{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:EU4KBC4QIXPAKKC4BCW6KVSKOQ","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":"fc9961c49015483d0ba28e8f02424f20df572bc498ba7eeec4eeafae8bc0c5cf","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2007-11-08T19:25:12Z","title_canon_sha256":"05c5dee93405beb1f72b2deea9e4d3f7bac0b84cf46e1f869af46bf48a31890c"},"schema_version":"1.0","source":{"id":"0711.1182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.1182","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"0711.1182v1","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.1182","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"EU4KBC4QIXPA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"EU4KBC4QIXPAKKC4","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"EU4KBC4Q","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:2f494831da977bd3efb82d3b139e61f15723b7bd0a2786f52e6a33440f7a84b4","target":"graph","created_at":"2026-05-18T02:03:53Z","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 present the main concepts and results for Graph Directed Markov Systems that have a finitely irreducible incidence matrix. We then see how these results change when the incidence matrix is not assumed to be finitely irreducible.","authors_text":"Andrei E. Ghenciu, R. Daniel Mauldin","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2007-11-08T19:25:12Z","title":"Conformal Graph Directed Markov Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1182","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":"sha256:94e4d9d926772b9379e4b2a8eeb46d97d49c176c048117d199778af5caeaa0fb","target":"record","created_at":"2026-05-18T02:03:53Z","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":"fc9961c49015483d0ba28e8f02424f20df572bc498ba7eeec4eeafae8bc0c5cf","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2007-11-08T19:25:12Z","title_canon_sha256":"05c5dee93405beb1f72b2deea9e4d3f7bac0b84cf46e1f869af46bf48a31890c"},"schema_version":"1.0","source":{"id":"0711.1182","kind":"arxiv","version":1}},"canonical_sha256":"2538a08b9045de05285c08ade5564a741e58f968fa844a37a3703203c378a773","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2538a08b9045de05285c08ade5564a741e58f968fa844a37a3703203c378a773","first_computed_at":"2026-05-18T02:03:53.204995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:53.204995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NiiUPmQPgP/60rNUct0BKrn4aIvHHW2MB1d+MWPp5j3SyFo2ZxWYWoawVbi20I3wolSESaPlyd/6i43CY2MECg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:53.205625Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.1182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94e4d9d926772b9379e4b2a8eeb46d97d49c176c048117d199778af5caeaa0fb","sha256:2f494831da977bd3efb82d3b139e61f15723b7bd0a2786f52e6a33440f7a84b4"],"state_sha256":"d8f0367c073c96e677992055c850c6f84d60ec327053d51591a6e5b494feabfa"}