{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DP4UMOCTFGOBMTHJMY25RHPUG4","short_pith_number":"pith:DP4UMOCT","canonical_record":{"source":{"id":"1703.01765","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-06T08:59:11Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"cf4b43227ec3fb120049a24adbe90b8cbb1c81594dfded8b0792475d7309bf90","abstract_canon_sha256":"ab6089b9cca172071cd5561000ec5746c76a95b0f3ea7492eb443411825dc2cf"},"schema_version":"1.0"},"canonical_sha256":"1bf9463853299c164ce96635d89df4371ee68c95c43944f1ee1a42c40e8d123a","source":{"kind":"arxiv","id":"1703.01765","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01765","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01765v2","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01765","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"DP4UMOCTFGOB","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DP4UMOCTFGOBMTHJ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DP4UMOCT","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DP4UMOCTFGOBMTHJMY25RHPUG4","target":"record","payload":{"canonical_record":{"source":{"id":"1703.01765","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-06T08:59:11Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"cf4b43227ec3fb120049a24adbe90b8cbb1c81594dfded8b0792475d7309bf90","abstract_canon_sha256":"ab6089b9cca172071cd5561000ec5746c76a95b0f3ea7492eb443411825dc2cf"},"schema_version":"1.0"},"canonical_sha256":"1bf9463853299c164ce96635d89df4371ee68c95c43944f1ee1a42c40e8d123a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:18.693027Z","signature_b64":"PFEd+FiO1dqo6sTTrUcxv0VzbL7M+6hcWD4bzWjbK2hmsFLMZ/cL/l11QAzulYgnCxXeGmC/4TOcffQ9UpRIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bf9463853299c164ce96635d89df4371ee68c95c43944f1ee1a42c40e8d123a","last_reissued_at":"2026-05-17T23:43:18.692426Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:18.692426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.01765","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LUjaUFcpGZolNWrBtg1VCWL8ujpMUoxRYH7JNid12MoF1WcxNA96XjZdSnNwHoOcjZkWFUvqvKnI1R4R1t8KDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:52:47.821093Z"},"content_sha256":"27fbb2a10125e51c959b71de27fcd0417fa697d74ac62a396435daf1a823e77a","schema_version":"1.0","event_id":"sha256:27fbb2a10125e51c959b71de27fcd0417fa697d74ac62a396435daf1a823e77a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DP4UMOCTFGOBMTHJMY25RHPUG4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the convex Poincar\\'e inequality and weak transportation inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Micha{\\l} Strzelecki, Rados{\\l}aw Adamczak","submitted_at":"2017-03-06T08:59:11Z","abstract_excerpt":"We prove that for a probability measure on $\\mathbb{R}^n$, the Poincar\\'e inequality for convex functions is equivalent to the weak transportation inequality with a quadratic-linear cost. This generalizes recent results by Gozlan et al. and Feldheim et al., concerning probability measures on the real line. The proof relies on modified logarithmic Sobolev inequalities of Bobkov-Ledoux type for convex and concave functions, which are of independent interest. We also present refined concentration inequalities for general (not necessarily Lipschitz) convex functions, complementing recent results b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01765","kind":"arxiv","version":2},"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":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WP1e7ClczztZNB3LWj6e/YJaks32ZeulXDLNR4YTd+6dttw17VbPHZpiYracPpfkchqUbjrPOff6veuB+xSVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:52:47.821459Z"},"content_sha256":"e406faa6a88cb9660b198e73ad09064d4994bbf9f1bc0c1869eb22d7f00329fc","schema_version":"1.0","event_id":"sha256:e406faa6a88cb9660b198e73ad09064d4994bbf9f1bc0c1869eb22d7f00329fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DP4UMOCTFGOBMTHJMY25RHPUG4/bundle.json","state_url":"https://pith.science/pith/DP4UMOCTFGOBMTHJMY25RHPUG4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DP4UMOCTFGOBMTHJMY25RHPUG4/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":"2026-06-28T21:52:47Z","links":{"resolver":"https://pith.science/pith/DP4UMOCTFGOBMTHJMY25RHPUG4","bundle":"https://pith.science/pith/DP4UMOCTFGOBMTHJMY25RHPUG4/bundle.json","state":"https://pith.science/pith/DP4UMOCTFGOBMTHJMY25RHPUG4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DP4UMOCTFGOBMTHJMY25RHPUG4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DP4UMOCTFGOBMTHJMY25RHPUG4","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":"ab6089b9cca172071cd5561000ec5746c76a95b0f3ea7492eb443411825dc2cf","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-06T08:59:11Z","title_canon_sha256":"cf4b43227ec3fb120049a24adbe90b8cbb1c81594dfded8b0792475d7309bf90"},"schema_version":"1.0","source":{"id":"1703.01765","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01765","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01765v2","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01765","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"DP4UMOCTFGOB","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DP4UMOCTFGOBMTHJ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DP4UMOCT","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:e406faa6a88cb9660b198e73ad09064d4994bbf9f1bc0c1869eb22d7f00329fc","target":"graph","created_at":"2026-05-17T23:43:18Z","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 prove that for a probability measure on $\\mathbb{R}^n$, the Poincar\\'e inequality for convex functions is equivalent to the weak transportation inequality with a quadratic-linear cost. This generalizes recent results by Gozlan et al. and Feldheim et al., concerning probability measures on the real line. The proof relies on modified logarithmic Sobolev inequalities of Bobkov-Ledoux type for convex and concave functions, which are of independent interest. We also present refined concentration inequalities for general (not necessarily Lipschitz) convex functions, complementing recent results b","authors_text":"Micha{\\l} Strzelecki, Rados{\\l}aw Adamczak","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-06T08:59:11Z","title":"On the convex Poincar\\'e inequality and weak transportation inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01765","kind":"arxiv","version":2},"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":"sha256:27fbb2a10125e51c959b71de27fcd0417fa697d74ac62a396435daf1a823e77a","target":"record","created_at":"2026-05-17T23:43:18Z","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":"ab6089b9cca172071cd5561000ec5746c76a95b0f3ea7492eb443411825dc2cf","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-06T08:59:11Z","title_canon_sha256":"cf4b43227ec3fb120049a24adbe90b8cbb1c81594dfded8b0792475d7309bf90"},"schema_version":"1.0","source":{"id":"1703.01765","kind":"arxiv","version":2}},"canonical_sha256":"1bf9463853299c164ce96635d89df4371ee68c95c43944f1ee1a42c40e8d123a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bf9463853299c164ce96635d89df4371ee68c95c43944f1ee1a42c40e8d123a","first_computed_at":"2026-05-17T23:43:18.692426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:18.692426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PFEd+FiO1dqo6sTTrUcxv0VzbL7M+6hcWD4bzWjbK2hmsFLMZ/cL/l11QAzulYgnCxXeGmC/4TOcffQ9UpRIDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:18.693027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01765","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27fbb2a10125e51c959b71de27fcd0417fa697d74ac62a396435daf1a823e77a","sha256:e406faa6a88cb9660b198e73ad09064d4994bbf9f1bc0c1869eb22d7f00329fc"],"state_sha256":"7570694cac527946c80b0bf8dda2314628a4a67f7ea305c2bba385d7c3edc9c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fbPEtuooXPxFCX5eN51HkKGfHImD3YDh3SOMvjYwA7oN3HHnZI4q9zGfzrmnzH2fEWefTx1N3yLAAuhsX69lAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T21:52:47.823308Z","bundle_sha256":"5812baaaa971e6fc316787a5577a5a5ac69c8ba8ab13f85fc43e1a49512cb8c5"}}