{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:PEBB5H2EKOZKENCDCD6IF657PG","short_pith_number":"pith:PEBB5H2E","schema_version":"1.0","canonical_sha256":"79021e9f4453b2a2344310fc82fbbf79bec7b5e7414ff7bd073de924408779fe","source":{"kind":"arxiv","id":"1006.5590","version":1},"attestation_state":"computed","paper":{"title":"Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroshi Kawabi, Michael R\\\"ockner, Sergio Albeverio","submitted_at":"2010-06-29T12:22:29Z","abstract_excerpt":"We prove $L^{p}$-uniqueness of Dirichlet operators for Gibbs measures on the path space $C(\\mathbb R, \\mathbb R^{d})$ associated with exponential type interactions in infinite volume by extending an SPDE approach presented in previous work by the last two named authors. We also give an SPDE characterization of the corresponding dynamics. In particular, we prove existence and uniqueness of a strong solution for the SPDE, though the self-interaction potential is not assumed to be differentiable, hence the drift is possibly discontinuous. As examples, to which our results apply, we mention the st"},"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":"1006.5590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-06-29T12:22:29Z","cross_cats_sorted":[],"title_canon_sha256":"52e04786f7ce3ff81822415de67fa6793a3872fd535c202ff5ad62bd52fc73f8","abstract_canon_sha256":"ff9efcd02633dbaf01f38ac5545a418984f8b163a17e9ea0e065b47bd977d3c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:14.244021Z","signature_b64":"viElggfmBCYXPV4ulGrfoiSsUbkbDlTwxjPnpUZwjR9+4Cg1fQr8l7nq1/xtixddJp7y946npvWEaiezeqQLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79021e9f4453b2a2344310fc82fbbf79bec7b5e7414ff7bd073de924408779fe","last_reissued_at":"2026-05-18T00:13:14.243403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:14.243403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroshi Kawabi, Michael R\\\"ockner, Sergio Albeverio","submitted_at":"2010-06-29T12:22:29Z","abstract_excerpt":"We prove $L^{p}$-uniqueness of Dirichlet operators for Gibbs measures on the path space $C(\\mathbb R, \\mathbb R^{d})$ associated with exponential type interactions in infinite volume by extending an SPDE approach presented in previous work by the last two named authors. We also give an SPDE characterization of the corresponding dynamics. In particular, we prove existence and uniqueness of a strong solution for the SPDE, though the self-interaction potential is not assumed to be differentiable, hence the drift is possibly discontinuous. As examples, to which our results apply, we mention the st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5590","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":""},"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":"1006.5590","created_at":"2026-05-18T00:13:14.243482+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.5590v1","created_at":"2026-05-18T00:13:14.243482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5590","created_at":"2026-05-18T00:13:14.243482+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEBB5H2EKOZK","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEBB5H2EKOZKENCD","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEBB5H2E","created_at":"2026-05-18T12:26:12.377268+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/PEBB5H2EKOZKENCDCD6IF657PG","json":"https://pith.science/pith/PEBB5H2EKOZKENCDCD6IF657PG.json","graph_json":"https://pith.science/api/pith-number/PEBB5H2EKOZKENCDCD6IF657PG/graph.json","events_json":"https://pith.science/api/pith-number/PEBB5H2EKOZKENCDCD6IF657PG/events.json","paper":"https://pith.science/paper/PEBB5H2E"},"agent_actions":{"view_html":"https://pith.science/pith/PEBB5H2EKOZKENCDCD6IF657PG","download_json":"https://pith.science/pith/PEBB5H2EKOZKENCDCD6IF657PG.json","view_paper":"https://pith.science/paper/PEBB5H2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.5590&json=true","fetch_graph":"https://pith.science/api/pith-number/PEBB5H2EKOZKENCDCD6IF657PG/graph.json","fetch_events":"https://pith.science/api/pith-number/PEBB5H2EKOZKENCDCD6IF657PG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEBB5H2EKOZKENCDCD6IF657PG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEBB5H2EKOZKENCDCD6IF657PG/action/storage_attestation","attest_author":"https://pith.science/pith/PEBB5H2EKOZKENCDCD6IF657PG/action/author_attestation","sign_citation":"https://pith.science/pith/PEBB5H2EKOZKENCDCD6IF657PG/action/citation_signature","submit_replication":"https://pith.science/pith/PEBB5H2EKOZKENCDCD6IF657PG/action/replication_record"}},"created_at":"2026-05-18T00:13:14.243482+00:00","updated_at":"2026-05-18T00:13:14.243482+00:00"}