79af09b17a973a8"},"schema_version":"1.0","source":{"id":"1112.4780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4780","created_at":"2026-05-18T04:05:58Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4780v1","created_at":"2026-05-18T04:05:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4780","created_at":"2026-05-18T04:05:58Z"},{"alias_kind":"pith_short_12","alias_value":"KJQLV663PYTK","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KJQLV663PYTKQZSA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KJQLV663","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:8529608476b2659fb0e0049ed22b4d0317efae9e557c765c6f89478fcf691060","target":"graph","created_at":"2026-05-18T04:05:58Z","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 a topological description of the space of quadratic rational maps with superattractive two-cycles: its \"non-escape locus\" M2 (the analog of the Mandelbrot set M) is locally connected, it is the continuous image of M under a canonical map, and it can be described as M (minus the 1/2-limb), mated with the lamination of the basilica. The latter statement is a refined version of a conjecture of Ben Wittner, which in its original version requires local connectivity of M to even be stated. Our methods of mating with a lamination also apply to dynamical matings of certain non-locally connecte","authors_text":"Dzmitry Dudko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-20T17:32:00Z","title":"Matings with laminations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4780","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:bc64a92a2961adf37f7ba0e98dbdb0b2ae324e4d1ceeddc5dd4b36f950ee137f","target":"record","created_at":"2026-05-18T04:05:58Z","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":"f6cd47a8851631c13ae0a773e827be8220a672a069bfae6eadda3e251bc51a4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-20T17:32:00Z","title_canon_sha256":"9d259a0c15650586d74f52fcdc88d81b3c0e18283873c611d79af09b17a973a8"},"schema_version":"1.0","source":{"id":"1112.4780","kind":"arxiv","version":1}},"canonical_sha256":"5260bafbdb7e26a86640bd77acfe35aa06235564868a12163a1b515134a9e4de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5260bafbdb7e26a86640bd77acfe35aa06235564868a12163a1b515134a9e4de","first_computed_at":"2026-05-18T04:05:58.075251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:58.075251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z2NHOzRWciHJM9N9gwJ4KhzX0hq6TvsFCQI1WfGHdQMFR7jaiRGbSVAICe7lfnea0K8OvXQL8YAAeZI4KBPyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:58.075872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc64a92a2961adf37f7ba0e98dbdb0b2ae324e4d1ceeddc5dd4b36f950ee137f","sha256:8529608476b2659fb0e0049ed22b4d0317efae9e557c765c6f89478fcf691060"],"state_sha256":"434f24fa75da7a9604c42cb753563d6f8060aadb384a4f898dab075fe24c9882"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QRtpp3Hjeg0UmFSrfIAwZ9dRvub+BQUyaLvv1iUW9/0u0eSxIZmFklI1ygGsrPHRiimqwWedM+/5zyeF9E37BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:32:33.273591Z","bundle_sha256":"c0d146cb8860c154027d9a83a01c373490460cebc5c5495fd891de39c8c76008"}}