{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4FUBMAYRDYAYWA4RGX75N6AV5E","short_pith_number":"pith:4FUBMAYR","canonical_record":{"source":{"id":"2607.15210","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-16T17:08:47Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"ce66c0a1a0f6ec03dc420adfe861d4e7773bfde757692ad89eff055f30c51f88","abstract_canon_sha256":"d32cd2d95f3d3831f0f3bc142ffdb2b59ed8a0885242876cedc47d7c24fd116a"},"schema_version":"1.0"},"canonical_sha256":"e1681603111e018b039135ffd6f815e9000e72acc3eab7e918a533a9e3c42ba2","source":{"kind":"arxiv","id":"2607.15210","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.15210","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.15210v1","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15210","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"pith_short_12","alias_value":"4FUBMAYRDYAY","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"pith_short_16","alias_value":"4FUBMAYRDYAYWA4R","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"pith_short_8","alias_value":"4FUBMAYR","created_at":"2026-07-17T01:22:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4FUBMAYRDYAYWA4RGX75N6AV5E","target":"record","payload":{"canonical_record":{"source":{"id":"2607.15210","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-16T17:08:47Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"ce66c0a1a0f6ec03dc420adfe861d4e7773bfde757692ad89eff055f30c51f88","abstract_canon_sha256":"d32cd2d95f3d3831f0f3bc142ffdb2b59ed8a0885242876cedc47d7c24fd116a"},"schema_version":"1.0"},"canonical_sha256":"e1681603111e018b039135ffd6f815e9000e72acc3eab7e918a533a9e3c42ba2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:22:14.725131Z","signature_b64":"W51IQi29Oe0yMhK6v6U3yBskNUD+1ZEygPbYHkWdU627U0b2tSpuCTzVX/z6YrKLoH0L+B4bIx6a1WzG3AgZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1681603111e018b039135ffd6f815e9000e72acc3eab7e918a533a9e3c42ba2","last_reissued_at":"2026-07-17T01:22:14.724284Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:22:14.724284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.15210","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":"2026-07-17T01:22:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SBdJIglYARm8TMO2HAbT/zHlJfwrImbjKM+vHyez++Dyp43UgUtfYzyL+ALOcvuE3OFqkg1M8KJ4rDW1KQXNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:59:13.400029Z"},"content_sha256":"40530f42bce62af7ea65d06b89c2be70d00151bae5eb880306ef8e4e26ee91ec","schema_version":"1.0","event_id":"sha256:40530f42bce62af7ea65d06b89c2be70d00151bae5eb880306ef8e4e26ee91ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4FUBMAYRDYAYWA4RGX75N6AV5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counterexamples to additivity of minimum output $p$-R\\'enyi entropy of quantum channels for $p>3/4$ and $0\\leq p<1/4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Benjamin Lovitz, Debbie Leung, Peixue Wu","submitted_at":"2026-07-16T17:08:47Z","abstract_excerpt":"Additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every R\\'enyi order $p>1$, at the von Neumann point $p=1$, and near $p=0$, while most of the interval $0<p<1$ has remained open. We prove that for every R\\'enyi order $p$ satisfying either $p>3/4$ or $0\\leq p<1/4$, there exist finite-dimensional projection-induced quantum channels such that additivity of the minimum output $p$-R\\'enyi entropy fails. The proof combines two correlated random-projection constructions: a product-conjugate Bell-state witness for $p>3/4$, and a trans"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15210","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/2607.15210/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":"2026-07-17T01:22:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"huuJe6ODinv3g4sWkEq1bgYiKc3n5wYvuNJOgDnRzIjYgVaaI7exMwp5HXCftRRcHpT7DUSuBvlw3QcsAFSMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:59:13.400556Z"},"content_sha256":"1439f5e8c75a3d064b0e319e5348a66467577eb7b0706e69586d7b69950e44ff","schema_version":"1.0","event_id":"sha256:1439f5e8c75a3d064b0e319e5348a66467577eb7b0706e69586d7b69950e44ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FUBMAYRDYAYWA4RGX75N6AV5E/bundle.json","state_url":"https://pith.science/pith/4FUBMAYRDYAYWA4RGX75N6AV5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FUBMAYRDYAYWA4RGX75N6AV5E/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":"2026-08-04T19:59:13Z","links":{"resolver":"https://pith.science/pith/4FUBMAYRDYAYWA4RGX75N6AV5E","bundle":"https://pith.science/pith/4FUBMAYRDYAYWA4RGX75N6AV5E/bundle.json","state":"https://pith.science/pith/4FUBMAYRDYAYWA4RGX75N6AV5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FUBMAYRDYAYWA4RGX75N6AV5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4FUBMAYRDYAYWA4RGX75N6AV5E","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":"d32cd2d95f3d3831f0f3bc142ffdb2b59ed8a0885242876cedc47d7c24fd116a","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-16T17:08:47Z","title_canon_sha256":"ce66c0a1a0f6ec03dc420adfe861d4e7773bfde757692ad89eff055f30c51f88"},"schema_version":"1.0","source":{"id":"2607.15210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.15210","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.15210v1","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15210","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"pith_short_12","alias_value":"4FUBMAYRDYAY","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"pith_short_16","alias_value":"4FUBMAYRDYAYWA4R","created_at":"2026-07-17T01:22:14Z"},{"alias_kind":"pith_short_8","alias_value":"4FUBMAYR","created_at":"2026-07-17T01:22:14Z"}],"graph_snapshots":[{"event_id":"sha256:1439f5e8c75a3d064b0e319e5348a66467577eb7b0706e69586d7b69950e44ff","target":"graph","created_at":"2026-07-17T01:22:14Z","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/2607.15210/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every R\\'enyi order $p>1$, at the von Neumann point $p=1$, and near $p=0$, while most of the interval $0<p<1$ has remained open. We prove that for every R\\'enyi order $p$ satisfying either $p>3/4$ or $0\\leq p<1/4$, there exist finite-dimensional projection-induced quantum channels such that additivity of the minimum output $p$-R\\'enyi entropy fails. The proof combines two correlated random-projection constructions: a product-conjugate Bell-state witness for $p>3/4$, and a trans","authors_text":"Benjamin Lovitz, Debbie Leung, Peixue Wu","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-16T17:08:47Z","title":"Counterexamples to additivity of minimum output $p$-R\\'enyi entropy of quantum channels for $p>3/4$ and $0\\leq p<1/4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15210","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":"sha256:40530f42bce62af7ea65d06b89c2be70d00151bae5eb880306ef8e4e26ee91ec","target":"record","created_at":"2026-07-17T01:22:14Z","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":"d32cd2d95f3d3831f0f3bc142ffdb2b59ed8a0885242876cedc47d7c24fd116a","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-16T17:08:47Z","title_canon_sha256":"ce66c0a1a0f6ec03dc420adfe861d4e7773bfde757692ad89eff055f30c51f88"},"schema_version":"1.0","source":{"id":"2607.15210","kind":"arxiv","version":1}},"canonical_sha256":"e1681603111e018b039135ffd6f815e9000e72acc3eab7e918a533a9e3c42ba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1681603111e018b039135ffd6f815e9000e72acc3eab7e918a533a9e3c42ba2","first_computed_at":"2026-07-17T01:22:14.724284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:22:14.724284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W51IQi29Oe0yMhK6v6U3yBskNUD+1ZEygPbYHkWdU627U0b2tSpuCTzVX/z6YrKLoH0L+B4bIx6a1WzG3AgZCw==","signature_status":"signed_v1","signed_at":"2026-07-17T01:22:14.725131Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.15210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40530f42bce62af7ea65d06b89c2be70d00151bae5eb880306ef8e4e26ee91ec","sha256:1439f5e8c75a3d064b0e319e5348a66467577eb7b0706e69586d7b69950e44ff"],"state_sha256":"bbeb96fc5819941aa46126866e7b21b563cd3371a6e068c52cc16a0369b2e8fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElhVsSPRxVfBIohUz6YcwGVtE1bYNdTjabEvdnXBPQ2bEdt+3/XwKPk4/KXMUVhmLl4J1So54EqlQfHYZIm2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:59:13.404628Z","bundle_sha256":"92f552cdc094670b577d1db72f855d89996cbcdb4b38e3486ca1874d04e59508"}}