{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YC4GLHQ75WFWYGVBIKGV7F3MLI","short_pith_number":"pith:YC4GLHQ7","schema_version":"1.0","canonical_sha256":"c0b8659e1fed8b6c1aa1428d5f976c5a107c2d23c618dae7a56f7faf0f3eafe4","source":{"kind":"arxiv","id":"1201.2524","version":2},"attestation_state":"computed","paper":{"title":"Restricted numerical shadow and geometry of quantum entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Charles F. Dunkl, Jaros{\\l}aw Adam Miszczak, John A. Holbrook, Karol \\.Zyczkowski, Piotr Gawron, Zbigniew Pucha{\\l}a","submitted_at":"2012-01-12T10:49:35Z","abstract_excerpt":"The restricted numerical range $W_R(A)$ of an operator $A$ acting on a $D$-dimensional Hilbert space is defined as a set of all possible expectation values of this operator among pure states which belong to a certain subset $R$ of the of set of pure quantum states of dimension $D$. One considers for instance the set of real states, or in the case of composite spaces, the set of product states and the set of maximally entangled states. Combining the operator theory with a probabilistic approach we introduce the restricted numerical shadow of $A$ -- a normalized probability distribution on the c"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.2524","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-01-12T10:49:35Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"4fcee3d5821cb9162f0b82d4dfb11a7accf6e4129f9d5b7c235c7e1a709c9bdc","abstract_canon_sha256":"f75bcf4c0a1f20894235a16d2f968dfa8e382b584a5cde4bfc3a70446d331eaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:04.608605Z","signature_b64":"/Xf4UqcKQYSHQ4P0xm6E8nMWzPSYGKd/fcbpR3xNAAEY+nRkZ7R5l+VDglbMtBzEW9jX/wZeyyfQ6yKD8DNEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0b8659e1fed8b6c1aa1428d5f976c5a107c2d23c618dae7a56f7faf0f3eafe4","last_reissued_at":"2026-05-18T03:44:04.607944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:04.607944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Restricted numerical shadow and geometry of quantum entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Charles F. Dunkl, Jaros{\\l}aw Adam Miszczak, John A. Holbrook, Karol \\.Zyczkowski, Piotr Gawron, Zbigniew Pucha{\\l}a","submitted_at":"2012-01-12T10:49:35Z","abstract_excerpt":"The restricted numerical range $W_R(A)$ of an operator $A$ acting on a $D$-dimensional Hilbert space is defined as a set of all possible expectation values of this operator among pure states which belong to a certain subset $R$ of the of set of pure quantum states of dimension $D$. One considers for instance the set of real states, or in the case of composite spaces, the set of product states and the set of maximally entangled states. Combining the operator theory with a probabilistic approach we introduce the restricted numerical shadow of $A$ -- a normalized probability distribution on the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2524","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1201.2524","created_at":"2026-05-18T03:44:04.608021+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.2524v2","created_at":"2026-05-18T03:44:04.608021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2524","created_at":"2026-05-18T03:44:04.608021+00:00"},{"alias_kind":"pith_short_12","alias_value":"YC4GLHQ75WFW","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"YC4GLHQ75WFWYGVB","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"YC4GLHQ7","created_at":"2026-05-18T12:27:27.928770+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI","json":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI.json","graph_json":"https://pith.science/api/pith-number/YC4GLHQ75WFWYGVBIKGV7F3MLI/graph.json","events_json":"https://pith.science/api/pith-number/YC4GLHQ75WFWYGVBIKGV7F3MLI/events.json","paper":"https://pith.science/paper/YC4GLHQ7"},"agent_actions":{"view_html":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI","download_json":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI.json","view_paper":"https://pith.science/paper/YC4GLHQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.2524&json=true","fetch_graph":"https://pith.science/api/pith-number/YC4GLHQ75WFWYGVBIKGV7F3MLI/graph.json","fetch_events":"https://pith.science/api/pith-number/YC4GLHQ75WFWYGVBIKGV7F3MLI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI/action/storage_attestation","attest_author":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI/action/author_attestation","sign_citation":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI/action/citation_signature","submit_replication":"https://pith.science/pith/YC4GLHQ75WFWYGVBIKGV7F3MLI/action/replication_record"}},"created_at":"2026-05-18T03:44:04.608021+00:00","updated_at":"2026-05-18T03:44:04.608021+00:00"}