{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:F7PQXCJ5A7IXLOI7WQZO6RDHS4","short_pith_number":"pith:F7PQXCJ5","canonical_record":{"source":{"id":"0712.4291","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-12-28T17:21:10Z","cross_cats_sorted":[],"title_canon_sha256":"3fd6a7fdd9e98e2a413e430207de851bcfc778d2b7a9ac44e1bb6c7431d69dbc","abstract_canon_sha256":"53d9fe1a5917f53ea0a05d344d17f0871e4a26cb7e609766950d6c33eb1d5f9c"},"schema_version":"1.0"},"canonical_sha256":"2fdf0b893d07d175b91fb432ef4467972a462f3f8361ffdb41228cdd2bff43a5","source":{"kind":"arxiv","id":"0712.4291","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4291","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4291v1","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4291","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"F7PQXCJ5A7IX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"F7PQXCJ5A7IXLOI7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"F7PQXCJ5","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:F7PQXCJ5A7IXLOI7WQZO6RDHS4","target":"record","payload":{"canonical_record":{"source":{"id":"0712.4291","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-12-28T17:21:10Z","cross_cats_sorted":[],"title_canon_sha256":"3fd6a7fdd9e98e2a413e430207de851bcfc778d2b7a9ac44e1bb6c7431d69dbc","abstract_canon_sha256":"53d9fe1a5917f53ea0a05d344d17f0871e4a26cb7e609766950d6c33eb1d5f9c"},"schema_version":"1.0"},"canonical_sha256":"2fdf0b893d07d175b91fb432ef4467972a462f3f8361ffdb41228cdd2bff43a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:27.892547Z","signature_b64":"cjwK4MHvjhGBGhKTOSihoyPgv/lrYfNbiQAMmXDOH2cshLkP9XhXhw0vadqJCoxIIiJAadOEPfOCHVadpaNNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fdf0b893d07d175b91fb432ef4467972a462f3f8361ffdb41228cdd2bff43a5","last_reissued_at":"2026-05-18T03:54:27.892022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:27.892022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.4291","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":"2026-05-18T03:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wzYgwW4wJD0jDujlSYNuaCAYupGtFjb0U4i4eN4gTfco721zy7XLApHHsNmXAVzrS9AlMSi4LCSPkm+LCeekDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T11:59:40.881128Z"},"content_sha256":"c498ca335228397a258a6043eb54a548671c2644fd5849a342080d1da7123777","schema_version":"1.0","event_id":"sha256:c498ca335228397a258a6043eb54a548671c2644fd5849a342080d1da7123777"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:F7PQXCJ5A7IXLOI7WQZO6RDHS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sampling of min-entropy relative to quantum knowledge","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Renato Renner, Robert Koenig","submitted_at":"2007-12-28T17:21:10Z","abstract_excerpt":"Let X_1, ..., X_n be a sequence of n classical random variables and consider a sample of r positions selected at random. Then, except with (exponentially in r) small probability, the min-entropy of the sample is not smaller than, roughly, a fraction r/n of the total min-entropy of all positions X_1, ..., X_n, which is optimal. Here, we show that this statement, originally proven by Vadhan [LNCS, vol. 2729, Springer, 2003] for the purely classical case, is still true if the min-entropy is measured relative to a quantum system. Because min-entropy quantifies the amount of randomness that can be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4291","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":"2026-05-18T03:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5AyYXu372ytvjR0VLN8jJ91KlGP3zsuammGGdr4UeFkaZkDV/SuMwHC1WJNQoPwqGksH2Xoxo4Mc+46m+kFtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T11:59:40.881654Z"},"content_sha256":"7fa50c328d5e9cff4a9ba3903b96d816b051b8797e9098bb7a2bccd3195f7b1f","schema_version":"1.0","event_id":"sha256:7fa50c328d5e9cff4a9ba3903b96d816b051b8797e9098bb7a2bccd3195f7b1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7PQXCJ5A7IXLOI7WQZO6RDHS4/bundle.json","state_url":"https://pith.science/pith/F7PQXCJ5A7IXLOI7WQZO6RDHS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7PQXCJ5A7IXLOI7WQZO6RDHS4/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":"2026-05-24T11:59:40Z","links":{"resolver":"https://pith.science/pith/F7PQXCJ5A7IXLOI7WQZO6RDHS4","bundle":"https://pith.science/pith/F7PQXCJ5A7IXLOI7WQZO6RDHS4/bundle.json","state":"https://pith.science/pith/F7PQXCJ5A7IXLOI7WQZO6RDHS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7PQXCJ5A7IXLOI7WQZO6RDHS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:F7PQXCJ5A7IXLOI7WQZO6RDHS4","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":"53d9fe1a5917f53ea0a05d344d17f0871e4a26cb7e609766950d6c33eb1d5f9c","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-12-28T17:21:10Z","title_canon_sha256":"3fd6a7fdd9e98e2a413e430207de851bcfc778d2b7a9ac44e1bb6c7431d69dbc"},"schema_version":"1.0","source":{"id":"0712.4291","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4291","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4291v1","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4291","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"F7PQXCJ5A7IX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"F7PQXCJ5A7IXLOI7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"F7PQXCJ5","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:7fa50c328d5e9cff4a9ba3903b96d816b051b8797e9098bb7a2bccd3195f7b1f","target":"graph","created_at":"2026-05-18T03:54:27Z","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":"Let X_1, ..., X_n be a sequence of n classical random variables and consider a sample of r positions selected at random. Then, except with (exponentially in r) small probability, the min-entropy of the sample is not smaller than, roughly, a fraction r/n of the total min-entropy of all positions X_1, ..., X_n, which is optimal. Here, we show that this statement, originally proven by Vadhan [LNCS, vol. 2729, Springer, 2003] for the purely classical case, is still true if the min-entropy is measured relative to a quantum system. Because min-entropy quantifies the amount of randomness that can be ","authors_text":"Renato Renner, Robert Koenig","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2007-12-28T17:21:10Z","title":"Sampling of min-entropy relative to quantum knowledge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4291","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:c498ca335228397a258a6043eb54a548671c2644fd5849a342080d1da7123777","target":"record","created_at":"2026-05-18T03:54:27Z","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":"53d9fe1a5917f53ea0a05d344d17f0871e4a26cb7e609766950d6c33eb1d5f9c","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-12-28T17:21:10Z","title_canon_sha256":"3fd6a7fdd9e98e2a413e430207de851bcfc778d2b7a9ac44e1bb6c7431d69dbc"},"schema_version":"1.0","source":{"id":"0712.4291","kind":"arxiv","version":1}},"canonical_sha256":"2fdf0b893d07d175b91fb432ef4467972a462f3f8361ffdb41228cdd2bff43a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fdf0b893d07d175b91fb432ef4467972a462f3f8361ffdb41228cdd2bff43a5","first_computed_at":"2026-05-18T03:54:27.892022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:27.892022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cjwK4MHvjhGBGhKTOSihoyPgv/lrYfNbiQAMmXDOH2cshLkP9XhXhw0vadqJCoxIIiJAadOEPfOCHVadpaNNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:27.892547Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.4291","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c498ca335228397a258a6043eb54a548671c2644fd5849a342080d1da7123777","sha256:7fa50c328d5e9cff4a9ba3903b96d816b051b8797e9098bb7a2bccd3195f7b1f"],"state_sha256":"ff85e9737046e9c2d2474319c1f1fe37d4ce66e333027c4a7220c1d713f1597c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M9tWizFdxEYSyEaicWbcU5jBBVk4XjYXOHUnv0BJgeJBA3rHkqC0UUgvMDAd/tGEv2lX/ijZj0Exc5wSdhVtAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T11:59:40.885428Z","bundle_sha256":"d5819b8553c554f73a5ec510dc3a9f807e55cd47b949713662120d82e2023924"}}