{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FUTNJ6VS6RSZQWSU4AJFSFGQVK","short_pith_number":"pith:FUTNJ6VS","canonical_record":{"source":{"id":"1106.1892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-09T19:58:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5d48130cbd151774f7ad20b157e69e6f7c38a62f8a8985d815201279208eb7f1","abstract_canon_sha256":"552611559a1f148021eeb397e22c17d5a83c1156bebdf4116e132554743a2170"},"schema_version":"1.0"},"canonical_sha256":"2d26d4fab2f465985a54e0125914d0aa8712e0173352508d1785c70169c6d51e","source":{"kind":"arxiv","id":"1106.1892","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1892","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1892v1","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1892","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"FUTNJ6VS6RSZ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FUTNJ6VS6RSZQWSU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FUTNJ6VS","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FUTNJ6VS6RSZQWSU4AJFSFGQVK","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-09T19:58:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5d48130cbd151774f7ad20b157e69e6f7c38a62f8a8985d815201279208eb7f1","abstract_canon_sha256":"552611559a1f148021eeb397e22c17d5a83c1156bebdf4116e132554743a2170"},"schema_version":"1.0"},"canonical_sha256":"2d26d4fab2f465985a54e0125914d0aa8712e0173352508d1785c70169c6d51e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:42.854683Z","signature_b64":"uvwIk09qmFTHVSMxx5d96SRCnecb7OlbWpeO9eMfAJjQ4JujUD6UdYg0tA7WD41oVZZRWAZCU5Mc4btBhYZ0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d26d4fab2f465985a54e0125914d0aa8712e0173352508d1785c70169c6d51e","last_reissued_at":"2026-05-18T04:19:42.853639Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:42.853639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1892","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":"2026-05-18T04:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbmKbXkBbb61mMAF7Au8q+8vPTFdyLxT38s0HifuI9XdfDmXMeyeqHcm+czukcGKkdvztYg+8Ps5bl/C1uf4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:00:28.170776Z"},"content_sha256":"c2fd8115e573716d61f849115a603fe7d01ab470043b0627553c5e2c39b5d5a9","schema_version":"1.0","event_id":"sha256:c2fd8115e573716d61f849115a603fe7d01ab470043b0627553c5e2c39b5d5a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FUTNJ6VS6RSZQWSU4AJFSFGQVK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Photon Antibunching, Sub-Poisson Statistics and Cauchy-Bunyakovsky and Bell's Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Igor V. Volovich","submitted_at":"2011-06-09T19:58:18Z","abstract_excerpt":"We discuss some mathematical aspects of photon antibunching and sub-Poisson photon statistics. It is known that Bell's inequalities for entangled states can be reduced to the Cauchy-Bunyakovsky inequalities. In this note some rigorous results on impossibility of classical hidden variables representations of certain quantum correlation functions are proved which are also based on the Cauchy-Bunyakovsky inequalities.\n  The difference K between the variance and the mean as a measure of non-classicality of a state is discussed. For the classical case K is nonnegative while for the n-particle state"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1892","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":"2026-05-18T04:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9KDVBYCH5jcgTlUudMRghswXYM3wWPz9LL6OFG3JW57WQSAPztvYrg/PzvdEcSJefAMC5khD8NTm79tQwaIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:00:28.171123Z"},"content_sha256":"9aff4675de28338777bc96629bbae55e695e28fdfb8aa6ecf6f253a4569c7cc3","schema_version":"1.0","event_id":"sha256:9aff4675de28338777bc96629bbae55e695e28fdfb8aa6ecf6f253a4569c7cc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUTNJ6VS6RSZQWSU4AJFSFGQVK/bundle.json","state_url":"https://pith.science/pith/FUTNJ6VS6RSZQWSU4AJFSFGQVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUTNJ6VS6RSZQWSU4AJFSFGQVK/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":"2026-05-28T10:00:28Z","links":{"resolver":"https://pith.science/pith/FUTNJ6VS6RSZQWSU4AJFSFGQVK","bundle":"https://pith.science/pith/FUTNJ6VS6RSZQWSU4AJFSFGQVK/bundle.json","state":"https://pith.science/pith/FUTNJ6VS6RSZQWSU4AJFSFGQVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUTNJ6VS6RSZQWSU4AJFSFGQVK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FUTNJ6VS6RSZQWSU4AJFSFGQVK","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":"552611559a1f148021eeb397e22c17d5a83c1156bebdf4116e132554743a2170","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-09T19:58:18Z","title_canon_sha256":"5d48130cbd151774f7ad20b157e69e6f7c38a62f8a8985d815201279208eb7f1"},"schema_version":"1.0","source":{"id":"1106.1892","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1892","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1892v1","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1892","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"FUTNJ6VS6RSZ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FUTNJ6VS6RSZQWSU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FUTNJ6VS","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:9aff4675de28338777bc96629bbae55e695e28fdfb8aa6ecf6f253a4569c7cc3","target":"graph","created_at":"2026-05-18T04:19:42Z","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 discuss some mathematical aspects of photon antibunching and sub-Poisson photon statistics. It is known that Bell's inequalities for entangled states can be reduced to the Cauchy-Bunyakovsky inequalities. In this note some rigorous results on impossibility of classical hidden variables representations of certain quantum correlation functions are proved which are also based on the Cauchy-Bunyakovsky inequalities.\n  The difference K between the variance and the mean as a measure of non-classicality of a state is discussed. For the classical case K is nonnegative while for the n-particle state","authors_text":"Igor V. Volovich","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-09T19:58:18Z","title":"Photon Antibunching, Sub-Poisson Statistics and Cauchy-Bunyakovsky and Bell's Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1892","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:c2fd8115e573716d61f849115a603fe7d01ab470043b0627553c5e2c39b5d5a9","target":"record","created_at":"2026-05-18T04:19:42Z","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":"552611559a1f148021eeb397e22c17d5a83c1156bebdf4116e132554743a2170","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-09T19:58:18Z","title_canon_sha256":"5d48130cbd151774f7ad20b157e69e6f7c38a62f8a8985d815201279208eb7f1"},"schema_version":"1.0","source":{"id":"1106.1892","kind":"arxiv","version":1}},"canonical_sha256":"2d26d4fab2f465985a54e0125914d0aa8712e0173352508d1785c70169c6d51e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d26d4fab2f465985a54e0125914d0aa8712e0173352508d1785c70169c6d51e","first_computed_at":"2026-05-18T04:19:42.853639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:42.853639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uvwIk09qmFTHVSMxx5d96SRCnecb7OlbWpeO9eMfAJjQ4JujUD6UdYg0tA7WD41oVZZRWAZCU5Mc4btBhYZ0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:42.854683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1892","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2fd8115e573716d61f849115a603fe7d01ab470043b0627553c5e2c39b5d5a9","sha256:9aff4675de28338777bc96629bbae55e695e28fdfb8aa6ecf6f253a4569c7cc3"],"state_sha256":"28c0ae89fa0b057959edf34577752b17a48b97ae1edc125f435a2e8c5a27a7b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C48zagl7t/S7Mo/j71Z9hkJSeulMYkJ2+Dg2Blf6aCBFkRhtFOTJKffA/4P8qAMy4TkyanFkZbool+wPeT/LAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:00:28.173120Z","bundle_sha256":"d123929de77c4a56b0ebdaf48ff285001ef65b5aed0063eb16f31ed1ffeaf85e"}}