{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5Z2EX6B37QAOVO6BSF2N2KOXOO","short_pith_number":"pith:5Z2EX6B3","canonical_record":{"source":{"id":"1001.4668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-01-26T12:17:14Z","cross_cats_sorted":[],"title_canon_sha256":"6121187ecbfbe2e5af6016c160852c454a0f82796511e1f0cf5f37e3f942d08f","abstract_canon_sha256":"574dbce2abad94ad7fb35ca91349248e00e6cec23ad13cda1a847f5d52351819"},"schema_version":"1.0"},"canonical_sha256":"ee744bf83bfc00eabbc19174dd29d7739af59b5d13ca35d1dd8b971741bf7240","source":{"kind":"arxiv","id":"1001.4668","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4668","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4668v2","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4668","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"5Z2EX6B37QAO","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5Z2EX6B37QAOVO6B","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5Z2EX6B3","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5Z2EX6B37QAOVO6BSF2N2KOXOO","target":"record","payload":{"canonical_record":{"source":{"id":"1001.4668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-01-26T12:17:14Z","cross_cats_sorted":[],"title_canon_sha256":"6121187ecbfbe2e5af6016c160852c454a0f82796511e1f0cf5f37e3f942d08f","abstract_canon_sha256":"574dbce2abad94ad7fb35ca91349248e00e6cec23ad13cda1a847f5d52351819"},"schema_version":"1.0"},"canonical_sha256":"ee744bf83bfc00eabbc19174dd29d7739af59b5d13ca35d1dd8b971741bf7240","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:47.252293Z","signature_b64":"uaAsaJvXaMAVFnyqtC0OGCw15oNEffGcmDGnTxB/cmR/jE3OkrkBK7KtAeMdYRhpRxWrQAKnDb8dl5z3iBUeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee744bf83bfc00eabbc19174dd29d7739af59b5d13ca35d1dd8b971741bf7240","last_reissued_at":"2026-05-18T04:13:47.251667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:47.251667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.4668","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":"2026-05-18T04:13:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8Hd7QNGGjMZhfl5vheAjewsQ9TB5q9l6E2Y69ddOo5zdsKWe0mEkgDSrhTFthqySp6l8Leal+vBJyz5FMbmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:14:58.322337Z"},"content_sha256":"52325fdf4feab7defd421031925df947eabb2871a161a2454b35b1fe09432506","schema_version":"1.0","event_id":"sha256:52325fdf4feab7defd421031925df947eabb2871a161a2454b35b1fe09432506"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5Z2EX6B37QAOVO6BSF2N2KOXOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropic Uncertainty Relations in Quantum Physics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Iwo Bialynicki-Birula, Lukasz Rudnicki","submitted_at":"2010-01-26T12:17:14Z","abstract_excerpt":"Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the R\\'enyi and the Shannon entropies. The advantages of these entropic uncertainty relations are pointed out and their more direct connection to the observed phenomena is emphasized. Several remaining open problems are mentioned"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4668","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":"2026-05-18T04:13:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"drchzPpYl6cZ9+4SF+BcuD2nVOSpHivWOV/P3SGYbtdIOJyNZtnUyMWaEKRNhzw/oBatL+jAJ3teUEYMfGibBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:14:58.322988Z"},"content_sha256":"b6464e0c87d9898c10295ef483f33a1d83ca88d213851a4642a36548e0f7ae7f","schema_version":"1.0","event_id":"sha256:b6464e0c87d9898c10295ef483f33a1d83ca88d213851a4642a36548e0f7ae7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Z2EX6B37QAOVO6BSF2N2KOXOO/bundle.json","state_url":"https://pith.science/pith/5Z2EX6B37QAOVO6BSF2N2KOXOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Z2EX6B37QAOVO6BSF2N2KOXOO/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":"2026-06-01T04:14:58Z","links":{"resolver":"https://pith.science/pith/5Z2EX6B37QAOVO6BSF2N2KOXOO","bundle":"https://pith.science/pith/5Z2EX6B37QAOVO6BSF2N2KOXOO/bundle.json","state":"https://pith.science/pith/5Z2EX6B37QAOVO6BSF2N2KOXOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Z2EX6B37QAOVO6BSF2N2KOXOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5Z2EX6B37QAOVO6BSF2N2KOXOO","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":"574dbce2abad94ad7fb35ca91349248e00e6cec23ad13cda1a847f5d52351819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-01-26T12:17:14Z","title_canon_sha256":"6121187ecbfbe2e5af6016c160852c454a0f82796511e1f0cf5f37e3f942d08f"},"schema_version":"1.0","source":{"id":"1001.4668","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4668","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4668v2","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4668","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"5Z2EX6B37QAO","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5Z2EX6B37QAOVO6B","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5Z2EX6B3","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:b6464e0c87d9898c10295ef483f33a1d83ca88d213851a4642a36548e0f7ae7f","target":"graph","created_at":"2026-05-18T04:13:47Z","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":"Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the R\\'enyi and the Shannon entropies. The advantages of these entropic uncertainty relations are pointed out and their more direct connection to the observed phenomena is emphasized. Several remaining open problems are mentioned","authors_text":"Iwo Bialynicki-Birula, Lukasz Rudnicki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-01-26T12:17:14Z","title":"Entropic Uncertainty Relations in Quantum Physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4668","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":"sha256:52325fdf4feab7defd421031925df947eabb2871a161a2454b35b1fe09432506","target":"record","created_at":"2026-05-18T04:13:47Z","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":"574dbce2abad94ad7fb35ca91349248e00e6cec23ad13cda1a847f5d52351819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-01-26T12:17:14Z","title_canon_sha256":"6121187ecbfbe2e5af6016c160852c454a0f82796511e1f0cf5f37e3f942d08f"},"schema_version":"1.0","source":{"id":"1001.4668","kind":"arxiv","version":2}},"canonical_sha256":"ee744bf83bfc00eabbc19174dd29d7739af59b5d13ca35d1dd8b971741bf7240","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee744bf83bfc00eabbc19174dd29d7739af59b5d13ca35d1dd8b971741bf7240","first_computed_at":"2026-05-18T04:13:47.251667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:47.251667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uaAsaJvXaMAVFnyqtC0OGCw15oNEffGcmDGnTxB/cmR/jE3OkrkBK7KtAeMdYRhpRxWrQAKnDb8dl5z3iBUeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:47.252293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.4668","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52325fdf4feab7defd421031925df947eabb2871a161a2454b35b1fe09432506","sha256:b6464e0c87d9898c10295ef483f33a1d83ca88d213851a4642a36548e0f7ae7f"],"state_sha256":"67acca0b50c33e9c11c4e1a168203e5b218cbfb5b180b0dfc64623929d03d543"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NxQBrQgsfEBDMZvPqRgE8M+0sPwIFq2LF4Ygnco4Gd4q3NlXubvyLZyox0g5JVvDjCTsfNXZxz3mjrTsmMoMDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:14:58.325891Z","bundle_sha256":"b9ee146aaae0c50beeb9eb4c63c23cfaa3d3d40189e0b6884606e58902e377b8"}}