{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OUNZDI5MWZ7I76QTU3H736FFG6","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":"df61568474bb18e999e9dbc01b79a5ff86cc474b45bcfae031c605af866d27a4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-27T21:56:54Z","title_canon_sha256":"071f38dc3b47f8cb418f3eb85e0e153b106ed5d5931bb3a424baea5f9646fd3b"},"schema_version":"1.0","source":{"id":"2411.18775","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18775","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18775v2","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18775","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"OUNZDI5MWZ7I","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_16","alias_value":"OUNZDI5MWZ7I76QT","created_at":"2026-07-05T11:40:51Z"},{"alias_kind":"pith_short_8","alias_value":"OUNZDI5M","created_at":"2026-07-05T11:40:51Z"}],"graph_snapshots":[{"event_id":"sha256:de9ec0cbf4d7aaf193b42306f2213ce46946ce46704123bfd46e6d467dcff1ed","target":"graph","created_at":"2026-07-05T11:40:51Z","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/2411.18775/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional Brownian motion (fBm) with a random diffusion coefficient (superstatistical fBm) together with a time-dependent random Hurst parameter. We provide here a dynamical foundation for such general family of models. We consider a dynamical system describing the motion of a test-particle surrounded by $N$ Brownian particles with different masses. This dynamic is gover","authors_text":"Christian Bender, Gianni Pagnini, Mirko D'Ovidio, Yana A. Butko","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-27T21:56:54Z","title":"Limit Theorems for the Dynamical Foundation of the Fractional Brownian Motion and Related Models of Anomalous Diffusion with Random Diffusion Coefficient and Time-Dependent Random Hurst parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18775","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:d11541eeb624f63b7c14d3cdf9d534e71aba987ee7e5ac14df891585a9eaea05","target":"record","created_at":"2026-07-05T11:40:51Z","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":"df61568474bb18e999e9dbc01b79a5ff86cc474b45bcfae031c605af866d27a4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-27T21:56:54Z","title_canon_sha256":"071f38dc3b47f8cb418f3eb85e0e153b106ed5d5931bb3a424baea5f9646fd3b"},"schema_version":"1.0","source":{"id":"2411.18775","kind":"arxiv","version":2}},"canonical_sha256":"751b91a3acb67e8ffa13a6cffdf8a537bc86b9502b22126066fedb29a64c1656","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"751b91a3acb67e8ffa13a6cffdf8a537bc86b9502b22126066fedb29a64c1656","first_computed_at":"2026-07-05T11:40:51.038137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:40:51.038137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ti5GJfgyh58oWweV+XOiOTVzSmcqKIuxxlu5kiwzjgMqfZTyunSWtxi1RINHx0daqV2ztabO9Pn3hkyyy6itBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:40:51.038657Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18775","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d11541eeb624f63b7c14d3cdf9d534e71aba987ee7e5ac14df891585a9eaea05","sha256:de9ec0cbf4d7aaf193b42306f2213ce46946ce46704123bfd46e6d467dcff1ed"],"state_sha256":"cfd1aa742904d404e4a096330189403e99b0bbd07bf44261042c1e053057bb50"}