{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2LUMZVRXOK3BDZR46D3JVOVD3M","short_pith_number":"pith:2LUMZVRX","schema_version":"1.0","canonical_sha256":"d2e8ccd63772b611e63cf0f69abaa3db291b2eca10597c598a95eafee2226845","source":{"kind":"arxiv","id":"1812.01824","version":1},"attestation_state":"computed","paper":{"title":"Approximation to Wiener measure on a general noncompact Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bo Wu","submitted_at":"2018-12-05T05:42:27Z","abstract_excerpt":"In prior work \\cite{AD} of Lars Andersson and Bruce K. Driver, the path space with finite interval over a compact Riemannian manifold is approximated by finite dimensional manifolds $H_{x,\\P} (M)$ consisting of piecewise geodesic paths adapted to partitions $\\P$ of $[0,T]$, and the associated Wiener measure is also approximated by a sequence of probability measures on finite dimensional manifolds. In this article, we will extend their results to the general path space(possibly with infinite interval) over a non-compact Riemannian manifold by using the cutoff method of compact Riemannian manifo"},"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":"1812.01824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-05T05:42:27Z","cross_cats_sorted":[],"title_canon_sha256":"60fe37d54b10dcfd7f93ede6aed82b914a40f7f053ee41c4cb0b30d9c7bd4027","abstract_canon_sha256":"4504970c60b7a8054a113b24ddb442790067aab052c414838411d7991929a988"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:00.527012Z","signature_b64":"Dq9qcudSGagGMeFL4F123/6ZmevJCFE4lyGWdngI2OjA0Zr8/XbOsXGylWubfH8Wx2NCcusRj3Y8NkUby7vrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2e8ccd63772b611e63cf0f69abaa3db291b2eca10597c598a95eafee2226845","last_reissued_at":"2026-05-17T23:59:00.526522Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:00.526522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation to Wiener measure on a general noncompact Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bo Wu","submitted_at":"2018-12-05T05:42:27Z","abstract_excerpt":"In prior work \\cite{AD} of Lars Andersson and Bruce K. Driver, the path space with finite interval over a compact Riemannian manifold is approximated by finite dimensional manifolds $H_{x,\\P} (M)$ consisting of piecewise geodesic paths adapted to partitions $\\P$ of $[0,T]$, and the associated Wiener measure is also approximated by a sequence of probability measures on finite dimensional manifolds. In this article, we will extend their results to the general path space(possibly with infinite interval) over a non-compact Riemannian manifold by using the cutoff method of compact Riemannian manifo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01824","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":"1812.01824","created_at":"2026-05-17T23:59:00.526603+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.01824v1","created_at":"2026-05-17T23:59:00.526603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01824","created_at":"2026-05-17T23:59:00.526603+00:00"},{"alias_kind":"pith_short_12","alias_value":"2LUMZVRXOK3B","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2LUMZVRXOK3BDZR4","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2LUMZVRX","created_at":"2026-05-18T12:32:02.567920+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/2LUMZVRXOK3BDZR46D3JVOVD3M","json":"https://pith.science/pith/2LUMZVRXOK3BDZR46D3JVOVD3M.json","graph_json":"https://pith.science/api/pith-number/2LUMZVRXOK3BDZR46D3JVOVD3M/graph.json","events_json":"https://pith.science/api/pith-number/2LUMZVRXOK3BDZR46D3JVOVD3M/events.json","paper":"https://pith.science/paper/2LUMZVRX"},"agent_actions":{"view_html":"https://pith.science/pith/2LUMZVRXOK3BDZR46D3JVOVD3M","download_json":"https://pith.science/pith/2LUMZVRXOK3BDZR46D3JVOVD3M.json","view_paper":"https://pith.science/paper/2LUMZVRX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.01824&json=true","fetch_graph":"https://pith.science/api/pith-number/2LUMZVRXOK3BDZR46D3JVOVD3M/graph.json","fetch_events":"https://pith.science/api/pith-number/2LUMZVRXOK3BDZR46D3JVOVD3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2LUMZVRXOK3BDZR46D3JVOVD3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2LUMZVRXOK3BDZR46D3JVOVD3M/action/storage_attestation","attest_author":"https://pith.science/pith/2LUMZVRXOK3BDZR46D3JVOVD3M/action/author_attestation","sign_citation":"https://pith.science/pith/2LUMZVRXOK3BDZR46D3JVOVD3M/action/citation_signature","submit_replication":"https://pith.science/pith/2LUMZVRXOK3BDZR46D3JVOVD3M/action/replication_record"}},"created_at":"2026-05-17T23:59:00.526603+00:00","updated_at":"2026-05-17T23:59:00.526603+00:00"}