{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EREGEC57CK3OU3JC6NVSFCO3XQ","short_pith_number":"pith:EREGEC57","canonical_record":{"source":{"id":"1401.7065","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-28T02:14:13Z","cross_cats_sorted":[],"title_canon_sha256":"717786da9132318a96257fbcc7e4493c29165f45e9c1bacbd0779c72e09d68b5","abstract_canon_sha256":"512e25dbe67899f47511891ebeea56ab2c0b266622d9a00088615c7cd254da02"},"schema_version":"1.0"},"canonical_sha256":"2448620bbf12b6ea6d22f36b2289dbbc3048197a24a6ae1b4dd2f4d5a0d95b70","source":{"kind":"arxiv","id":"1401.7065","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7065","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7065v2","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7065","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"EREGEC57CK3O","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EREGEC57CK3OU3JC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EREGEC57","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EREGEC57CK3OU3JC6NVSFCO3XQ","target":"record","payload":{"canonical_record":{"source":{"id":"1401.7065","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-28T02:14:13Z","cross_cats_sorted":[],"title_canon_sha256":"717786da9132318a96257fbcc7e4493c29165f45e9c1bacbd0779c72e09d68b5","abstract_canon_sha256":"512e25dbe67899f47511891ebeea56ab2c0b266622d9a00088615c7cd254da02"},"schema_version":"1.0"},"canonical_sha256":"2448620bbf12b6ea6d22f36b2289dbbc3048197a24a6ae1b4dd2f4d5a0d95b70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:51.939741Z","signature_b64":"hv0bdnCx7HsEjkiq/Y4AdcGiXbWH0VzQPbIq1IutfD87wXyy8UDYWUcTEY7DYrbYFpA/Ef5P3S94J5TygoqqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2448620bbf12b6ea6d22f36b2289dbbc3048197a24a6ae1b4dd2f4d5a0d95b70","last_reissued_at":"2026-05-18T01:11:51.939404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:51.939404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.7065","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":"2026-05-18T01:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dDE3Txc76FBH0WEFOjfS3xnAXRLQyYKd+kShIZhJYrx2+qBFSj9VtX/vFiiqMNipA2W6rAnxok/EmeLiSRDMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:01:00.345701Z"},"content_sha256":"abac6c35ea9c68cb7b2d932bffb9f1d1bcf949447092658935b380296ad89cb2","schema_version":"1.0","event_id":"sha256:abac6c35ea9c68cb7b2d932bffb9f1d1bcf949447092658935b380296ad89cb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EREGEC57CK3OU3JC6NVSFCO3XQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixed f-divergence and inequalities for log concave functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Elisabeth M. Werner, Umut Caglar","submitted_at":"2014-01-28T02:14:13Z","abstract_excerpt":"Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kullback Leibler divergence for log concave functions. Special cases of $f$-divergences are mixed $L_\\lambda$-affine surface areas for log concave functions. For those, we establish various affine isoperime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7065","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":"2026-05-18T01:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eked3AXaytPrTupw2/BmAFyqqGVpJKN+8LucMwLPyuZblDUbRi2pcG0uaOhWNSvbbfNT/XXx+ZxnCdFVPhLtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:01:00.346052Z"},"content_sha256":"3cab7ee419fefb2b7cded07303bfaee9206f671e21d2b600e6c3345b757ec780","schema_version":"1.0","event_id":"sha256:3cab7ee419fefb2b7cded07303bfaee9206f671e21d2b600e6c3345b757ec780"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EREGEC57CK3OU3JC6NVSFCO3XQ/bundle.json","state_url":"https://pith.science/pith/EREGEC57CK3OU3JC6NVSFCO3XQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EREGEC57CK3OU3JC6NVSFCO3XQ/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":"2026-05-31T03:01:00Z","links":{"resolver":"https://pith.science/pith/EREGEC57CK3OU3JC6NVSFCO3XQ","bundle":"https://pith.science/pith/EREGEC57CK3OU3JC6NVSFCO3XQ/bundle.json","state":"https://pith.science/pith/EREGEC57CK3OU3JC6NVSFCO3XQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EREGEC57CK3OU3JC6NVSFCO3XQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EREGEC57CK3OU3JC6NVSFCO3XQ","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":"512e25dbe67899f47511891ebeea56ab2c0b266622d9a00088615c7cd254da02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-28T02:14:13Z","title_canon_sha256":"717786da9132318a96257fbcc7e4493c29165f45e9c1bacbd0779c72e09d68b5"},"schema_version":"1.0","source":{"id":"1401.7065","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7065","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7065v2","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7065","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"EREGEC57CK3O","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EREGEC57CK3OU3JC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EREGEC57","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:3cab7ee419fefb2b7cded07303bfaee9206f671e21d2b600e6c3345b757ec780","target":"graph","created_at":"2026-05-18T01:11:51Z","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":"Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kullback Leibler divergence for log concave functions. Special cases of $f$-divergences are mixed $L_\\lambda$-affine surface areas for log concave functions. For those, we establish various affine isoperime","authors_text":"Elisabeth M. Werner, Umut Caglar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-28T02:14:13Z","title":"Mixed f-divergence and inequalities for log concave functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7065","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:abac6c35ea9c68cb7b2d932bffb9f1d1bcf949447092658935b380296ad89cb2","target":"record","created_at":"2026-05-18T01:11:51Z","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":"512e25dbe67899f47511891ebeea56ab2c0b266622d9a00088615c7cd254da02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-28T02:14:13Z","title_canon_sha256":"717786da9132318a96257fbcc7e4493c29165f45e9c1bacbd0779c72e09d68b5"},"schema_version":"1.0","source":{"id":"1401.7065","kind":"arxiv","version":2}},"canonical_sha256":"2448620bbf12b6ea6d22f36b2289dbbc3048197a24a6ae1b4dd2f4d5a0d95b70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2448620bbf12b6ea6d22f36b2289dbbc3048197a24a6ae1b4dd2f4d5a0d95b70","first_computed_at":"2026-05-18T01:11:51.939404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:51.939404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hv0bdnCx7HsEjkiq/Y4AdcGiXbWH0VzQPbIq1IutfD87wXyy8UDYWUcTEY7DYrbYFpA/Ef5P3S94J5TygoqqBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:51.939741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7065","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abac6c35ea9c68cb7b2d932bffb9f1d1bcf949447092658935b380296ad89cb2","sha256:3cab7ee419fefb2b7cded07303bfaee9206f671e21d2b600e6c3345b757ec780"],"state_sha256":"611113a61ea8442491f26f68ff0e08279d0247d7f479b8bb7f4795a57cda304b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3443yQMAaffyAzpJ58RxZexa87EuV5qkqDkj21o4FyMf2pe958RG1Ctt1KBr4QEOUYcg0ygn6fUCxIIK/qsOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:01:00.348117Z","bundle_sha256":"ebf32c444d5bc22c93d5480ef413fbe72ddb5bce19d6d324450c7d0b56a6af82"}}