{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UV6E7JJWYNO3M6KFGYRTNUTIHE","short_pith_number":"pith:UV6E7JJW","canonical_record":{"source":{"id":"1407.4910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-18T08:25:18Z","cross_cats_sorted":[],"title_canon_sha256":"83728f91ba0fc4f65b73f069d86f378bf1787175b0aec21badc40960d14f2510","abstract_canon_sha256":"114e148341ed61ab467649304583b145532e186eebb0de61b944f1cb8c7832e4"},"schema_version":"1.0"},"canonical_sha256":"a57c4fa536c35db67945362336d268390e02a141b2cef559d2d09a955c6f37c1","source":{"kind":"arxiv","id":"1407.4910","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4910","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4910v2","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4910","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"UV6E7JJWYNO3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UV6E7JJWYNO3M6KF","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UV6E7JJW","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UV6E7JJWYNO3M6KFGYRTNUTIHE","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-18T08:25:18Z","cross_cats_sorted":[],"title_canon_sha256":"83728f91ba0fc4f65b73f069d86f378bf1787175b0aec21badc40960d14f2510","abstract_canon_sha256":"114e148341ed61ab467649304583b145532e186eebb0de61b944f1cb8c7832e4"},"schema_version":"1.0"},"canonical_sha256":"a57c4fa536c35db67945362336d268390e02a141b2cef559d2d09a955c6f37c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:48.377140Z","signature_b64":"lLiVGNQ7Hh5jAODHPRhL2Wj+FS6eqfRJgbfawmGT+miU97c14ubvJMOf92UEyTJpB6KNNRe4lGiCCTKE12D+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a57c4fa536c35db67945362336d268390e02a141b2cef559d2d09a955c6f37c1","last_reissued_at":"2026-05-18T00:54:48.376749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:48.376749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4910","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":"2026-05-18T00:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WG2QZu1XPIQHOKzGOF/8PQIc9IBXBBdX36gAAPt46Va88i8tSWIN8w22iNLB0orAlh2XSreowxCUMorar/J0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:45:46.464077Z"},"content_sha256":"4316a2b59dc0882afdc7b033d4abd3c9f5743f00129d8feeaf3004b40e57126e","schema_version":"1.0","event_id":"sha256:4316a2b59dc0882afdc7b033d4abd3c9f5743f00129d8feeaf3004b40e57126e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UV6E7JJWYNO3M6KFGYRTNUTIHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak Poincar\\'e Inequality for Convolution Probability Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Li-Juan Cheng, Shao-Qin Zhang","submitted_at":"2014-07-18T08:25:18Z","abstract_excerpt":"By using Lyapunov conditions, weak Poincar\\'e inequalities are established for some probability measures on a manifold $(M,g)$. These results are further applied to the convolution of two probability measures on $\\R^d$. Along with explicit results we study concrete examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4910","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":"2026-05-18T00:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XEENGbDPMBBdctkhwed1dd3x0AXM72Imc395dusiQODiCPfvxzYk77CA8G1vpcjGZrdLPJcsEJoiZujjKUq3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:45:46.464436Z"},"content_sha256":"eae7a4955d703a023b89b114e856f9d4ed6e1ad3f7626a84d16f429ab0e9f510","schema_version":"1.0","event_id":"sha256:eae7a4955d703a023b89b114e856f9d4ed6e1ad3f7626a84d16f429ab0e9f510"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UV6E7JJWYNO3M6KFGYRTNUTIHE/bundle.json","state_url":"https://pith.science/pith/UV6E7JJWYNO3M6KFGYRTNUTIHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UV6E7JJWYNO3M6KFGYRTNUTIHE/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":"2026-06-25T19:45:46Z","links":{"resolver":"https://pith.science/pith/UV6E7JJWYNO3M6KFGYRTNUTIHE","bundle":"https://pith.science/pith/UV6E7JJWYNO3M6KFGYRTNUTIHE/bundle.json","state":"https://pith.science/pith/UV6E7JJWYNO3M6KFGYRTNUTIHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UV6E7JJWYNO3M6KFGYRTNUTIHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UV6E7JJWYNO3M6KFGYRTNUTIHE","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":"114e148341ed61ab467649304583b145532e186eebb0de61b944f1cb8c7832e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-18T08:25:18Z","title_canon_sha256":"83728f91ba0fc4f65b73f069d86f378bf1787175b0aec21badc40960d14f2510"},"schema_version":"1.0","source":{"id":"1407.4910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4910","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4910v2","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4910","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"UV6E7JJWYNO3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UV6E7JJWYNO3M6KF","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UV6E7JJW","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:eae7a4955d703a023b89b114e856f9d4ed6e1ad3f7626a84d16f429ab0e9f510","target":"graph","created_at":"2026-05-18T00:54:48Z","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":"By using Lyapunov conditions, weak Poincar\\'e inequalities are established for some probability measures on a manifold $(M,g)$. These results are further applied to the convolution of two probability measures on $\\R^d$. Along with explicit results we study concrete examples.","authors_text":"Li-Juan Cheng, Shao-Qin Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-18T08:25:18Z","title":"Weak Poincar\\'e Inequality for Convolution Probability Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4910","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":"sha256:4316a2b59dc0882afdc7b033d4abd3c9f5743f00129d8feeaf3004b40e57126e","target":"record","created_at":"2026-05-18T00:54:48Z","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":"114e148341ed61ab467649304583b145532e186eebb0de61b944f1cb8c7832e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-18T08:25:18Z","title_canon_sha256":"83728f91ba0fc4f65b73f069d86f378bf1787175b0aec21badc40960d14f2510"},"schema_version":"1.0","source":{"id":"1407.4910","kind":"arxiv","version":2}},"canonical_sha256":"a57c4fa536c35db67945362336d268390e02a141b2cef559d2d09a955c6f37c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a57c4fa536c35db67945362336d268390e02a141b2cef559d2d09a955c6f37c1","first_computed_at":"2026-05-18T00:54:48.376749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:48.376749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lLiVGNQ7Hh5jAODHPRhL2Wj+FS6eqfRJgbfawmGT+miU97c14ubvJMOf92UEyTJpB6KNNRe4lGiCCTKE12D+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:48.377140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4316a2b59dc0882afdc7b033d4abd3c9f5743f00129d8feeaf3004b40e57126e","sha256:eae7a4955d703a023b89b114e856f9d4ed6e1ad3f7626a84d16f429ab0e9f510"],"state_sha256":"2dcbaae6f2f5b3a5ba7c839f9c99d7d3cfdcbae067c0cab4ff13474da6335b41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5+gxNaHnVM01tDyHrDaqDWHAxQ1nsL/7MxSSCHlwJnTeda/TN5EogQ1UgaNrOJv5pB8vI+i/lGZTW8sePVs7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:45:46.466817Z","bundle_sha256":"ee117209f7d9efb88e956b43487bc6551e77f5c30e2c8c10cbb27fc8ddda66b2"}}