{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JTBGTAF6WASUXTFBZ6TG6DT2LO","short_pith_number":"pith:JTBGTAF6","canonical_record":{"source":{"id":"1903.00214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-01T09:05:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"212d83256dd1617631588ef010268e7d47ffb535ac79c7f607636bcd0b6f8706","abstract_canon_sha256":"49c3ab19bad4459b42b925646bd317add5971fadb4c67f1526085c4c6903cc33"},"schema_version":"1.0"},"canonical_sha256":"4cc26980beb0254bcca1cfa66f0e7a5ba4bc5cabd358386fd6a57aa0444d0aee","source":{"kind":"arxiv","id":"1903.00214","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00214","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00214v1","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00214","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"JTBGTAF6WASU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JTBGTAF6WASUXTFB","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JTBGTAF6","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JTBGTAF6WASUXTFBZ6TG6DT2LO","target":"record","payload":{"canonical_record":{"source":{"id":"1903.00214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-01T09:05:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"212d83256dd1617631588ef010268e7d47ffb535ac79c7f607636bcd0b6f8706","abstract_canon_sha256":"49c3ab19bad4459b42b925646bd317add5971fadb4c67f1526085c4c6903cc33"},"schema_version":"1.0"},"canonical_sha256":"4cc26980beb0254bcca1cfa66f0e7a5ba4bc5cabd358386fd6a57aa0444d0aee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:20.510992Z","signature_b64":"W7oGQj7SwCIivhZTTJraDr7rFiMu9gX1r8OJk643HOm9quDC8XuvE/gOuZc8M0wjQ/SsORAsBlCFv9aeSxD6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cc26980beb0254bcca1cfa66f0e7a5ba4bc5cabd358386fd6a57aa0444d0aee","last_reissued_at":"2026-05-17T23:52:20.510308Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:20.510308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.00214","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":"2026-05-17T23:52:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NQQ1klYjcP1vA8Z2Ff0d0OPT9t2NpDIuyhaWYFmIbNVmN3gPhq/KoCxqcAaFHYLqMOpE8cA9BTEHPpMDN09oCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:52:36.379659Z"},"content_sha256":"ede0f0ed8b096c4f26e1f21c993dfe9ae43c3143534c4a6c81fc85e0d0eecd1d","schema_version":"1.0","event_id":"sha256:ede0f0ed8b096c4f26e1f21c993dfe9ae43c3143534c4a6c81fc85e0d0eecd1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JTBGTAF6WASUXTFBZ6TG6DT2LO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A family of Beckner inequalities under various curvature-dimension conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Ivan Gentil (ICJ), Simon Zugmeyer (ICJ)","submitted_at":"2019-03-01T09:05:10Z","abstract_excerpt":"In this paper, we offer a proof for a family of functional inequalities interpolating between the Poincar{\\'e} and the logarithmic Sobolev (standard and weighted) inequalities. The proofs rely both on entropy flows and on a CD($\\rho$, n) condition, either with $\\rho$ = 0 and n > 0, or with $\\rho$ > 0 and n $\\in$ R. As such, results are valid in the case of a Riemannian manifold, which constitutes a generalization to what was proved in [BGS18, Ngu18]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00214","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":"2026-05-17T23:52:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O3aIft07YC2f6sSPmOh307db+PMsZQSRst8BJVpJKedaIz8eESpdidTduzs4NRH8WoilqMKsjYcC+pG6xtIwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:52:36.380001Z"},"content_sha256":"bbaa0fdb3153bd684f544ff4e547345f338c3489579b151324442f2046bbb9af","schema_version":"1.0","event_id":"sha256:bbaa0fdb3153bd684f544ff4e547345f338c3489579b151324442f2046bbb9af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTBGTAF6WASUXTFBZ6TG6DT2LO/bundle.json","state_url":"https://pith.science/pith/JTBGTAF6WASUXTFBZ6TG6DT2LO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTBGTAF6WASUXTFBZ6TG6DT2LO/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":"2026-07-02T19:52:36Z","links":{"resolver":"https://pith.science/pith/JTBGTAF6WASUXTFBZ6TG6DT2LO","bundle":"https://pith.science/pith/JTBGTAF6WASUXTFBZ6TG6DT2LO/bundle.json","state":"https://pith.science/pith/JTBGTAF6WASUXTFBZ6TG6DT2LO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTBGTAF6WASUXTFBZ6TG6DT2LO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JTBGTAF6WASUXTFBZ6TG6DT2LO","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":"49c3ab19bad4459b42b925646bd317add5971fadb4c67f1526085c4c6903cc33","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-01T09:05:10Z","title_canon_sha256":"212d83256dd1617631588ef010268e7d47ffb535ac79c7f607636bcd0b6f8706"},"schema_version":"1.0","source":{"id":"1903.00214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00214","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00214v1","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00214","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"JTBGTAF6WASU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JTBGTAF6WASUXTFB","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JTBGTAF6","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:bbaa0fdb3153bd684f544ff4e547345f338c3489579b151324442f2046bbb9af","target":"graph","created_at":"2026-05-17T23:52:20Z","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":"In this paper, we offer a proof for a family of functional inequalities interpolating between the Poincar{\\'e} and the logarithmic Sobolev (standard and weighted) inequalities. The proofs rely both on entropy flows and on a CD($\\rho$, n) condition, either with $\\rho$ = 0 and n > 0, or with $\\rho$ > 0 and n $\\in$ R. As such, results are valid in the case of a Riemannian manifold, which constitutes a generalization to what was proved in [BGS18, Ngu18].","authors_text":"Ivan Gentil (ICJ), Simon Zugmeyer (ICJ)","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-01T09:05:10Z","title":"A family of Beckner inequalities under various curvature-dimension conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00214","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:ede0f0ed8b096c4f26e1f21c993dfe9ae43c3143534c4a6c81fc85e0d0eecd1d","target":"record","created_at":"2026-05-17T23:52:20Z","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":"49c3ab19bad4459b42b925646bd317add5971fadb4c67f1526085c4c6903cc33","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-01T09:05:10Z","title_canon_sha256":"212d83256dd1617631588ef010268e7d47ffb535ac79c7f607636bcd0b6f8706"},"schema_version":"1.0","source":{"id":"1903.00214","kind":"arxiv","version":1}},"canonical_sha256":"4cc26980beb0254bcca1cfa66f0e7a5ba4bc5cabd358386fd6a57aa0444d0aee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cc26980beb0254bcca1cfa66f0e7a5ba4bc5cabd358386fd6a57aa0444d0aee","first_computed_at":"2026-05-17T23:52:20.510308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:20.510308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W7oGQj7SwCIivhZTTJraDr7rFiMu9gX1r8OJk643HOm9quDC8XuvE/gOuZc8M0wjQ/SsORAsBlCFv9aeSxD6Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:20.510992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ede0f0ed8b096c4f26e1f21c993dfe9ae43c3143534c4a6c81fc85e0d0eecd1d","sha256:bbaa0fdb3153bd684f544ff4e547345f338c3489579b151324442f2046bbb9af"],"state_sha256":"f0d0e00c58d2df03211a3ef478636f39248c448cb82d7b192b61c2bab9252391"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wPPFyKbgVED2ZFCDLaX+pst64IZDoAAdqkfcfHR4gvbqmpEgpRikTvz04t3/SIot9cNKRDIAWktXpfDoWHzSAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T19:52:36.381929Z","bundle_sha256":"9eb32f6b47b2acb5acebf9c25e4fb3ce2186d568f972895b5dc2a6ded37d0ae5"}}