{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4MKMGN36EZNGQOXO37PICTNOCP","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":"39d6e8a798a279b275778ca2ba99d1698412b335f0650912271c543bcb78cf3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-26T06:14:21Z","title_canon_sha256":"54c991f0b82c6597a09988f7468b7626fc3233d0baf6bcd7051adb020558f088"},"schema_version":"1.0","source":{"id":"1710.09555","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09555","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09555v3","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09555","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"4MKMGN36EZNG","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4MKMGN36EZNGQOXO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4MKMGN36","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:8ba413b78afc46c4032a6113feca550e5ea8d0e544d43d9eb99684687c5727b7","target":"graph","created_at":"2026-05-18T00:19:16Z","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":"Let ${\\bf A} = (A_1, \\dots, A_m)$ be an $m$-tuple of bounded linear operators acting on a Hilbert space ${\\cal H}$. Their joint $(p,q)$-matricial range $\\Lambda_{p,q}({\\bf A})$ is the collection of $(B_1, \\dots, B_m) \\in {\\bf M}_q^m$, where $I_p\\otimes B_j$ is a compression of $A_j$ on a $pq$-dimensional subspace. This definition covers various kinds of generalized numerical ranges for different values of $p,q,m$. In this paper, it is shown that $\\Lambda_{p,q}({\\bf A})$ is star-shaped if the dimension of $\\cal H$ is sufficiently large. If $\\dim {\\cal H}$ is infinite, we extend the definition o","authors_text":"Chi-Kwong Li, Nung-sing Sze, Pan-Shun Lau, Yiu-Tung Poon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-26T06:14:21Z","title":"Convexity and Star-shapedness of Matricial Range"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09555","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":"sha256:36bd641b33368cdf0efefc35c4b06530010a0ce1cde1b1348a9b2d99d085907b","target":"record","created_at":"2026-05-18T00:19:16Z","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":"39d6e8a798a279b275778ca2ba99d1698412b335f0650912271c543bcb78cf3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-26T06:14:21Z","title_canon_sha256":"54c991f0b82c6597a09988f7468b7626fc3233d0baf6bcd7051adb020558f088"},"schema_version":"1.0","source":{"id":"1710.09555","kind":"arxiv","version":3}},"canonical_sha256":"e314c3377e265a683aeedfde814dae13c43dee2de5913126463eb8cdfa5ae69a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e314c3377e265a683aeedfde814dae13c43dee2de5913126463eb8cdfa5ae69a","first_computed_at":"2026-05-18T00:19:16.913190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:16.913190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gx5lfKiljmMZYOALxILYTVfie0guc2iurmex85E7ulXfgnRP69S2LJAUllErtm3KYj/VlzBLH8Sc9wMOy7XCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:16.913713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09555","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36bd641b33368cdf0efefc35c4b06530010a0ce1cde1b1348a9b2d99d085907b","sha256:8ba413b78afc46c4032a6113feca550e5ea8d0e544d43d9eb99684687c5727b7"],"state_sha256":"450e5ea4145bb682dab3b2fa8a91e16e515c8d373f16824c98f5ec23b9c1a25d"}