{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WZ2EZ3QPPRDOA4C3ONXIU4KKB7","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":"cca37c79e13541fff3c29898c6b0ab8f5c8c519c83f5b006cbddd5fe229ceb22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-09-02T08:29:13Z","title_canon_sha256":"c2ea8bc284742a0197cd5c6eacc996849558ac97b0bc40c4c81c84615d10400e"},"schema_version":"1.0","source":{"id":"0709.0092","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.0092","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"0709.0092v3","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.0092","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"WZ2EZ3QPPRDO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WZ2EZ3QPPRDOA4C3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WZ2EZ3QP","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:aad547fd1c6f281ee05e75e412e16804733d6a27fd7860ff2be1b483ba8159cf","target":"graph","created_at":"2026-05-18T02:58:12Z","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 make the first steps towards an understanding of the ergodic properties of a rational map defined over a complete algebraically closed non-archimedean field. For such a rational map R, we construct a natural invariant probability measure m_R which reprensents the asymptotic distribution of preimages of non-exceptional point. We show that this measure is exponentially mixing, and satisfies the central limit theorem. We prove some general bounds on the metric entropy of m_R, and on the topological entropy of R. We finally prove that rational maps with vanishing topological entropy have potent","authors_text":"Charles Favre, Juan Rivera-Letelier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-09-02T08:29:13Z","title":"Theorie ergodique des fractions rationnelles sur un corps ultrametrique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0092","kind":"arxiv","version":3},"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":"sha256:61e49e4d9662b72a7e8b5e93c95766ab0c1242c90dd8d96c1a9e8423030c65a4","target":"record","created_at":"2026-05-18T02:58:12Z","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":"cca37c79e13541fff3c29898c6b0ab8f5c8c519c83f5b006cbddd5fe229ceb22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-09-02T08:29:13Z","title_canon_sha256":"c2ea8bc284742a0197cd5c6eacc996849558ac97b0bc40c4c81c84615d10400e"},"schema_version":"1.0","source":{"id":"0709.0092","kind":"arxiv","version":3}},"canonical_sha256":"b6744cee0f7c46e0705b736e8a714a0fc1cdf2cbc51312e94b9aa2339a6981c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6744cee0f7c46e0705b736e8a714a0fc1cdf2cbc51312e94b9aa2339a6981c6","first_computed_at":"2026-05-18T02:58:12.373491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:12.373491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L4pO+oFJOfOfnt/rWpiBinJoVa+E9oOQ5jV3Uxftvaewt4SK9LXFo4YtFLL0lTAo1RqG6FUHckNrAk8YGiJyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:12.374332Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.0092","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61e49e4d9662b72a7e8b5e93c95766ab0c1242c90dd8d96c1a9e8423030c65a4","sha256:aad547fd1c6f281ee05e75e412e16804733d6a27fd7860ff2be1b483ba8159cf"],"state_sha256":"46bf4e6edbd95c635a5db544700543f997826f853f9fb79ccd21a17d2e2dbf95"}