{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HZRX2R5KCUQSSHZDYR3GMUSSKM","short_pith_number":"pith:HZRX2R5K","canonical_record":{"source":{"id":"1907.02870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-05T14:49:13Z","cross_cats_sorted":[],"title_canon_sha256":"d0212ec47a6656b8db5effa93fb83d0dbb04ad0c3c885ddf042a5fa15b8d26e1","abstract_canon_sha256":"ac6f7812a1d65b4434c2c22c1d583eac7ea2ad08288a3959d88784e45ee6d6c3"},"schema_version":"1.0"},"canonical_sha256":"3e637d47aa1521291f23c476665252533d01e611fbf07595f860309af90514d6","source":{"kind":"arxiv","id":"1907.02870","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02870","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02870v2","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02870","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"pith_short_12","alias_value":"HZRX2R5KCUQS","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"pith_short_16","alias_value":"HZRX2R5KCUQSSHZD","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"pith_short_8","alias_value":"HZRX2R5K","created_at":"2026-07-05T04:15:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HZRX2R5KCUQSSHZDYR3GMUSSKM","target":"record","payload":{"canonical_record":{"source":{"id":"1907.02870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-05T14:49:13Z","cross_cats_sorted":[],"title_canon_sha256":"d0212ec47a6656b8db5effa93fb83d0dbb04ad0c3c885ddf042a5fa15b8d26e1","abstract_canon_sha256":"ac6f7812a1d65b4434c2c22c1d583eac7ea2ad08288a3959d88784e45ee6d6c3"},"schema_version":"1.0"},"canonical_sha256":"3e637d47aa1521291f23c476665252533d01e611fbf07595f860309af90514d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:15:26.477911Z","signature_b64":"FeEzk81PvB/4PqYx9Na7KBVMgbdYnxII7efw0hmcXX76BstrklCnhVz/8ZK09cPDrI/WH/eRvwwNaoJ15EtLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e637d47aa1521291f23c476665252533d01e611fbf07595f860309af90514d6","last_reissued_at":"2026-07-05T04:15:26.477453Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:15:26.477453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.02870","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:15:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w44nQmdvCGsd8kIns1XIDP+v8C5qaVQZJiK8ar02pizte9IsYxjPrMQuLA6lGbEOrVy3QJ148j0j/oiXfrKWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:48:29.299456Z"},"content_sha256":"bdfa70c9710afc79dee9f14fdc4c6f143c4fbf3c8c91bf384a068058ec96bce5","schema_version":"1.0","event_id":"sha256:bdfa70c9710afc79dee9f14fdc4c6f143c4fbf3c8c91bf384a068058ec96bce5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HZRX2R5KCUQSSHZDYR3GMUSSKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant graphs of rational maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guizhen Cui, Jinsong Zeng, Yan Gao","submitted_at":"2019-07-05T14:49:13Z","abstract_excerpt":"Let $f$ be a postcritically finite rational map. We prove that, as $n$ large enough, there exists an $f^n$-invariant (finite connected) graph on $\\widehat{\\mathbb{C}}$ such that it contains the postcritical set of $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02870","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.02870/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:15:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5qA36Mh33Zvs7NgzZwqko0w0pLxoEUXg+Y9I7cs/V8s6a/0LZSOXJ0h7f8Bv5HsbBhTZl60qyjE6AIl5HAxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:48:29.300013Z"},"content_sha256":"0f3d028cd590f004a98d9d51101fa32a4f74c40f343ed3c44d9b48068586894f","schema_version":"1.0","event_id":"sha256:0f3d028cd590f004a98d9d51101fa32a4f74c40f343ed3c44d9b48068586894f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HZRX2R5KCUQSSHZDYR3GMUSSKM/bundle.json","state_url":"https://pith.science/pith/HZRX2R5KCUQSSHZDYR3GMUSSKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HZRX2R5KCUQSSHZDYR3GMUSSKM/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":"2026-08-17T01:48:29Z","links":{"resolver":"https://pith.science/pith/HZRX2R5KCUQSSHZDYR3GMUSSKM","bundle":"https://pith.science/pith/HZRX2R5KCUQSSHZDYR3GMUSSKM/bundle.json","state":"https://pith.science/pith/HZRX2R5KCUQSSHZDYR3GMUSSKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HZRX2R5KCUQSSHZDYR3GMUSSKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HZRX2R5KCUQSSHZDYR3GMUSSKM","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":"ac6f7812a1d65b4434c2c22c1d583eac7ea2ad08288a3959d88784e45ee6d6c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-05T14:49:13Z","title_canon_sha256":"d0212ec47a6656b8db5effa93fb83d0dbb04ad0c3c885ddf042a5fa15b8d26e1"},"schema_version":"1.0","source":{"id":"1907.02870","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02870","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02870v2","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02870","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"pith_short_12","alias_value":"HZRX2R5KCUQS","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"pith_short_16","alias_value":"HZRX2R5KCUQSSHZD","created_at":"2026-07-05T04:15:26Z"},{"alias_kind":"pith_short_8","alias_value":"HZRX2R5K","created_at":"2026-07-05T04:15:26Z"}],"graph_snapshots":[{"event_id":"sha256:0f3d028cd590f004a98d9d51101fa32a4f74c40f343ed3c44d9b48068586894f","target":"graph","created_at":"2026-07-05T04:15:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.02870/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f$ be a postcritically finite rational map. We prove that, as $n$ large enough, there exists an $f^n$-invariant (finite connected) graph on $\\widehat{\\mathbb{C}}$ such that it contains the postcritical set of $f$.","authors_text":"Guizhen Cui, Jinsong Zeng, Yan Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-05T14:49:13Z","title":"Invariant graphs of rational maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02870","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:bdfa70c9710afc79dee9f14fdc4c6f143c4fbf3c8c91bf384a068058ec96bce5","target":"record","created_at":"2026-07-05T04:15:26Z","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":"ac6f7812a1d65b4434c2c22c1d583eac7ea2ad08288a3959d88784e45ee6d6c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-05T14:49:13Z","title_canon_sha256":"d0212ec47a6656b8db5effa93fb83d0dbb04ad0c3c885ddf042a5fa15b8d26e1"},"schema_version":"1.0","source":{"id":"1907.02870","kind":"arxiv","version":2}},"canonical_sha256":"3e637d47aa1521291f23c476665252533d01e611fbf07595f860309af90514d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e637d47aa1521291f23c476665252533d01e611fbf07595f860309af90514d6","first_computed_at":"2026-07-05T04:15:26.477453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:15:26.477453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FeEzk81PvB/4PqYx9Na7KBVMgbdYnxII7efw0hmcXX76BstrklCnhVz/8ZK09cPDrI/WH/eRvwwNaoJ15EtLCA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:15:26.477911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02870","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdfa70c9710afc79dee9f14fdc4c6f143c4fbf3c8c91bf384a068058ec96bce5","sha256:0f3d028cd590f004a98d9d51101fa32a4f74c40f343ed3c44d9b48068586894f"],"state_sha256":"d10494673d8bf2b0a104dea5351041164b0785f1acc16cdca55184cb37d5e0d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwhyI1EaBWDZ/nahyCN/daCkDwo1Eq/W0P2kDmXsUvyMhEOfyrUDf1mCkisM99vYvphBOiunBUFvu40k3mXHCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T01:48:29.305663Z","bundle_sha256":"1b88458149779ba18ef8698dc7612ac40b02f9bf30f4698a7db79acd4fe69eab"}}