{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HRCO2W3X7653MHLMI5MY5DYC4O","short_pith_number":"pith:HRCO2W3X","canonical_record":{"source":{"id":"1103.3186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T14:48:44Z","cross_cats_sorted":["math-ph","math.MP","physics.atom-ph","physics.data-an"],"title_canon_sha256":"d84d444e33e59e0cba6824c87b65d8dafcd334ecc1a7866c34fc7a809fb50598","abstract_canon_sha256":"3be32cabbf18247311dab604290e0ff9bbd51ffeb0e5c2500a297ef1149ae09f"},"schema_version":"1.0"},"canonical_sha256":"3c44ed5b77ffbbb61d6c47598e8f02e39565e5d33112bfcf7a61eeeac01a112c","source":{"kind":"arxiv","id":"1103.3186","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3186","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3186v1","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3186","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"HRCO2W3X7653","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HRCO2W3X7653MHLM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HRCO2W3X","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HRCO2W3X7653MHLMI5MY5DYC4O","target":"record","payload":{"canonical_record":{"source":{"id":"1103.3186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T14:48:44Z","cross_cats_sorted":["math-ph","math.MP","physics.atom-ph","physics.data-an"],"title_canon_sha256":"d84d444e33e59e0cba6824c87b65d8dafcd334ecc1a7866c34fc7a809fb50598","abstract_canon_sha256":"3be32cabbf18247311dab604290e0ff9bbd51ffeb0e5c2500a297ef1149ae09f"},"schema_version":"1.0"},"canonical_sha256":"3c44ed5b77ffbbb61d6c47598e8f02e39565e5d33112bfcf7a61eeeac01a112c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:34.051287Z","signature_b64":"TbAG6Rf/kPMxugRt1mDqx0zu9+rMr+LeLlfuw7xTkkUQQ3UcUdk3k1LBVJEbDhbZARugFolf3UXJ9LklABnZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c44ed5b77ffbbb61d6c47598e8f02e39565e5d33112bfcf7a61eeeac01a112c","last_reissued_at":"2026-05-18T04:26:34.050567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:34.050567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.3186","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":"2026-05-18T04:26:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YVHemxvjwQAVi8HhirqNvW9NUouW/+4O3R5Kn8cLtPNsKAJM36tf7aF0GpK5HaX0AYvpuL/j6MIIcRHBnAuPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:54:39.400732Z"},"content_sha256":"0d57d5b1cdef7b5c1bbb30f9ae5d462ff6d9a050dc15e45f3a310cb93c9dd60f","schema_version":"1.0","event_id":"sha256:0d57d5b1cdef7b5c1bbb30f9ae5d462ff6d9a050dc15e45f3a310cb93c9dd60f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HRCO2W3X7653MHLMI5MY5DYC4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information and Entanglement Measures in Quantum Systems With Applications to Atomic Physics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.atom-ph","physics.data-an"],"primary_cat":"quant-ph","authors_text":"Daniel Manzano","submitted_at":"2011-03-16T14:48:44Z","abstract_excerpt":"This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the proposal and analysis of a new set of measures of spreading for orthogonal polynomials, to quantum computation and learning devices and to the analysis of entanglement in systems of identical fermions, in this field we propose a separability criteria for pure states of N identical fermions and the entanglement of two-electron atoms is studied, a new separability cr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3186","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":"2026-05-18T04:26:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ORDy9iRGpKZv8/AJQxOg4Q+XCmrT10FcRTVKqaE/REzEu2xeG2sFoTxjBRhTHgUyPVz5UP69Tn+JfU3ugKNPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:54:39.401090Z"},"content_sha256":"a5fb435e10b901490aff12837b73c8a0400222f4c7fa126a4000d00a09e8c18f","schema_version":"1.0","event_id":"sha256:a5fb435e10b901490aff12837b73c8a0400222f4c7fa126a4000d00a09e8c18f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRCO2W3X7653MHLMI5MY5DYC4O/bundle.json","state_url":"https://pith.science/pith/HRCO2W3X7653MHLMI5MY5DYC4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRCO2W3X7653MHLMI5MY5DYC4O/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":"2026-06-04T18:54:39Z","links":{"resolver":"https://pith.science/pith/HRCO2W3X7653MHLMI5MY5DYC4O","bundle":"https://pith.science/pith/HRCO2W3X7653MHLMI5MY5DYC4O/bundle.json","state":"https://pith.science/pith/HRCO2W3X7653MHLMI5MY5DYC4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRCO2W3X7653MHLMI5MY5DYC4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HRCO2W3X7653MHLMI5MY5DYC4O","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":"3be32cabbf18247311dab604290e0ff9bbd51ffeb0e5c2500a297ef1149ae09f","cross_cats_sorted":["math-ph","math.MP","physics.atom-ph","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T14:48:44Z","title_canon_sha256":"d84d444e33e59e0cba6824c87b65d8dafcd334ecc1a7866c34fc7a809fb50598"},"schema_version":"1.0","source":{"id":"1103.3186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3186","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3186v1","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3186","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"HRCO2W3X7653","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HRCO2W3X7653MHLM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HRCO2W3X","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:a5fb435e10b901490aff12837b73c8a0400222f4c7fa126a4000d00a09e8c18f","target":"graph","created_at":"2026-05-18T04:26:34Z","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":"This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the proposal and analysis of a new set of measures of spreading for orthogonal polynomials, to quantum computation and learning devices and to the analysis of entanglement in systems of identical fermions, in this field we propose a separability criteria for pure states of N identical fermions and the entanglement of two-electron atoms is studied, a new separability cr","authors_text":"Daniel Manzano","cross_cats":["math-ph","math.MP","physics.atom-ph","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T14:48:44Z","title":"Information and Entanglement Measures in Quantum Systems With Applications to Atomic Physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3186","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":"sha256:0d57d5b1cdef7b5c1bbb30f9ae5d462ff6d9a050dc15e45f3a310cb93c9dd60f","target":"record","created_at":"2026-05-18T04:26:34Z","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":"3be32cabbf18247311dab604290e0ff9bbd51ffeb0e5c2500a297ef1149ae09f","cross_cats_sorted":["math-ph","math.MP","physics.atom-ph","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T14:48:44Z","title_canon_sha256":"d84d444e33e59e0cba6824c87b65d8dafcd334ecc1a7866c34fc7a809fb50598"},"schema_version":"1.0","source":{"id":"1103.3186","kind":"arxiv","version":1}},"canonical_sha256":"3c44ed5b77ffbbb61d6c47598e8f02e39565e5d33112bfcf7a61eeeac01a112c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c44ed5b77ffbbb61d6c47598e8f02e39565e5d33112bfcf7a61eeeac01a112c","first_computed_at":"2026-05-18T04:26:34.050567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:34.050567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TbAG6Rf/kPMxugRt1mDqx0zu9+rMr+LeLlfuw7xTkkUQQ3UcUdk3k1LBVJEbDhbZARugFolf3UXJ9LklABnZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:34.051287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d57d5b1cdef7b5c1bbb30f9ae5d462ff6d9a050dc15e45f3a310cb93c9dd60f","sha256:a5fb435e10b901490aff12837b73c8a0400222f4c7fa126a4000d00a09e8c18f"],"state_sha256":"39b6b414fd4562d5ba2474850a3a848bf29ab5b8090a313af7b2482fd5d90025"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"410nhr0RDJwYJHFGzI0msTm+8Ku5m4rnfWXRLE6vh7hHigtpNDiKycKVQiv0oGnoC1ypQYdXAGVTLMNR4uF7Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:54:39.403092Z","bundle_sha256":"f664b0fcc0d5b91ca803e95bb0fd0b3c02bfdf47978577829a61616bc8e1107e"}}