{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NAX3UF5CFKNP2SBIATMAX2NRR6","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":"126b2587d84f364d21ed87cd035bae4b08e87b39b4ed6b94f113fa5e67d09870","cross_cats_sorted":["math-ph","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-05T11:22:19Z","title_canon_sha256":"07c4333bccb59370006033ab47b67fddc005792d48601f5cbaf89eb3a17a560b"},"schema_version":"1.0","source":{"id":"1207.1227","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1227","created_at":"2026-05-18T03:33:25Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1227v2","created_at":"2026-05-18T03:33:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1227","created_at":"2026-05-18T03:33:25Z"},{"alias_kind":"pith_short_12","alias_value":"NAX3UF5CFKNP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NAX3UF5CFKNP2SBI","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NAX3UF5C","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:4b9e6d713b5cfd73c123789ab7b688ee05fac8c7d0bf9ddd25cb4c0f8d4c4f4e","target":"graph","created_at":"2026-05-18T03:33:25Z","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 associate with k hermitian N\\times N matrices a probability measure on R^k. It is supported on the joint numerical range of the k-tuple of matrices. We call this measure the joint numerical shadow of these matrices. Let k=2. A pair of hermitian N\\times N matrices defines a complex N\\times N matrix. The joint numerical range and the joint numerical shadow of the pair of hermitian matrices coincide with the numerical range and the numerical shadow, respectively, of this complex matrix. We study relationships between the dynamics of quantum maps on the set of quantum states, on one hand, and t","authors_text":"Eugene Gutkin, Karol Zyczkowski","cross_cats":["math-ph","math.MP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-05T11:22:19Z","title":"Joint numerical ranges, quantum maps, and joint numerical shadows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1227","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":"sha256:066a23f6ec3fdb14da604be9854bb3524c6ca070e7f249adceb0b36fc002cffd","target":"record","created_at":"2026-05-18T03:33:25Z","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":"126b2587d84f364d21ed87cd035bae4b08e87b39b4ed6b94f113fa5e67d09870","cross_cats_sorted":["math-ph","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-05T11:22:19Z","title_canon_sha256":"07c4333bccb59370006033ab47b67fddc005792d48601f5cbaf89eb3a17a560b"},"schema_version":"1.0","source":{"id":"1207.1227","kind":"arxiv","version":2}},"canonical_sha256":"682fba17a22a9afd482804d80be9b18f8d2957e3d120513346e138c2bc5ffe54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"682fba17a22a9afd482804d80be9b18f8d2957e3d120513346e138c2bc5ffe54","first_computed_at":"2026-05-18T03:33:25.899783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:25.899783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dcf7moVmRokI52Ic4QWfpV1Xm6J9sNsqToJAlTiS0RWkOXO4qqXVND+BoEWBAFfOBtsXznAmucPr8oMHwJVhDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:25.900325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1227","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:066a23f6ec3fdb14da604be9854bb3524c6ca070e7f249adceb0b36fc002cffd","sha256:4b9e6d713b5cfd73c123789ab7b688ee05fac8c7d0bf9ddd25cb4c0f8d4c4f4e"],"state_sha256":"a8d0668a102a1b6fab682ac861a97282554e758b00392f14cc123c19a16c8298"}