{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:S7RNJZCOOMADIEAER7OE7YBW5C","short_pith_number":"pith:S7RNJZCO","canonical_record":{"source":{"id":"2608.04947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T15:15:19Z","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"title_canon_sha256":"933879fe355465813d20281e747acf5a4a2a038740e0629b071d29e884e8a67d","abstract_canon_sha256":"a230bbac48b1e96628c6ea95eda677a305e263b9f0947307ee3237c86770b246"},"schema_version":"1.0"},"canonical_sha256":"97e2d4e44e73003410048fdc4fe036e89d0ac9b74250f012be5ee652afd84018","source":{"kind":"arxiv","id":"2608.04947","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04947","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04947v1","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04947","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"S7RNJZCOOMAD","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"pith_short_16","alias_value":"S7RNJZCOOMADIEAE","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"pith_short_8","alias_value":"S7RNJZCO","created_at":"2026-08-06T01:47:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:S7RNJZCOOMADIEAER7OE7YBW5C","target":"record","payload":{"canonical_record":{"source":{"id":"2608.04947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T15:15:19Z","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"title_canon_sha256":"933879fe355465813d20281e747acf5a4a2a038740e0629b071d29e884e8a67d","abstract_canon_sha256":"a230bbac48b1e96628c6ea95eda677a305e263b9f0947307ee3237c86770b246"},"schema_version":"1.0"},"canonical_sha256":"97e2d4e44e73003410048fdc4fe036e89d0ac9b74250f012be5ee652afd84018","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:47:45.291331Z","signature_b64":"zQLi4dA5XoNcVwp/OKOMaRS99ZXSwInCaUqusla2NSJl4iQHgxRShyGOjPIC8ru3isYVEHS/xrv7KXBS6wSiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97e2d4e44e73003410048fdc4fe036e89d0ac9b74250f012be5ee652afd84018","last_reissued_at":"2026-08-06T01:47:45.289857Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:47:45.289857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.04947","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":"2026-08-06T01:47:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6JbmYUgRhxQpXd9TUbLXjUtKd4i5V3oAFg3bXBuUZ/fLbaXr/tiHkJ5ZxpEUFKBn4f6z8DEJzI5TLpA71ZUkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:49:25.192088Z"},"content_sha256":"d44587c87cfd10fd97d977cbf0d6ff6b934b8f8a58e49e6d7d566191f4aeb5f0","schema_version":"1.0","event_id":"sha256:d44587c87cfd10fd97d977cbf0d6ff6b934b8f8a58e49e6d7d566191f4aeb5f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:S7RNJZCOOMADIEAER7OE7YBW5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp Continuity of Petz and Sandwiched R\\'enyi Conditional Entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"primary_cat":"quant-ph","authors_text":"Hao-Chung Cheng, Po-Chieh Liu","submitted_at":"2026-08-05T15:15:19Z","abstract_excerpt":"We determine the sharp modulus of continuity, in trace distance, of the optimized Petz and sandwiched R\\'enyi conditional entropies for every order $\\alpha\\in[\\frac12,1)$. If two bipartite states are within trace distance $\\delta$, then both conditional entropies differ by at most $\\frac{1}{1-\\alpha}\n  \\log[(1-\\varepsilon)^{\\alpha}\n  +(D-1)^{1-\\alpha}\\varepsilon^{\\alpha}]$, where $\\varepsilon := \\min\\{\\delta,1-1/D\\}$ and $D$ is the effective dimension, given by the dimension of the first subsystem times the largest possible Schmidt rank. For every distance constraint $\\delta\\in[0,1]$, the boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04947","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/2608.04947/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":"2026-08-06T01:47:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iu10xLW9VmjsiiLeHAaMxsCkIk3SvqfX0IybCPCD6VZxlezzMWF1WXMwrDAEH7Ptd44KYAtCrMVvDDJ6rCqwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:49:25.192651Z"},"content_sha256":"f0ba27a29c58eee243ca162afc26346ba0b82f252e00e6a564ed4e4f125b983b","schema_version":"1.0","event_id":"sha256:f0ba27a29c58eee243ca162afc26346ba0b82f252e00e6a564ed4e4f125b983b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7RNJZCOOMADIEAER7OE7YBW5C/bundle.json","state_url":"https://pith.science/pith/S7RNJZCOOMADIEAER7OE7YBW5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7RNJZCOOMADIEAER7OE7YBW5C/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":"2026-08-16T21:49:25Z","links":{"resolver":"https://pith.science/pith/S7RNJZCOOMADIEAER7OE7YBW5C","bundle":"https://pith.science/pith/S7RNJZCOOMADIEAER7OE7YBW5C/bundle.json","state":"https://pith.science/pith/S7RNJZCOOMADIEAER7OE7YBW5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7RNJZCOOMADIEAER7OE7YBW5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S7RNJZCOOMADIEAER7OE7YBW5C","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":"a230bbac48b1e96628c6ea95eda677a305e263b9f0947307ee3237c86770b246","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T15:15:19Z","title_canon_sha256":"933879fe355465813d20281e747acf5a4a2a038740e0629b071d29e884e8a67d"},"schema_version":"1.0","source":{"id":"2608.04947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04947","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04947v1","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04947","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"S7RNJZCOOMAD","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"pith_short_16","alias_value":"S7RNJZCOOMADIEAE","created_at":"2026-08-06T01:47:45Z"},{"alias_kind":"pith_short_8","alias_value":"S7RNJZCO","created_at":"2026-08-06T01:47:45Z"}],"graph_snapshots":[{"event_id":"sha256:f0ba27a29c58eee243ca162afc26346ba0b82f252e00e6a564ed4e4f125b983b","target":"graph","created_at":"2026-08-06T01:47:45Z","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/2608.04947/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the sharp modulus of continuity, in trace distance, of the optimized Petz and sandwiched R\\'enyi conditional entropies for every order $\\alpha\\in[\\frac12,1)$. If two bipartite states are within trace distance $\\delta$, then both conditional entropies differ by at most $\\frac{1}{1-\\alpha}\n  \\log[(1-\\varepsilon)^{\\alpha}\n  +(D-1)^{1-\\alpha}\\varepsilon^{\\alpha}]$, where $\\varepsilon := \\min\\{\\delta,1-1/D\\}$ and $D$ is the effective dimension, given by the dimension of the first subsystem times the largest possible Schmidt rank. For every distance constraint $\\delta\\in[0,1]$, the boun","authors_text":"Hao-Chung Cheng, Po-Chieh Liu","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T15:15:19Z","title":"Sharp Continuity of Petz and Sandwiched R\\'enyi Conditional Entropies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04947","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:d44587c87cfd10fd97d977cbf0d6ff6b934b8f8a58e49e6d7d566191f4aeb5f0","target":"record","created_at":"2026-08-06T01:47:45Z","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":"a230bbac48b1e96628c6ea95eda677a305e263b9f0947307ee3237c86770b246","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T15:15:19Z","title_canon_sha256":"933879fe355465813d20281e747acf5a4a2a038740e0629b071d29e884e8a67d"},"schema_version":"1.0","source":{"id":"2608.04947","kind":"arxiv","version":1}},"canonical_sha256":"97e2d4e44e73003410048fdc4fe036e89d0ac9b74250f012be5ee652afd84018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97e2d4e44e73003410048fdc4fe036e89d0ac9b74250f012be5ee652afd84018","first_computed_at":"2026-08-06T01:47:45.289857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-06T01:47:45.289857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zQLi4dA5XoNcVwp/OKOMaRS99ZXSwInCaUqusla2NSJl4iQHgxRShyGOjPIC8ru3isYVEHS/xrv7KXBS6wSiAQ==","signature_status":"signed_v1","signed_at":"2026-08-06T01:47:45.291331Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.04947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d44587c87cfd10fd97d977cbf0d6ff6b934b8f8a58e49e6d7d566191f4aeb5f0","sha256:f0ba27a29c58eee243ca162afc26346ba0b82f252e00e6a564ed4e4f125b983b"],"state_sha256":"0245524d8bbd2ce41eec8313f8c65e6c36d5a231a05c2787ab9cd8a4be98d5f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wDJ2SP2cEINXeB7CuJ4ZOQrpetsahg/lWvs3Wk7sxp9MvRm48A1oGQtSb6Bd4NVkypOHHFT3tcyizsIgwOa0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T21:49:25.196452Z","bundle_sha256":"a219f13a6e39f939c76449d7048b766cf7ef72ceaa104fe7a31f94120cf7b329"}}