{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IYUY3YNTYCVRJK4KSZRJKXEAST","short_pith_number":"pith:IYUY3YNT","schema_version":"1.0","canonical_sha256":"46298de1b3c0ab14ab8a9662955c8094d70b19120d221a84311eff8197b6c5de","source":{"kind":"arxiv","id":"1107.4842","version":1},"attestation_state":"computed","paper":{"title":"Local Poincar\\'e inequalities from stable curvature conditions on metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MG"],"primary_cat":"math.DG","authors_text":"Tapio Rajala","submitted_at":"2011-07-25T05:34:14Z","abstract_excerpt":"We prove local Poincar\\'e inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is that of weak CD(K,N) spaces as defined by Lott and Villani. The second class of spaces we study consists of spaces where we have a flow satisfying an evolution variational inequality for either the R\\'enyi entropy functional $E_N(\\rho m) = -\\int_X \\rho^{1-1/N} dm$ or the Shannon entropy functional $E_\\infty(\\rho m) = \\int_X \\rho \\log \\rho dm$. We also prove that if the R\\'enyi entropy functional is strongl"},"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":"1107.4842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-25T05:34:14Z","cross_cats_sorted":["math.AP","math.FA","math.MG"],"title_canon_sha256":"68b051a33afb7e37f4ef6196bebf0f7e87db32b35c2140f47934a74321daf5fa","abstract_canon_sha256":"d4c6f79522608e9cb10f2dd2abaa37bb839ecb6fb524071e0d68e3877bd10b9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:54.513906Z","signature_b64":"cn5Pz3tgPKMxnhNLUNEyva4w2VDwtlJ247WPMpgalKlJ6qejxXp+J7riI2pdRkvOxNUY/V3U5PwNS3KYibLbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46298de1b3c0ab14ab8a9662955c8094d70b19120d221a84311eff8197b6c5de","last_reissued_at":"2026-05-18T04:16:54.513455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:54.513455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Poincar\\'e inequalities from stable curvature conditions on metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MG"],"primary_cat":"math.DG","authors_text":"Tapio Rajala","submitted_at":"2011-07-25T05:34:14Z","abstract_excerpt":"We prove local Poincar\\'e inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is that of weak CD(K,N) spaces as defined by Lott and Villani. The second class of spaces we study consists of spaces where we have a flow satisfying an evolution variational inequality for either the R\\'enyi entropy functional $E_N(\\rho m) = -\\int_X \\rho^{1-1/N} dm$ or the Shannon entropy functional $E_\\infty(\\rho m) = \\int_X \\rho \\log \\rho dm$. We also prove that if the R\\'enyi entropy functional is strongl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4842","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":"1107.4842","created_at":"2026-05-18T04:16:54.513510+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.4842v1","created_at":"2026-05-18T04:16:54.513510+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4842","created_at":"2026-05-18T04:16:54.513510+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYUY3YNTYCVR","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYUY3YNTYCVRJK4K","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYUY3YNT","created_at":"2026-05-18T12:26:32.869790+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/IYUY3YNTYCVRJK4KSZRJKXEAST","json":"https://pith.science/pith/IYUY3YNTYCVRJK4KSZRJKXEAST.json","graph_json":"https://pith.science/api/pith-number/IYUY3YNTYCVRJK4KSZRJKXEAST/graph.json","events_json":"https://pith.science/api/pith-number/IYUY3YNTYCVRJK4KSZRJKXEAST/events.json","paper":"https://pith.science/paper/IYUY3YNT"},"agent_actions":{"view_html":"https://pith.science/pith/IYUY3YNTYCVRJK4KSZRJKXEAST","download_json":"https://pith.science/pith/IYUY3YNTYCVRJK4KSZRJKXEAST.json","view_paper":"https://pith.science/paper/IYUY3YNT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.4842&json=true","fetch_graph":"https://pith.science/api/pith-number/IYUY3YNTYCVRJK4KSZRJKXEAST/graph.json","fetch_events":"https://pith.science/api/pith-number/IYUY3YNTYCVRJK4KSZRJKXEAST/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYUY3YNTYCVRJK4KSZRJKXEAST/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYUY3YNTYCVRJK4KSZRJKXEAST/action/storage_attestation","attest_author":"https://pith.science/pith/IYUY3YNTYCVRJK4KSZRJKXEAST/action/author_attestation","sign_citation":"https://pith.science/pith/IYUY3YNTYCVRJK4KSZRJKXEAST/action/citation_signature","submit_replication":"https://pith.science/pith/IYUY3YNTYCVRJK4KSZRJKXEAST/action/replication_record"}},"created_at":"2026-05-18T04:16:54.513510+00:00","updated_at":"2026-05-18T04:16:54.513510+00:00"}