{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GQWNSIUFDEGGILWXONZREFQNBH","short_pith_number":"pith:GQWNSIUF","canonical_record":{"source":{"id":"1111.5526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-23T15:27:24Z","cross_cats_sorted":["math.AP","math.FA","math.MG"],"title_canon_sha256":"d61f437ee5363a9b0b13cce045d9afcc56409d10aaba181988031fb87208b860","abstract_canon_sha256":"a8fca0154bfdd242619420a8eff6b67dfcd648dcfce914cd7fecd0b1446389b1"},"schema_version":"1.0"},"canonical_sha256":"342cd92285190c642ed7737312160d09c6fb71a7c737c7af4c69c254e53eda67","source":{"kind":"arxiv","id":"1111.5526","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5526","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5526v1","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5526","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"GQWNSIUFDEGG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GQWNSIUFDEGGILWX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GQWNSIUF","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GQWNSIUFDEGGILWXONZREFQNBH","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-23T15:27:24Z","cross_cats_sorted":["math.AP","math.FA","math.MG"],"title_canon_sha256":"d61f437ee5363a9b0b13cce045d9afcc56409d10aaba181988031fb87208b860","abstract_canon_sha256":"a8fca0154bfdd242619420a8eff6b67dfcd648dcfce914cd7fecd0b1446389b1"},"schema_version":"1.0"},"canonical_sha256":"342cd92285190c642ed7737312160d09c6fb71a7c737c7af4c69c254e53eda67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:43.559626Z","signature_b64":"GnvPgCO2S2UF36BxJO2TTvKdW4QgPD5lrqWlyy+C2d0nuj0s1dv4PzQjNGIS1FRaYxPNSNfr5PzEX5spN5QZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"342cd92285190c642ed7737312160d09c6fb71a7c737c7af4c69c254e53eda67","last_reissued_at":"2026-05-18T04:07:43.559128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:43.559128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5526","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e69PkeU5Ez3tsFQvQofVJEWKLRrPLlMIaybAtFRep2+cpIjhQjRQQjq5/m9/99kP7RPgHgbosZ6EOAs7d0aBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:10:46.177711Z"},"content_sha256":"484ffd4193855928d0fa319dafc873ed9cabec9d29cadf3ebb1cde799650f479","schema_version":"1.0","event_id":"sha256:484ffd4193855928d0fa319dafc873ed9cabec9d29cadf3ebb1cde799650f479"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GQWNSIUFDEGGILWXONZREFQNBH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm","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":"2011-11-23T15:27:24Z","abstract_excerpt":"We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincar\\'e inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class of convex functionals that a local Poincar\\'e inequality is implied by the weak displacement convexity of the functional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5526","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0DIAYriS1FRLl5nQEQTtinRx1Qa26Sjr0XhaA/hi9W+5ZHChdBbrKAe92bC1+oDzjnTWmsoDQbkH+5Ly6mCYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:10:46.178420Z"},"content_sha256":"1c076e6b084bc4f8f7a6eb86c1c699c0bf24384a8d806c5742801652b20bb8a8","schema_version":"1.0","event_id":"sha256:1c076e6b084bc4f8f7a6eb86c1c699c0bf24384a8d806c5742801652b20bb8a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQWNSIUFDEGGILWXONZREFQNBH/bundle.json","state_url":"https://pith.science/pith/GQWNSIUFDEGGILWXONZREFQNBH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQWNSIUFDEGGILWXONZREFQNBH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T06:10:46Z","links":{"resolver":"https://pith.science/pith/GQWNSIUFDEGGILWXONZREFQNBH","bundle":"https://pith.science/pith/GQWNSIUFDEGGILWXONZREFQNBH/bundle.json","state":"https://pith.science/pith/GQWNSIUFDEGGILWXONZREFQNBH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQWNSIUFDEGGILWXONZREFQNBH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GQWNSIUFDEGGILWXONZREFQNBH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a8fca0154bfdd242619420a8eff6b67dfcd648dcfce914cd7fecd0b1446389b1","cross_cats_sorted":["math.AP","math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-23T15:27:24Z","title_canon_sha256":"d61f437ee5363a9b0b13cce045d9afcc56409d10aaba181988031fb87208b860"},"schema_version":"1.0","source":{"id":"1111.5526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5526","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5526v1","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5526","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"GQWNSIUFDEGG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GQWNSIUFDEGGILWX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GQWNSIUF","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:1c076e6b084bc4f8f7a6eb86c1c699c0bf24384a8d806c5742801652b20bb8a8","target":"graph","created_at":"2026-05-18T04:07:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincar\\'e inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class of convex functionals that a local Poincar\\'e inequality is implied by the weak displacement convexity of the functional.","authors_text":"Tapio Rajala","cross_cats":["math.AP","math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-23T15:27:24Z","title":"Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5526","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:484ffd4193855928d0fa319dafc873ed9cabec9d29cadf3ebb1cde799650f479","target":"record","created_at":"2026-05-18T04:07:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a8fca0154bfdd242619420a8eff6b67dfcd648dcfce914cd7fecd0b1446389b1","cross_cats_sorted":["math.AP","math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-23T15:27:24Z","title_canon_sha256":"d61f437ee5363a9b0b13cce045d9afcc56409d10aaba181988031fb87208b860"},"schema_version":"1.0","source":{"id":"1111.5526","kind":"arxiv","version":1}},"canonical_sha256":"342cd92285190c642ed7737312160d09c6fb71a7c737c7af4c69c254e53eda67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"342cd92285190c642ed7737312160d09c6fb71a7c737c7af4c69c254e53eda67","first_computed_at":"2026-05-18T04:07:43.559128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:43.559128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GnvPgCO2S2UF36BxJO2TTvKdW4QgPD5lrqWlyy+C2d0nuj0s1dv4PzQjNGIS1FRaYxPNSNfr5PzEX5spN5QZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:43.559626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:484ffd4193855928d0fa319dafc873ed9cabec9d29cadf3ebb1cde799650f479","sha256:1c076e6b084bc4f8f7a6eb86c1c699c0bf24384a8d806c5742801652b20bb8a8"],"state_sha256":"dfd7885c50845d35359c672f84874bd59e1f4fef4e73ae546ffb85de12240105"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gqjWGS0DrqmSuQoT9SE9KTwTYWnB2ERgYdkCksQjl6q+d+tGG4i7Pb7Q6z4uUlu1w8X+11i8cvFjbuJjMcUHDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:10:46.182087Z","bundle_sha256":"fe1418ee58197718ac5677da70d854f7248a1911220ba5bf2d77a6cfcc3b04ed"}}