{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KLREFKTOXNDTJEK3EW33AHAXLA","short_pith_number":"pith:KLREFKTO","canonical_record":{"source":{"id":"2606.27349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-06-25T17:54:49Z","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"47ffec4c4ec232f0e6b16b693d071b7475a93a2926545049ef8690b398ab4c50","abstract_canon_sha256":"ecf0a536bc2b17119517014a2709022a917f83b48281824fe960301a0d1e1a21"},"schema_version":"1.0"},"canonical_sha256":"52e242aa6ebb4734915b25b7b01c17582f0df4333331f6b2c999624729068c06","source":{"kind":"arxiv","id":"2606.27349","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27349","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27349v1","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27349","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"KLREFKTOXNDT","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_16","alias_value":"KLREFKTOXNDTJEK3","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_8","alias_value":"KLREFKTO","created_at":"2026-06-26T01:16:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KLREFKTOXNDTJEK3EW33AHAXLA","target":"record","payload":{"canonical_record":{"source":{"id":"2606.27349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-06-25T17:54:49Z","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"47ffec4c4ec232f0e6b16b693d071b7475a93a2926545049ef8690b398ab4c50","abstract_canon_sha256":"ecf0a536bc2b17119517014a2709022a917f83b48281824fe960301a0d1e1a21"},"schema_version":"1.0"},"canonical_sha256":"52e242aa6ebb4734915b25b7b01c17582f0df4333331f6b2c999624729068c06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:16:19.487596Z","signature_b64":"aMhvBQGp0ysqR6KzmPT14EqywcuKfUvjTnon1DMZjlySgYUJ3JPGQraYrZObau1jf1xQKg6/k8tNjfhXO/vUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52e242aa6ebb4734915b25b7b01c17582f0df4333331f6b2c999624729068c06","last_reissued_at":"2026-06-26T01:16:19.487069Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:16:19.487069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.27349","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":"2026-06-26T01:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Op2pxxIwxLEqr7HEBgm95wAL5nCHutQOEe6wk11yw8+gASVU37QcpaerI1oHgusl+Z8Ht0C7K3RfbmCTbDQMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-09-05T23:20:04.241734Z"},"content_sha256":"ff81ea6babe64b290f8a6dc88a183e0d5ad714b8d4195f693a1ef3209fd1a04a","schema_version":"1.0","event_id":"sha256:ff81ea6babe64b290f8a6dc88a183e0d5ad714b8d4195f693a1ef3209fd1a04a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KLREFKTOXNDTJEK3EW33AHAXLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"All you need is log","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.IT","authors_text":"Akshay Balsubramani","submitted_at":"2026-06-25T17:54:49Z","abstract_excerpt":"Comparing two probability distributions is a basic building block of statistics and machine learning, and the right family is well understood: the R\\'enyi divergences of order $\\alpha\\in[0,\\infty]$ are the unique family monotone under data processing and additive on independent products. Many problems instead compare more than two distributions at once -- multi-population fairness, multi-prior PAC-Bayes bounds, multi-hypothesis testing -- and the right multi-distribution generalization of the R\\'enyi family has been an open question.\n  We characterize it. Every functional of $W$-tuples of dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27349","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27349/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-26T01:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JSX77NGT52v1FFQWzbtFqJazoFGacw1Ou4t7JJPh/ZDXyiGxvDn68Mr6XdkJ+bCetkjVLqe2fNYKXMuQrAXMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-09-05T23:20:04.242241Z"},"content_sha256":"84856747332bded3c59bebb7c7bdcf211afa7e51997cf636a63f960cc175eeeb","schema_version":"1.0","event_id":"sha256:84856747332bded3c59bebb7c7bdcf211afa7e51997cf636a63f960cc175eeeb"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:KLREFKTOXNDTJEK3EW33AHAXLA","target":"integrity","payload":{"note":"Identifier '10.1109/tit.2016.2590465' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"M. Ashok Kumar and Rajesh Sundaresan. Minimization problems based on relativeα-entropy I: forward projection. IEEE Transactions on Information Theory, 62(9):5063–5080, 2016. doi: 10.1109/TIT.2016.2590465","arxiv_id":"2606.27349","detector":"doi_compliance","evidence":{"doi":"10.1109/tit.2016.2590465","arxiv_id":null,"ref_index":29,"raw_excerpt":"M. Ashok Kumar and Rajesh Sundaresan. Minimization problems based on relativeα-entropy I: forward projection. IEEE Transactions on Information Theory, 62(9):5063–5080, 2016. doi: 10.1109/TIT.2016.2590465","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"]},"severity":"critical","ref_index":29,"audited_at":"2026-07-09T14:35:11.194832Z","event_type":"pith.integrity.v1","detected_doi":"10.1109/tit.2016.2590465","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"217b95be112495d2db8a7c57ae0e8395a54e9b1f9fda9798800dcdd1d8127809","paper_version":2,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":9431,"payload_sha256":"893ddcc900c60ae07674d46cc14956ce9e91d8752fad54e80239ef8f6c56fabb","signature_b64":"8aS5YMUVQ254oGZGwvxrfVrMEAKuAfnLFT1s8Z7uzmQtdE8uP97UDz6ACWzOE/zQ2HE1eVYGF7WKZlmLqAaeCg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T14:37:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rLpIR+dGmRp/gARg+9WVY6nmGAh8ybWGltQu7/rjYHHuFThWbWRxbX/XAxmdw/FWp2RaYM5RJGnf6TlqSH3HCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-09-05T23:20:04.246146Z"},"content_sha256":"33b4f13b74625cc288e55d01e8097301c3ff80ea87a54ffa08350045b7355b73","schema_version":"1.0","event_id":"sha256:33b4f13b74625cc288e55d01e8097301c3ff80ea87a54ffa08350045b7355b73"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:KLREFKTOXNDTJEK3EW33AHAXLA","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1109/TIT.2024.3437073.41) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Muhammad Usman Farooq, T obias Fritz, Erkka Haapasalo, and Marco T omamichel. Matrix majorization in large samples. IEEE Transactions on Information Theory, 70(11):3118–3144, 2024. doi: 10.1109/TIT.2024.3437073. 41","arxiv_id":"2606.27349","detector":"doi_compliance","evidence":{"ref_index":16,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"Muhammad Usman Farooq, T obias Fritz, Erkka Haapasalo, and Marco T omamichel. Matrix majorization in large samples. IEEE Transactions on Information Theory, 70(11):3118–3144, 2024. doi: 10.1109/TIT.2024.3437073. 41","reconstructed_doi":"10.1109/TIT.2024.3437073.41"},"severity":"advisory","ref_index":16,"audited_at":"2026-07-09T14:35:11.194832Z","event_type":"pith.integrity.v1","detected_doi":"10.1109/TIT.2024.3437073.41","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"f92a18724914696f4984033bffe32b99ebd386e6603fd3e7e2fffc1e8adf51df","paper_version":2,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":9430,"payload_sha256":"bdab59c9a9e2a06df7424c42c2da7f7c177bf8564146e7084c112ef302b59b16","signature_b64":"++hYImBoz3kA3kxk66JCHCedeTtMN9AZV2nWUMSkuhSxEWRhWBjWSEA4+QEtdwfew92WMKHDmRMCiTZN9tNCCQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T14:37:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+F+761iucD/NRJfWOH+1U6QwzZgTL4Q3FfQVYV9JvWJn1bcrbwocsRlE6UEmgGOBIQkGfSOAXAW4WqK+U18BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-09-05T23:20:04.246523Z"},"content_sha256":"9419e2e438482322603f7244becf709315c92c98df34e895911c67028ba01c9c","schema_version":"1.0","event_id":"sha256:9419e2e438482322603f7244becf709315c92c98df34e895911c67028ba01c9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLREFKTOXNDTJEK3EW33AHAXLA/bundle.json","state_url":"https://pith.science/pith/KLREFKTOXNDTJEK3EW33AHAXLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLREFKTOXNDTJEK3EW33AHAXLA/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":"2026-09-05T23:20:04Z","links":{"resolver":"https://pith.science/pith/KLREFKTOXNDTJEK3EW33AHAXLA","bundle":"https://pith.science/pith/KLREFKTOXNDTJEK3EW33AHAXLA/bundle.json","state":"https://pith.science/pith/KLREFKTOXNDTJEK3EW33AHAXLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLREFKTOXNDTJEK3EW33AHAXLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KLREFKTOXNDTJEK3EW33AHAXLA","merge_version":"pith-open-graph-merge-v1","event_count":4,"valid_event_count":4,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ecf0a536bc2b17119517014a2709022a917f83b48281824fe960301a0d1e1a21","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-06-25T17:54:49Z","title_canon_sha256":"47ffec4c4ec232f0e6b16b693d071b7475a93a2926545049ef8690b398ab4c50"},"schema_version":"1.0","source":{"id":"2606.27349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27349","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27349v1","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27349","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"KLREFKTOXNDT","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_16","alias_value":"KLREFKTOXNDTJEK3","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_8","alias_value":"KLREFKTO","created_at":"2026-06-26T01:16:19Z"}],"graph_snapshots":[{"event_id":"sha256:84856747332bded3c59bebb7c7bdcf211afa7e51997cf636a63f960cc175eeeb","target":"graph","created_at":"2026-06-26T01:16:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.27349/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Comparing two probability distributions is a basic building block of statistics and machine learning, and the right family is well understood: the R\\'enyi divergences of order $\\alpha\\in[0,\\infty]$ are the unique family monotone under data processing and additive on independent products. Many problems instead compare more than two distributions at once -- multi-population fairness, multi-prior PAC-Bayes bounds, multi-hypothesis testing -- and the right multi-distribution generalization of the R\\'enyi family has been an open question.\n  We characterize it. Every functional of $W$-tuples of dist","authors_text":"Akshay Balsubramani","cross_cats":["math.IT","math.PR","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-06-25T17:54:49Z","title":"All you need is log"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27349","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:ff81ea6babe64b290f8a6dc88a183e0d5ad714b8d4195f693a1ef3209fd1a04a","target":"record","created_at":"2026-06-26T01:16:19Z","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":"ecf0a536bc2b17119517014a2709022a917f83b48281824fe960301a0d1e1a21","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-06-25T17:54:49Z","title_canon_sha256":"47ffec4c4ec232f0e6b16b693d071b7475a93a2926545049ef8690b398ab4c50"},"schema_version":"1.0","source":{"id":"2606.27349","kind":"arxiv","version":1}},"canonical_sha256":"52e242aa6ebb4734915b25b7b01c17582f0df4333331f6b2c999624729068c06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52e242aa6ebb4734915b25b7b01c17582f0df4333331f6b2c999624729068c06","first_computed_at":"2026-06-26T01:16:19.487069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:19.487069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMhvBQGp0ysqR6KzmPT14EqywcuKfUvjTnon1DMZjlySgYUJ3JPGQraYrZObau1jf1xQKg6/k8tNjfhXO/vUCA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:19.487596Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27349","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:33b4f13b74625cc288e55d01e8097301c3ff80ea87a54ffa08350045b7355b73","sha256:9419e2e438482322603f7244becf709315c92c98df34e895911c67028ba01c9c"]}],"invalid_events":[],"applied_event_ids":["sha256:ff81ea6babe64b290f8a6dc88a183e0d5ad714b8d4195f693a1ef3209fd1a04a","sha256:84856747332bded3c59bebb7c7bdcf211afa7e51997cf636a63f960cc175eeeb"],"state_sha256":"2085fced49ea1e5a0a45616388d1afef696ad69aa47679e113ca0e3aa274cecd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ANBXtW6efQRG/G6rWk39RnBIbsFmBe/SgQRXP88Ua/zgMtjVBGnRT/Lt/qeIQb+Tab/ApqVKfPmkmsh18VG8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-09-05T23:20:04.248984Z","bundle_sha256":"dc032054a40d9136a0414b2b897c25dbca127f975aa31c9fbda23011339ba728"}}