{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2CHOEESJYSDZXVMGUF26ZNGMQ3","short_pith_number":"pith:2CHOEESJ","canonical_record":{"source":{"id":"1202.4810","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-22T02:56:55Z","cross_cats_sorted":[],"title_canon_sha256":"2a1d1d5af46dee2200521d38dc14bbcfb7720ed8c908e7dfe11b4c20ee816fe9","abstract_canon_sha256":"84492ac1a01265a7c2b2ef42be1c03629583ab0781c8a06fc253374dca3d6fca"},"schema_version":"1.0"},"canonical_sha256":"d08ee21249c4879bd586a175ecb4cc86d9cfb50b7898a3095a043baaf82aa35e","source":{"kind":"arxiv","id":"1202.4810","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4810","created_at":"2026-05-18T01:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4810v3","created_at":"2026-05-18T01:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4810","created_at":"2026-05-18T01:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"2CHOEESJYSDZ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2CHOEESJYSDZXVMG","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2CHOEESJ","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2CHOEESJYSDZXVMGUF26ZNGMQ3","target":"record","payload":{"canonical_record":{"source":{"id":"1202.4810","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-22T02:56:55Z","cross_cats_sorted":[],"title_canon_sha256":"2a1d1d5af46dee2200521d38dc14bbcfb7720ed8c908e7dfe11b4c20ee816fe9","abstract_canon_sha256":"84492ac1a01265a7c2b2ef42be1c03629583ab0781c8a06fc253374dca3d6fca"},"schema_version":"1.0"},"canonical_sha256":"d08ee21249c4879bd586a175ecb4cc86d9cfb50b7898a3095a043baaf82aa35e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:22.592073Z","signature_b64":"X5A6aY8E+65sDb+qe2Og58tRNZo/PhbkrNg2UOekYv9IyuZo4p4YlkbSto/kk2SKAi4m9THwr+mw0ePea8IUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d08ee21249c4879bd586a175ecb4cc86d9cfb50b7898a3095a043baaf82aa35e","last_reissued_at":"2026-05-18T01:58:22.591574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:22.591574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.4810","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6zlWOE5I3/mwTWk9175lU+dKbIgehmSoxjmkBMudSjX7byKN+vB0sgf1lTFs6kpqT3rhX1BSaVt58gC9ZPpICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:43:12.482421Z"},"content_sha256":"967db31b9febef8c6414b0755d1d746953e0edd70e13edf3e460a6ca18ee9b37","schema_version":"1.0","event_id":"sha256:967db31b9febef8c6414b0755d1d746953e0edd70e13edf3e460a6ca18ee9b37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2CHOEESJYSDZXVMGUF26ZNGMQ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probability density of quantum expectation values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lorenzo Campos Venuti, Paolo Zanardi","submitted_at":"2012-02-22T02:56:55Z","abstract_excerpt":"We consider the quantum expectation value \\mathcal{A}=\\<\\psi|A|\\psi\\> of an observable A over the state |\\psi\\> . We derive the exact probability distribution of \\mathcal{A} seen as a random variable when |\\psi\\> varies over the set of all pure states equipped with the Haar-induced measure. The probability density is obtained with elementary means by computing its characteristic function, both for non-degenerate and degenerate observables. To illustrate our results we compare the exact predictions for few concrete examples with the concentration bounds obtained using Levy's lemma. Finally we c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4810","kind":"arxiv","version":3},"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":"2026-05-18T01:58:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0GlqiSgpcvNRYumcxl3iZEY/6LH2ghHZt4I35AeTo/51ilFyfqYfG//29Ov2lM8Cn5HXaPygcGFsQOEdbMDyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:43:12.483031Z"},"content_sha256":"f484a2875f8a32d2d902bab6a6c3c8e2e4f25f70f48442ff5a4231b6f44998bd","schema_version":"1.0","event_id":"sha256:f484a2875f8a32d2d902bab6a6c3c8e2e4f25f70f48442ff5a4231b6f44998bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/bundle.json","state_url":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/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":"2026-05-30T15:43:12Z","links":{"resolver":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3","bundle":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/bundle.json","state":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2CHOEESJYSDZXVMGUF26ZNGMQ3","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":"84492ac1a01265a7c2b2ef42be1c03629583ab0781c8a06fc253374dca3d6fca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-22T02:56:55Z","title_canon_sha256":"2a1d1d5af46dee2200521d38dc14bbcfb7720ed8c908e7dfe11b4c20ee816fe9"},"schema_version":"1.0","source":{"id":"1202.4810","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4810","created_at":"2026-05-18T01:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4810v3","created_at":"2026-05-18T01:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4810","created_at":"2026-05-18T01:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"2CHOEESJYSDZ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2CHOEESJYSDZXVMG","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2CHOEESJ","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:f484a2875f8a32d2d902bab6a6c3c8e2e4f25f70f48442ff5a4231b6f44998bd","target":"graph","created_at":"2026-05-18T01:58:22Z","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":"We consider the quantum expectation value \\mathcal{A}=\\<\\psi|A|\\psi\\> of an observable A over the state |\\psi\\> . We derive the exact probability distribution of \\mathcal{A} seen as a random variable when |\\psi\\> varies over the set of all pure states equipped with the Haar-induced measure. The probability density is obtained with elementary means by computing its characteristic function, both for non-degenerate and degenerate observables. To illustrate our results we compare the exact predictions for few concrete examples with the concentration bounds obtained using Levy's lemma. Finally we c","authors_text":"Lorenzo Campos Venuti, Paolo Zanardi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-22T02:56:55Z","title":"Probability density of quantum expectation values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4810","kind":"arxiv","version":3},"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":"sha256:967db31b9febef8c6414b0755d1d746953e0edd70e13edf3e460a6ca18ee9b37","target":"record","created_at":"2026-05-18T01:58:22Z","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":"84492ac1a01265a7c2b2ef42be1c03629583ab0781c8a06fc253374dca3d6fca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-22T02:56:55Z","title_canon_sha256":"2a1d1d5af46dee2200521d38dc14bbcfb7720ed8c908e7dfe11b4c20ee816fe9"},"schema_version":"1.0","source":{"id":"1202.4810","kind":"arxiv","version":3}},"canonical_sha256":"d08ee21249c4879bd586a175ecb4cc86d9cfb50b7898a3095a043baaf82aa35e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d08ee21249c4879bd586a175ecb4cc86d9cfb50b7898a3095a043baaf82aa35e","first_computed_at":"2026-05-18T01:58:22.591574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:22.591574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X5A6aY8E+65sDb+qe2Og58tRNZo/PhbkrNg2UOekYv9IyuZo4p4YlkbSto/kk2SKAi4m9THwr+mw0ePea8IUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:22.592073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4810","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:967db31b9febef8c6414b0755d1d746953e0edd70e13edf3e460a6ca18ee9b37","sha256:f484a2875f8a32d2d902bab6a6c3c8e2e4f25f70f48442ff5a4231b6f44998bd"],"state_sha256":"d3892b867941ee10f8298a13489a72fd959e2a4a27b9495f524c427fa0a78953"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5k5XWBbwHDeIziYkIhPWILEby06qh9zAUXWzm8fVS0IESE7XZqh65JZzhEV7HM/KE0fqVeOw5swesK1CR8U+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:43:12.485970Z","bundle_sha256":"4e326e4274fa93adef104c922cce4c59ee7496e214396a32b4a73141a5ef6952"}}