{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7KVI33BWWQW2QJLELDBH7BXO3T","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":"548d47791e3480fe6d3bc497eda9766e1fb0998957deca6fe72c4450104bb937","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T10:25:28Z","title_canon_sha256":"8048949ed8210f0b4f74a15c8bb2eeb97c0622e24c60dad1c8abaabb4aef5008"},"schema_version":"1.0","source":{"id":"2606.02036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02036","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02036v1","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02036","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"7KVI33BWWQW2","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"pith_short_16","alias_value":"7KVI33BWWQW2QJLE","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"pith_short_8","alias_value":"7KVI33BW","created_at":"2026-06-02T02:05:04Z"}],"graph_snapshots":[{"event_id":"sha256:7d02f395abc7ec21385c3f911cd15a278b09871dbf58deb32ba8fbf757eb732e","target":"graph","created_at":"2026-06-02T02:05:04Z","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/2606.02036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study self-intersection local times for a stochastic process $x(u(\\cdot),t)$, where $u$ is a Gaussian process of the form $u(t)=\\int^t_0k(t,s)\\mathrm{d}{w(s)}$, $k$ is a deterministic kernel of the Volterra type, $w$ is a Wiener process, and $x$ is a solution to the \\emph{equation with interaction}. Equations with interaction are a class of interacting particle system described by stochastic differential equations whose coefficients depend on a random measure (initial distribution of particles) transformed by the flow of solutions. Considering the occupation measure of $u$ as","authors_text":"Olga Izyumtseva, Wasiur R. KhudaBukhsh","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T10:25:28Z","title":"Self-intersection local times for Volterra Gaussian processes in stochastic flows with interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02036","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:e41282521282b40e683b672bbfdbd25d5d055015ecbcb83ba2de02e934748758","target":"record","created_at":"2026-06-02T02:05:04Z","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":"548d47791e3480fe6d3bc497eda9766e1fb0998957deca6fe72c4450104bb937","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T10:25:28Z","title_canon_sha256":"8048949ed8210f0b4f74a15c8bb2eeb97c0622e24c60dad1c8abaabb4aef5008"},"schema_version":"1.0","source":{"id":"2606.02036","kind":"arxiv","version":1}},"canonical_sha256":"faaa8dec36b42da8256458c27f86eedcec9b7ae8113fa45260d4d7f1f797ba1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faaa8dec36b42da8256458c27f86eedcec9b7ae8113fa45260d4d7f1f797ba1d","first_computed_at":"2026-06-02T02:05:04.163940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:05:04.163940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"piFzSdgmFLpMPTNEzhHdKAHd6g0RmqoxTll3MBuihDkxZt3gFVxJQvC959CEMdMGRSn7zv9dmd4y/2yujjHLDQ==","signature_status":"signed_v1","signed_at":"2026-06-02T02:05:04.164354Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e41282521282b40e683b672bbfdbd25d5d055015ecbcb83ba2de02e934748758","sha256:7d02f395abc7ec21385c3f911cd15a278b09871dbf58deb32ba8fbf757eb732e"],"state_sha256":"95ad2a70f8815675b6865477e8e3447dede279d06fa1f97c409ec3aa274f65e7"}