{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TFJQ2KN5HP2AWFYN2744YPHZO4","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":"086e0217aaa74ecef93fe46aeafe2552fbbe51e43ad15d12c9b5fab9aef5585a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-23T06:16:33Z","title_canon_sha256":"bf9d69985c89836fdd19b91a8c3b241b03435c94d91c02c7e9cc2a574ffc6b47"},"schema_version":"1.0","source":{"id":"0909.4130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.4130","created_at":"2026-05-18T04:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"0909.4130v1","created_at":"2026-05-18T04:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4130","created_at":"2026-05-18T04:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"TFJQ2KN5HP2A","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TFJQ2KN5HP2AWFYN","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TFJQ2KN5","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:9342b48e77e9fb8cfa22f6e9002eefa8de29d15557a7e32b5fad3904dcc1c5c3","target":"graph","created_at":"2026-05-18T04:14:29Z","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 paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on invariant subsets, by means of graph theoretic properties.","authors_text":"Cesar E. Silva, Hansheng Diao","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-23T06:16:33Z","title":"Digraph Representations Of Rational Functions Over $p$-adic Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4130","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":"sha256:57ab7e4dddb3693ca1b091db72f7be31da92c0d0fdd7043bdb82826a4b68620a","target":"record","created_at":"2026-05-18T04:14:29Z","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":"086e0217aaa74ecef93fe46aeafe2552fbbe51e43ad15d12c9b5fab9aef5585a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-23T06:16:33Z","title_canon_sha256":"bf9d69985c89836fdd19b91a8c3b241b03435c94d91c02c7e9cc2a574ffc6b47"},"schema_version":"1.0","source":{"id":"0909.4130","kind":"arxiv","version":1}},"canonical_sha256":"99530d29bd3bf40b170dd7f9cc3cf977169522e5078053763c8ef71088736d24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99530d29bd3bf40b170dd7f9cc3cf977169522e5078053763c8ef71088736d24","first_computed_at":"2026-05-18T04:14:29.680802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:29.680802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"36sfp24EzHnpLtLtaJQIrCSd8jbrbYi8msFpsazpKS6TwPW/473XrQOOgnGMdyfDGqQpB9bIfkhIN5UuW3i/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:29.681285Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.4130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57ab7e4dddb3693ca1b091db72f7be31da92c0d0fdd7043bdb82826a4b68620a","sha256:9342b48e77e9fb8cfa22f6e9002eefa8de29d15557a7e32b5fad3904dcc1c5c3"],"state_sha256":"84e61bb792a99ce0acf1ee8212797a71215e331273aaef51a4c9eae6bd04cfd9"}