{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7KVI33BWWQW2QJLELDBH7BXO3T","short_pith_number":"pith:7KVI33BW","schema_version":"1.0","canonical_sha256":"faaa8dec36b42da8256458c27f86eedcec9b7ae8113fa45260d4d7f1f797ba1d","source":{"kind":"arxiv","id":"2606.02036","version":1},"attestation_state":"computed","paper":{"title":"Self-intersection local times for Volterra Gaussian processes in stochastic flows with interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.PR","authors_text":"Olga Izyumtseva, Wasiur R. KhudaBukhsh","submitted_at":"2026-06-01T10:25:28Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.02036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T10:25:28Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"8048949ed8210f0b4f74a15c8bb2eeb97c0622e24c60dad1c8abaabb4aef5008","abstract_canon_sha256":"548d47791e3480fe6d3bc497eda9766e1fb0998957deca6fe72c4450104bb937"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:05:04.164354Z","signature_b64":"piFzSdgmFLpMPTNEzhHdKAHd6g0RmqoxTll3MBuihDkxZt3gFVxJQvC959CEMdMGRSn7zv9dmd4y/2yujjHLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faaa8dec36b42da8256458c27f86eedcec9b7ae8113fa45260d4d7f1f797ba1d","last_reissued_at":"2026-06-02T02:05:04.163940Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:05:04.163940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-intersection local times for Volterra Gaussian processes in stochastic flows with interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.PR","authors_text":"Olga Izyumtseva, Wasiur R. KhudaBukhsh","submitted_at":"2026-06-01T10:25:28Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02036","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02036/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.02036","created_at":"2026-06-02T02:05:04.163997+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.02036v1","created_at":"2026-06-02T02:05:04.163997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02036","created_at":"2026-06-02T02:05:04.163997+00:00"},{"alias_kind":"pith_short_12","alias_value":"7KVI33BWWQW2","created_at":"2026-06-02T02:05:04.163997+00:00"},{"alias_kind":"pith_short_16","alias_value":"7KVI33BWWQW2QJLE","created_at":"2026-06-02T02:05:04.163997+00:00"},{"alias_kind":"pith_short_8","alias_value":"7KVI33BW","created_at":"2026-06-02T02:05:04.163997+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T","json":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T.json","graph_json":"https://pith.science/api/pith-number/7KVI33BWWQW2QJLELDBH7BXO3T/graph.json","events_json":"https://pith.science/api/pith-number/7KVI33BWWQW2QJLELDBH7BXO3T/events.json","paper":"https://pith.science/paper/7KVI33BW"},"agent_actions":{"view_html":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T","download_json":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T.json","view_paper":"https://pith.science/paper/7KVI33BW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.02036&json=true","fetch_graph":"https://pith.science/api/pith-number/7KVI33BWWQW2QJLELDBH7BXO3T/graph.json","fetch_events":"https://pith.science/api/pith-number/7KVI33BWWQW2QJLELDBH7BXO3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T/action/storage_attestation","attest_author":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T/action/author_attestation","sign_citation":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T/action/citation_signature","submit_replication":"https://pith.science/pith/7KVI33BWWQW2QJLELDBH7BXO3T/action/replication_record"}},"created_at":"2026-06-02T02:05:04.163997+00:00","updated_at":"2026-06-02T02:05:04.163997+00:00"}