{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XHTZD6EONTDXPL6MFWXVCJUAOE","short_pith_number":"pith:XHTZD6EO","canonical_record":{"source":{"id":"1711.00668","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-02T09:59:34Z","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"title_canon_sha256":"841e852ed2e6dec1eb9845a5a50f8b635c070e9ab0aa7d0deaf8e7769848b75f","abstract_canon_sha256":"431b36f17ec1eb38fef3ac2f383255756a634f47cbb43b0b39e1bd3a327ed1be"},"schema_version":"1.0"},"canonical_sha256":"b9e791f88e6cc777afcc2daf512680713e3e04e1a3fbb127b320b0a202b88892","source":{"kind":"arxiv","id":"1711.00668","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00668","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00668v3","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00668","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"XHTZD6EONTDX","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XHTZD6EONTDXPL6M","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XHTZD6EO","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XHTZD6EONTDXPL6MFWXVCJUAOE","target":"record","payload":{"canonical_record":{"source":{"id":"1711.00668","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-02T09:59:34Z","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"title_canon_sha256":"841e852ed2e6dec1eb9845a5a50f8b635c070e9ab0aa7d0deaf8e7769848b75f","abstract_canon_sha256":"431b36f17ec1eb38fef3ac2f383255756a634f47cbb43b0b39e1bd3a327ed1be"},"schema_version":"1.0"},"canonical_sha256":"b9e791f88e6cc777afcc2daf512680713e3e04e1a3fbb127b320b0a202b88892","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:50.841750Z","signature_b64":"EG47KZTYNiMYLm5X+fOyyRgg7Xg15aIHgk2zIV6UtRHBWrOO0izLEm/QzKSipz+Oo441fQIklKVYQXrXpMyNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9e791f88e6cc777afcc2daf512680713e3e04e1a3fbb127b320b0a202b88892","last_reissued_at":"2026-05-18T00:21:50.841179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:50.841179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.00668","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yqH/whf7NRFMy901+kdZvSN9mDzI8/wdu5rzFcntWoojLZvctEXLOVWq6MsfQBkPHRGKEDZ5qCH2ZzTr+SPuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:03:56.733113Z"},"content_sha256":"5289056a4f97d274affc55bd1c7344f259937102837e388ad9ef750ab22352ce","schema_version":"1.0","event_id":"sha256:5289056a4f97d274affc55bd1c7344f259937102837e388ad9ef750ab22352ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XHTZD6EONTDXPL6MFWXVCJUAOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the isoperimetric constant, covariance inequalities and $L_p$-Poincar\\'{e} inequalities in dimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Adrien Saumard, Jon A. Wellner","submitted_at":"2017-11-02T09:59:34Z","abstract_excerpt":"Firstly, we derive in dimension one a new covariance inequality of $L_{1}-L_{\\infty}$ type that characterizes the isoperimetric constant as the best constant achieving the inequality. Secondly, we generalize our result to $L_{p}-L_{q}$ bounds for the covariance. Consequently, we recover Cheeger's inequality without using the co-area formula. We also prove a generalized weighted Hardy type inequality that is needed to derive our covariance inequalities and that is of independent interest. Finally, we explore some consequences of our covariance inequalities for $L_{p}$-Poincar\\'{e} inequalities "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00668","kind":"arxiv","version":3},"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":"2026-05-18T00:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8nKNt/DFgmcnBk9AALqrglE2TcTuUu3q0Gpvyds0wvRLVuRzFWI5QgWC1o8vIqj3OG6V7a7wYXJMhi3dRj2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:03:56.733783Z"},"content_sha256":"f5da4e5b258137227d44ad1ae34ccee2dc547499f348ad309227c7f4f127e942","schema_version":"1.0","event_id":"sha256:f5da4e5b258137227d44ad1ae34ccee2dc547499f348ad309227c7f4f127e942"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHTZD6EONTDXPL6MFWXVCJUAOE/bundle.json","state_url":"https://pith.science/pith/XHTZD6EONTDXPL6MFWXVCJUAOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHTZD6EONTDXPL6MFWXVCJUAOE/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":"2026-05-26T11:03:56Z","links":{"resolver":"https://pith.science/pith/XHTZD6EONTDXPL6MFWXVCJUAOE","bundle":"https://pith.science/pith/XHTZD6EONTDXPL6MFWXVCJUAOE/bundle.json","state":"https://pith.science/pith/XHTZD6EONTDXPL6MFWXVCJUAOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHTZD6EONTDXPL6MFWXVCJUAOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XHTZD6EONTDXPL6MFWXVCJUAOE","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":"431b36f17ec1eb38fef3ac2f383255756a634f47cbb43b0b39e1bd3a327ed1be","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-02T09:59:34Z","title_canon_sha256":"841e852ed2e6dec1eb9845a5a50f8b635c070e9ab0aa7d0deaf8e7769848b75f"},"schema_version":"1.0","source":{"id":"1711.00668","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00668","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00668v3","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00668","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"XHTZD6EONTDX","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XHTZD6EONTDXPL6M","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XHTZD6EO","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:f5da4e5b258137227d44ad1ae34ccee2dc547499f348ad309227c7f4f127e942","target":"graph","created_at":"2026-05-18T00:21:50Z","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":"Firstly, we derive in dimension one a new covariance inequality of $L_{1}-L_{\\infty}$ type that characterizes the isoperimetric constant as the best constant achieving the inequality. Secondly, we generalize our result to $L_{p}-L_{q}$ bounds for the covariance. Consequently, we recover Cheeger's inequality without using the co-area formula. We also prove a generalized weighted Hardy type inequality that is needed to derive our covariance inequalities and that is of independent interest. Finally, we explore some consequences of our covariance inequalities for $L_{p}$-Poincar\\'{e} inequalities ","authors_text":"Adrien Saumard, Jon A. Wellner","cross_cats":["math.FA","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-02T09:59:34Z","title":"On the isoperimetric constant, covariance inequalities and $L_p$-Poincar\\'{e} inequalities in dimension one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00668","kind":"arxiv","version":3},"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":"sha256:5289056a4f97d274affc55bd1c7344f259937102837e388ad9ef750ab22352ce","target":"record","created_at":"2026-05-18T00:21:50Z","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":"431b36f17ec1eb38fef3ac2f383255756a634f47cbb43b0b39e1bd3a327ed1be","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-02T09:59:34Z","title_canon_sha256":"841e852ed2e6dec1eb9845a5a50f8b635c070e9ab0aa7d0deaf8e7769848b75f"},"schema_version":"1.0","source":{"id":"1711.00668","kind":"arxiv","version":3}},"canonical_sha256":"b9e791f88e6cc777afcc2daf512680713e3e04e1a3fbb127b320b0a202b88892","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9e791f88e6cc777afcc2daf512680713e3e04e1a3fbb127b320b0a202b88892","first_computed_at":"2026-05-18T00:21:50.841179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:50.841179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EG47KZTYNiMYLm5X+fOyyRgg7Xg15aIHgk2zIV6UtRHBWrOO0izLEm/QzKSipz+Oo441fQIklKVYQXrXpMyNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:50.841750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00668","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5289056a4f97d274affc55bd1c7344f259937102837e388ad9ef750ab22352ce","sha256:f5da4e5b258137227d44ad1ae34ccee2dc547499f348ad309227c7f4f127e942"],"state_sha256":"c2494ec0d10e836b05c5aa6cb150ee26e649f9b0073c26e572475599068dbdbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RYlaCRcwSN1hUZCRne6YD1ooQCv/d7jk7AukAbFBdc0juftbi+QAtFck7eQPz0+ep+3Ia2x5HylGBprr1PxHBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:03:56.737482Z","bundle_sha256":"0134d73fe95d1e927dbc72c15f77527fd7f420f0053c43daf24fc0e639e45673"}}