{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:GKMUMVJLVDWBORT42MLIKNXE6G","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":"63930bb466455c894c050259728c748c21ad9490588b04924e657ce63f7c08d6","cross_cats_sorted":["math.SP"],"license":"","primary_cat":"math.DS","submitted_at":"2005-01-06T00:58:02Z","title_canon_sha256":"45a4950615e69f11e5f7810a6dc51f2e8a7ad92084d9b61cfe79b6672872f986"},"schema_version":"1.0","source":{"id":"math/0501077","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501077","created_at":"2026-05-18T01:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501077v3","created_at":"2026-05-18T01:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501077","created_at":"2026-05-18T01:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"GKMUMVJLVDWB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GKMUMVJLVDWBORT4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GKMUMVJL","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:59450c4df9e7c0789d3929b62406794abb64982c18ec65b702267efa371c053f","target":"graph","created_at":"2026-05-18T01:38:26Z","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"},"paper":{"abstract_excerpt":"We introduce an harmonic analysis for iterated function systems (IFS) (X, mu) which is based on a Markov process on certain paths. The probabilities are determined by a weight function W on X. From W we define a transition operator R_W acting on functions on X, and a corresponding class of R_W-harmonic functions. The properties of these functions determine the spectral theory of L^2(mu). For affine IFSs we establish orthogonal bases in L^2(mu). These bases are generated by paths with infinite repetition of finite words. We use this in the last section to analyze tiles in R^d.","authors_text":"Dorin Ervin Dutkay, Palle E.T. Jorgensen","cross_cats":["math.SP"],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2005-01-06T00:58:02Z","title":"Iterated function systems, Ruelle operators, and invariant projective measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501077","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":"sha256:205f4da1a8b89da51accf7d03aa8649146518a6966594f248f489ab8598c6a95","target":"record","created_at":"2026-05-18T01:38:26Z","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":"63930bb466455c894c050259728c748c21ad9490588b04924e657ce63f7c08d6","cross_cats_sorted":["math.SP"],"license":"","primary_cat":"math.DS","submitted_at":"2005-01-06T00:58:02Z","title_canon_sha256":"45a4950615e69f11e5f7810a6dc51f2e8a7ad92084d9b61cfe79b6672872f986"},"schema_version":"1.0","source":{"id":"math/0501077","kind":"arxiv","version":3}},"canonical_sha256":"329946552ba8ec17467cd3168536e4f186cffa2338bce464a4f4bacbf35d9ee2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"329946552ba8ec17467cd3168536e4f186cffa2338bce464a4f4bacbf35d9ee2","first_computed_at":"2026-05-18T01:38:26.984483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:26.984483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bBzmwBvBlhQv8O3VxtAUssEVLTdBFEAHOygYf4YXI36F4yLqhS8T0iMRaQtFSRJJGNyz6MaxaJDzyIrEegUuAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:26.985053Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501077","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:205f4da1a8b89da51accf7d03aa8649146518a6966594f248f489ab8598c6a95","sha256:59450c4df9e7c0789d3929b62406794abb64982c18ec65b702267efa371c053f"],"state_sha256":"505374f254501af5da0605ba1bcb5e248d6ee8459883acbaf17abc856594bece"}