{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:QLIGFL7ORDTPWQOOA7E3REUGF5","short_pith_number":"pith:QLIGFL7O","schema_version":"1.0","canonical_sha256":"82d062afee88e6fb41ce07c9b892862f7f547a240e3234317070872613d76296","source":{"kind":"arxiv","id":"1908.01387","version":1},"attestation_state":"computed","paper":{"title":"A Sub-Gaussian estimate for Dirichlet Heat Kernels on Tubular Neighbourhoods and Tightness of Conditional Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Olaf Wittich","submitted_at":"2019-08-04T19:06:15Z","abstract_excerpt":"We prove tightness of a family of path measures $\\nu_{\\varepsilon}$ on tubes $L(\\varepsilon)$ of small diameters around a closed and connected submanifold $L$ of another Riemannian manifold $M$. Together with a convergence result for Dirichlet semigroups on tubular neighbourhoods, that implies weak convergence of the measures as the tube radius $\\varepsilon$ tends to zero to a measure supported by the path space of the submanifold. As a consequence, we obtain weak convergence of the measures obtained by conditioning Brownian motion to stay within the tubes $L(\\varepsilon)$ up to a finite time "},"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":"1908.01387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-04T19:06:15Z","cross_cats_sorted":[],"title_canon_sha256":"1aa2b4402aef0548517e3ee6f273a5b889b68ff32a292dc5372d287f7162510a","abstract_canon_sha256":"ae14c5b227856c6bd7f24e23c1d418b1edd5b783060c6382be1ebbed7f4c6318"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:29.940574Z","signature_b64":"i36QEy+apWXRMGB7OPizuBTEdVsLU4rxDo6GdEyQeUzCXQfIkxovYDQM18NySDTW1S6NQ69OPMBhtvat5Bc9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82d062afee88e6fb41ce07c9b892862f7f547a240e3234317070872613d76296","last_reissued_at":"2026-07-04T23:51:29.940167Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:29.940167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Sub-Gaussian estimate for Dirichlet Heat Kernels on Tubular Neighbourhoods and Tightness of Conditional Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Olaf Wittich","submitted_at":"2019-08-04T19:06:15Z","abstract_excerpt":"We prove tightness of a family of path measures $\\nu_{\\varepsilon}$ on tubes $L(\\varepsilon)$ of small diameters around a closed and connected submanifold $L$ of another Riemannian manifold $M$. Together with a convergence result for Dirichlet semigroups on tubular neighbourhoods, that implies weak convergence of the measures as the tube radius $\\varepsilon$ tends to zero to a measure supported by the path space of the submanifold. As a consequence, we obtain weak convergence of the measures obtained by conditioning Brownian motion to stay within the tubes $L(\\varepsilon)$ up to a finite time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01387","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/1908.01387/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":"1908.01387","created_at":"2026-07-04T23:51:29.940223+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.01387v1","created_at":"2026-07-04T23:51:29.940223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01387","created_at":"2026-07-04T23:51:29.940223+00:00"},{"alias_kind":"pith_short_12","alias_value":"QLIGFL7ORDTP","created_at":"2026-07-04T23:51:29.940223+00:00"},{"alias_kind":"pith_short_16","alias_value":"QLIGFL7ORDTPWQOO","created_at":"2026-07-04T23:51:29.940223+00:00"},{"alias_kind":"pith_short_8","alias_value":"QLIGFL7O","created_at":"2026-07-04T23:51:29.940223+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/QLIGFL7ORDTPWQOOA7E3REUGF5","json":"https://pith.science/pith/QLIGFL7ORDTPWQOOA7E3REUGF5.json","graph_json":"https://pith.science/api/pith-number/QLIGFL7ORDTPWQOOA7E3REUGF5/graph.json","events_json":"https://pith.science/api/pith-number/QLIGFL7ORDTPWQOOA7E3REUGF5/events.json","paper":"https://pith.science/paper/QLIGFL7O"},"agent_actions":{"view_html":"https://pith.science/pith/QLIGFL7ORDTPWQOOA7E3REUGF5","download_json":"https://pith.science/pith/QLIGFL7ORDTPWQOOA7E3REUGF5.json","view_paper":"https://pith.science/paper/QLIGFL7O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.01387&json=true","fetch_graph":"https://pith.science/api/pith-number/QLIGFL7ORDTPWQOOA7E3REUGF5/graph.json","fetch_events":"https://pith.science/api/pith-number/QLIGFL7ORDTPWQOOA7E3REUGF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QLIGFL7ORDTPWQOOA7E3REUGF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QLIGFL7ORDTPWQOOA7E3REUGF5/action/storage_attestation","attest_author":"https://pith.science/pith/QLIGFL7ORDTPWQOOA7E3REUGF5/action/author_attestation","sign_citation":"https://pith.science/pith/QLIGFL7ORDTPWQOOA7E3REUGF5/action/citation_signature","submit_replication":"https://pith.science/pith/QLIGFL7ORDTPWQOOA7E3REUGF5/action/replication_record"}},"created_at":"2026-07-04T23:51:29.940223+00:00","updated_at":"2026-07-04T23:51:29.940223+00:00"}