{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E2HFBKPZ4TGUSTHMC7ZIUQP2XJ","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":"1bbb897b750becb48d7e47c606fdfa96e8fdc3bbb284936977a0d00b5cf48071","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-16T12:28:46Z","title_canon_sha256":"d2977d62b62d54e548951f9b7a70d5a93884c7517423bcbee243f3a2fa1e6407"},"schema_version":"1.0","source":{"id":"2606.17857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17857","created_at":"2026-06-19T16:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17857v1","created_at":"2026-06-19T16:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17857","created_at":"2026-06-19T16:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"E2HFBKPZ4TGU","created_at":"2026-06-19T16:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"E2HFBKPZ4TGUSTHM","created_at":"2026-06-19T16:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"E2HFBKPZ","created_at":"2026-06-19T16:10:41Z"}],"graph_snapshots":[{"event_id":"sha256:7edd5b71f94e7d75a1b3da9e2cb5d88fa1bc6998f9285d2be3fdae239581c54f","target":"graph","created_at":"2026-06-19T16:10:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.17857/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article surveys the mathematical contributions of Manfred Denker, with a focus on themes that connect ergodic theory, probability theory, dynamical systems, fractal geometry, and statistics. Denker's highly influential work includes a systematic study of the statistical properties of dynamical systems, the development of limit theorems for dependent processes, and the use of thermodynamic formalism to relate geometric and measure-theoretic properties.\n  Particular emphasis is placed on the emergence of probabilistic behavior in deterministic systems, including central limit theorems, inva","authors_text":"Christian Wolf, Herold Dehling, Manuel Stadlbauer, Martin Schmoll, Suzanne Boyd","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-16T12:28:46Z","title":"From Ergodic Theory and Probability to Fractal Geometry and Dynamics: Themes in the Work of Manfred Denker"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17857","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:fbefbd7e9ef23295657b944dce26291676fa0db5ed27aa623871ec07deec7099","target":"record","created_at":"2026-06-19T16:10:41Z","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":"1bbb897b750becb48d7e47c606fdfa96e8fdc3bbb284936977a0d00b5cf48071","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-16T12:28:46Z","title_canon_sha256":"d2977d62b62d54e548951f9b7a70d5a93884c7517423bcbee243f3a2fa1e6407"},"schema_version":"1.0","source":{"id":"2606.17857","kind":"arxiv","version":1}},"canonical_sha256":"268e50a9f9e4cd494cec17f28a41faba4bc909e3e6326cb7b0db4600bc232243","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"268e50a9f9e4cd494cec17f28a41faba4bc909e3e6326cb7b0db4600bc232243","first_computed_at":"2026-06-19T16:10:41.726199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:41.726199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPwrmGPlty4gb4leNh4YvH+vcmfko/MMRdjBXAu4OwOH6nxYIKvVT3QIhc/+h7zpFR08xxcfX/1M5Kms12QZCg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:41.726663Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbefbd7e9ef23295657b944dce26291676fa0db5ed27aa623871ec07deec7099","sha256:7edd5b71f94e7d75a1b3da9e2cb5d88fa1bc6998f9285d2be3fdae239581c54f"],"state_sha256":"997cdf1c4504fbba6c967332abeec25be6da79a9108d8eca936daf76528d3f8a"}