{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UCRIQN3L5UGP2WQMWLDMIET3AW","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":"cd456db4fac2ae41643454bc274ddda1aac69ab05c9d7de3f0bf4bff86717b9b","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.DS","submitted_at":"2007-01-19T15:25:14Z","title_canon_sha256":"92b8bcc1ca9045ed365c6b2c3b8b21e401bfa18016299839b36ff3d6e1c71e30"},"schema_version":"1.0","source":{"id":"math/0701541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701541","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701541v2","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701541","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"UCRIQN3L5UGP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UCRIQN3L5UGP2WQM","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UCRIQN3L","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:4b75605042c24b0c1f42c2a735442f3631c785e517b5461d38e949128f5b6abb","target":"graph","created_at":"2026-05-18T04:41:06Z","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 description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain degree of regularity this description is complete in the sense that we identify all values with non-empty level sets and determine their Hausdorff dimension. This result is also partially new for the finite alphabet case.","authors_text":"Marc Kesseb\\\"ohmer, Mariusz Urbanski","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2007-01-19T15:25:14Z","title":"Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701541","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:b22a950540471b86af4f1625e9b83ceb1bca2c54b18ffb827d9ea2dc41af1084","target":"record","created_at":"2026-05-18T04:41:06Z","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":"cd456db4fac2ae41643454bc274ddda1aac69ab05c9d7de3f0bf4bff86717b9b","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.DS","submitted_at":"2007-01-19T15:25:14Z","title_canon_sha256":"92b8bcc1ca9045ed365c6b2c3b8b21e401bfa18016299839b36ff3d6e1c71e30"},"schema_version":"1.0","source":{"id":"math/0701541","kind":"arxiv","version":2}},"canonical_sha256":"a0a288376bed0cfd5a0cb2c6c4127b059f39840aee1c399f1336977dd60802ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0a288376bed0cfd5a0cb2c6c4127b059f39840aee1c399f1336977dd60802ce","first_computed_at":"2026-05-18T04:41:06.123032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:06.123032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3+2WgI6f43qSeXUpbO6WYDOp1YshjODYRmIJPlfiw69gesHijyOSWgB9i2K++yVKp76beNUixDslra9v6+J2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:06.123470Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b22a950540471b86af4f1625e9b83ceb1bca2c54b18ffb827d9ea2dc41af1084","sha256:4b75605042c24b0c1f42c2a735442f3631c785e517b5461d38e949128f5b6abb"],"state_sha256":"4187338ded931e16fa21a7461a461abadf4164056583294010703b3b2ba8aa2d"}