{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OS244IAQHHMI6ZQMJBD3RU46N2","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":"fe9f1ab827928744200494defcb82e33841d613aac3014b90d598431a79cf84f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-19T15:36:53Z","title_canon_sha256":"cfa877973b827826671a6f00313009a2c02fe8f596af585f1dc2bcfbcb4425f9"},"schema_version":"1.0","source":{"id":"2412.14956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.14956","created_at":"2026-07-05T10:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"2412.14956v2","created_at":"2026-07-05T10:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14956","created_at":"2026-07-05T10:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"OS244IAQHHMI","created_at":"2026-07-05T10:04:21Z"},{"alias_kind":"pith_short_16","alias_value":"OS244IAQHHMI6ZQM","created_at":"2026-07-05T10:04:21Z"},{"alias_kind":"pith_short_8","alias_value":"OS244IAQ","created_at":"2026-07-05T10:04:21Z"}],"graph_snapshots":[{"event_id":"sha256:40336f08bbba12e5d9eb8a415c0b55cd7ff1493eabe9babc14decc4dbaa28687","target":"graph","created_at":"2026-07-05T10:04:21Z","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/2412.14956/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of the solution. A maximum principle is proved and used to derive uniqueness. Existence is established by providing a stochastic representation based on anomalous processes constructed as a time change via the undershooting of an independent subordinator. This leads to general non-stepped processes with intervals of constancy representing a sticky or trapping effect. Our theory allows these intervals to be dependent on t","authors_text":"Bruno Toaldo, Enrico Scalas, Giacomo Ascione, Lorenzo Torricelli","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-19T15:36:53Z","title":"Time-changed Markov processes and coupled non-local equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14956","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:fc4babbf08121c2fbaceafdc8b060a8778a76118cf7c8f2e1598f94ae3a444c2","target":"record","created_at":"2026-07-05T10:04:21Z","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":"fe9f1ab827928744200494defcb82e33841d613aac3014b90d598431a79cf84f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-19T15:36:53Z","title_canon_sha256":"cfa877973b827826671a6f00313009a2c02fe8f596af585f1dc2bcfbcb4425f9"},"schema_version":"1.0","source":{"id":"2412.14956","kind":"arxiv","version":2}},"canonical_sha256":"74b5ce201039d88f660c4847b8d39e6eaa0eb50c5cca6001bd7e9a77d3cfa621","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74b5ce201039d88f660c4847b8d39e6eaa0eb50c5cca6001bd7e9a77d3cfa621","first_computed_at":"2026-07-05T10:04:21.108859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:04:21.108859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QECaFQt3QNxvBjsrGLMPm9QlOC5vmfJ7qPl7jJjjjdZDHS/g0ecYpJkoGxLdgj0Bj3GAYzc4+UaPgDvRr216DA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:04:21.109289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.14956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc4babbf08121c2fbaceafdc8b060a8778a76118cf7c8f2e1598f94ae3a444c2","sha256:40336f08bbba12e5d9eb8a415c0b55cd7ff1493eabe9babc14decc4dbaa28687"],"state_sha256":"d49cdd68118fdd32f6a751c53570e40f819698f381b647728bd1db468d26b614"}