{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:A4RZKJD7JWKH4URLIB4TJP43RV","short_pith_number":"pith:A4RZKJD7","schema_version":"1.0","canonical_sha256":"072395247f4d947e522b407934bf9b8d72d5775678b27520360598d43997a30f","source":{"kind":"arxiv","id":"2402.15130","version":4},"attestation_state":"computed","paper":{"title":"Diffusion Processes on $p$-Wasserstein Space over Banach Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Panpan Ren, Simon Wittmann","submitted_at":"2024-02-23T06:32:01Z","abstract_excerpt":"To study diffusion processes on the p-Wasserstein space $\\mathscr P_p$ for $p\\in [1,\\infty)$ over a separable, reflexive Banach space $X$, we present a criterion on the quasi-regularity of Dirichlet forms in $L^2(\\mathscr P_p,\\Lambda)$ for a reference probability $\\Lambda$ on $\\mathscr P_p$. It is formulated in terms of an upper bound condition with the uniform norm of the intrinsic derivative. We find a versatile class of quasi-regular local Dirichlet forms on $\\mathscr P_p$ by using images of Dirichlet forms on the tangent space $L^p(X\\to X,\\mu_0)$ at a reference point $\\mu_0\\in\\mathscr P_p$"},"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":"2402.15130","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-02-23T06:32:01Z","cross_cats_sorted":[],"title_canon_sha256":"b999d0cc0584096cc3f79a6172e3c19a4256c4930b2da4f46a2fd2a8dbcd95bf","abstract_canon_sha256":"62193da61117af1bfeb68a83776eeefbcdf2689cfe4bc331694adaaa8f4a4a3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:09.777135Z","signature_b64":"i2bdn/AuhLKDrMoRoO9wnK+LmfMkaOkASqIUdnLRsmdRdUrQgb2dhVo2AFrH+vf+gw8fbr41Hw9sE/PPDCXoDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"072395247f4d947e522b407934bf9b8d72d5775678b27520360598d43997a30f","last_reissued_at":"2026-07-05T11:28:09.776429Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:09.776429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diffusion Processes on $p$-Wasserstein Space over Banach Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Panpan Ren, Simon Wittmann","submitted_at":"2024-02-23T06:32:01Z","abstract_excerpt":"To study diffusion processes on the p-Wasserstein space $\\mathscr P_p$ for $p\\in [1,\\infty)$ over a separable, reflexive Banach space $X$, we present a criterion on the quasi-regularity of Dirichlet forms in $L^2(\\mathscr P_p,\\Lambda)$ for a reference probability $\\Lambda$ on $\\mathscr P_p$. It is formulated in terms of an upper bound condition with the uniform norm of the intrinsic derivative. We find a versatile class of quasi-regular local Dirichlet forms on $\\mathscr P_p$ by using images of Dirichlet forms on the tangent space $L^p(X\\to X,\\mu_0)$ at a reference point $\\mu_0\\in\\mathscr P_p$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.15130","kind":"arxiv","version":4},"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/2402.15130/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":"2402.15130","created_at":"2026-07-05T11:28:09.776537+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.15130v4","created_at":"2026-07-05T11:28:09.776537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.15130","created_at":"2026-07-05T11:28:09.776537+00:00"},{"alias_kind":"pith_short_12","alias_value":"A4RZKJD7JWKH","created_at":"2026-07-05T11:28:09.776537+00:00"},{"alias_kind":"pith_short_16","alias_value":"A4RZKJD7JWKH4URL","created_at":"2026-07-05T11:28:09.776537+00:00"},{"alias_kind":"pith_short_8","alias_value":"A4RZKJD7","created_at":"2026-07-05T11:28:09.776537+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06646","citing_title":"Diffusion enabled Optimal Transport distances for graph matching","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2506.12755","citing_title":"Stochastic intrinsic gradient flows on the Wasserstein space","ref_index":31,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV","json":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV.json","graph_json":"https://pith.science/api/pith-number/A4RZKJD7JWKH4URLIB4TJP43RV/graph.json","events_json":"https://pith.science/api/pith-number/A4RZKJD7JWKH4URLIB4TJP43RV/events.json","paper":"https://pith.science/paper/A4RZKJD7"},"agent_actions":{"view_html":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV","download_json":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV.json","view_paper":"https://pith.science/paper/A4RZKJD7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.15130&json=true","fetch_graph":"https://pith.science/api/pith-number/A4RZKJD7JWKH4URLIB4TJP43RV/graph.json","fetch_events":"https://pith.science/api/pith-number/A4RZKJD7JWKH4URLIB4TJP43RV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV/action/storage_attestation","attest_author":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV/action/author_attestation","sign_citation":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV/action/citation_signature","submit_replication":"https://pith.science/pith/A4RZKJD7JWKH4URLIB4TJP43RV/action/replication_record"}},"created_at":"2026-07-05T11:28:09.776537+00:00","updated_at":"2026-07-05T11:28:09.776537+00:00"}