{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:ITULJISV6EDR4DHRCSKHT4VA4M","short_pith_number":"pith:ITULJISV","schema_version":"1.0","canonical_sha256":"44e8b4a255f1071e0cf1149479f2a0e3141fc3d9072944308e144138851bfde7","source":{"kind":"arxiv","id":"0905.3007","version":1},"attestation_state":"computed","paper":{"title":"A Poincar\\'e Inequality on Loop Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bo Wu, Xin Chen, Xue-Mei Li","submitted_at":"2009-05-19T00:03:43Z","abstract_excerpt":"We investigate properties of measures in infinite dimensional spaces in terms of Poincar\\'e inequalities.\n  A Poincar\\'e inequality states that the $L^2$ variance of an admissible function is controlled by the homogeneous $H^1$ norm. In the case of Loop spaces, it was observed by L. Gross that the homogeneous $H^1$ norm alone may not control the $L^2$ norm and a potential term involving the end value of the Brownian bridge is introduced. Aida, on the other hand, introduced a weight on the Dirichlet form. We show that Aida's modified Logarithmic Sobolev inequality implies weak Logarithmic Sobol"},"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":"0905.3007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-19T00:03:43Z","cross_cats_sorted":[],"title_canon_sha256":"0359b8ef472c239b6fe0f50cac9e54be00e63072747e4d36ce572d08c913a807","abstract_canon_sha256":"61d84c088d9bfcf7cc80bc906ee3d7a3b6d76cbaba298734134720a0fe319f21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:32.870014Z","signature_b64":"4Z5VYrQQBGwaP5vPCOX9HW38Mex1zFdNr1ry/bamCX4YGHYLX/ufZC8/5PiK4TlwrEBurz6WUlh0+akU0zPJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44e8b4a255f1071e0cf1149479f2a0e3141fc3d9072944308e144138851bfde7","last_reissued_at":"2026-05-18T01:15:32.869372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:32.869372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Poincar\\'e Inequality on Loop Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bo Wu, Xin Chen, Xue-Mei Li","submitted_at":"2009-05-19T00:03:43Z","abstract_excerpt":"We investigate properties of measures in infinite dimensional spaces in terms of Poincar\\'e inequalities.\n  A Poincar\\'e inequality states that the $L^2$ variance of an admissible function is controlled by the homogeneous $H^1$ norm. In the case of Loop spaces, it was observed by L. Gross that the homogeneous $H^1$ norm alone may not control the $L^2$ norm and a potential term involving the end value of the Brownian bridge is introduced. Aida, on the other hand, introduced a weight on the Dirichlet form. We show that Aida's modified Logarithmic Sobolev inequality implies weak Logarithmic Sobol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3007","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":"0905.3007","created_at":"2026-05-18T01:15:32.869451+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.3007v1","created_at":"2026-05-18T01:15:32.869451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3007","created_at":"2026-05-18T01:15:32.869451+00:00"},{"alias_kind":"pith_short_12","alias_value":"ITULJISV6EDR","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"ITULJISV6EDR4DHR","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"ITULJISV","created_at":"2026-05-18T12:26:00.592388+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/ITULJISV6EDR4DHRCSKHT4VA4M","json":"https://pith.science/pith/ITULJISV6EDR4DHRCSKHT4VA4M.json","graph_json":"https://pith.science/api/pith-number/ITULJISV6EDR4DHRCSKHT4VA4M/graph.json","events_json":"https://pith.science/api/pith-number/ITULJISV6EDR4DHRCSKHT4VA4M/events.json","paper":"https://pith.science/paper/ITULJISV"},"agent_actions":{"view_html":"https://pith.science/pith/ITULJISV6EDR4DHRCSKHT4VA4M","download_json":"https://pith.science/pith/ITULJISV6EDR4DHRCSKHT4VA4M.json","view_paper":"https://pith.science/paper/ITULJISV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.3007&json=true","fetch_graph":"https://pith.science/api/pith-number/ITULJISV6EDR4DHRCSKHT4VA4M/graph.json","fetch_events":"https://pith.science/api/pith-number/ITULJISV6EDR4DHRCSKHT4VA4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ITULJISV6EDR4DHRCSKHT4VA4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ITULJISV6EDR4DHRCSKHT4VA4M/action/storage_attestation","attest_author":"https://pith.science/pith/ITULJISV6EDR4DHRCSKHT4VA4M/action/author_attestation","sign_citation":"https://pith.science/pith/ITULJISV6EDR4DHRCSKHT4VA4M/action/citation_signature","submit_replication":"https://pith.science/pith/ITULJISV6EDR4DHRCSKHT4VA4M/action/replication_record"}},"created_at":"2026-05-18T01:15:32.869451+00:00","updated_at":"2026-05-18T01:15:32.869451+00:00"}