{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Q3YZYXCAZG5XS2QTDUPMZLRDKB","short_pith_number":"pith:Q3YZYXCA","schema_version":"1.0","canonical_sha256":"86f19c5c40c9bb796a131d1eccae23507f84f58005f3b6e4146efa20d534c3a1","source":{"kind":"arxiv","id":"1403.1960","version":2},"attestation_state":"computed","paper":{"title":"The complex geomety of a domain related to $\\mu$-synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"J. Agler, N. J. Young, Z. A. Lykova","submitted_at":"2014-03-08T10:45:34Z","abstract_excerpt":"We describe the basic complex geometry and function theory of the {\\em pentablock} $\\mathcal{P}$, which is the bounded domain in $\\mathbb{C}^3$ given by \\[ \\mathcal{P}= \\{(a_{21}, \\mathrm{tr} A, \\det A): A= \\begin{bmatrix} a_{ij}\\end{bmatrix}_{i,j=1}^2 \\in \\mathbb{B}\\} \\] where $\\mathbb{B}$ denotes the open unit ball in the space of $2\\times 2$ complex matrices. We prove several characterizations of the domain. We describe its distinguished boundary and exhibit a $4$-parameter group of automorphisms of $\\mathcal{P}$. We show that $\\mathcal{P}$ is intimately connected with the problem of $\\mu$-"},"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":"1403.1960","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-03-08T10:45:34Z","cross_cats_sorted":[],"title_canon_sha256":"7f875fe43c8b197ca50b7ba250b6f0f8c125b6bb92bd551f3d7d8fd264c85cf2","abstract_canon_sha256":"bd9b135e92519b311e317e36aed288f6bdb8beed3551232c2a1e718e126231a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:45.297454Z","signature_b64":"rk4LsVk6tB0xbzcrsu62afcXDfeK6Bk9jp3WesyOzwO+cU/d9g174YSo4QmSFPuoh6vBzhA7sy/S99SkB/JpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86f19c5c40c9bb796a131d1eccae23507f84f58005f3b6e4146efa20d534c3a1","last_reissued_at":"2026-05-18T02:43:45.296846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:45.296846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The complex geomety of a domain related to $\\mu$-synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"J. Agler, N. J. Young, Z. A. Lykova","submitted_at":"2014-03-08T10:45:34Z","abstract_excerpt":"We describe the basic complex geometry and function theory of the {\\em pentablock} $\\mathcal{P}$, which is the bounded domain in $\\mathbb{C}^3$ given by \\[ \\mathcal{P}= \\{(a_{21}, \\mathrm{tr} A, \\det A): A= \\begin{bmatrix} a_{ij}\\end{bmatrix}_{i,j=1}^2 \\in \\mathbb{B}\\} \\] where $\\mathbb{B}$ denotes the open unit ball in the space of $2\\times 2$ complex matrices. We prove several characterizations of the domain. We describe its distinguished boundary and exhibit a $4$-parameter group of automorphisms of $\\mathcal{P}$. We show that $\\mathcal{P}$ is intimately connected with the problem of $\\mu$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1960","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":"1403.1960","created_at":"2026-05-18T02:43:45.296969+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.1960v2","created_at":"2026-05-18T02:43:45.296969+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1960","created_at":"2026-05-18T02:43:45.296969+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q3YZYXCAZG5X","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q3YZYXCAZG5XS2QT","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q3YZYXCA","created_at":"2026-05-18T12:28:43.426989+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/Q3YZYXCAZG5XS2QTDUPMZLRDKB","json":"https://pith.science/pith/Q3YZYXCAZG5XS2QTDUPMZLRDKB.json","graph_json":"https://pith.science/api/pith-number/Q3YZYXCAZG5XS2QTDUPMZLRDKB/graph.json","events_json":"https://pith.science/api/pith-number/Q3YZYXCAZG5XS2QTDUPMZLRDKB/events.json","paper":"https://pith.science/paper/Q3YZYXCA"},"agent_actions":{"view_html":"https://pith.science/pith/Q3YZYXCAZG5XS2QTDUPMZLRDKB","download_json":"https://pith.science/pith/Q3YZYXCAZG5XS2QTDUPMZLRDKB.json","view_paper":"https://pith.science/paper/Q3YZYXCA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.1960&json=true","fetch_graph":"https://pith.science/api/pith-number/Q3YZYXCAZG5XS2QTDUPMZLRDKB/graph.json","fetch_events":"https://pith.science/api/pith-number/Q3YZYXCAZG5XS2QTDUPMZLRDKB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q3YZYXCAZG5XS2QTDUPMZLRDKB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q3YZYXCAZG5XS2QTDUPMZLRDKB/action/storage_attestation","attest_author":"https://pith.science/pith/Q3YZYXCAZG5XS2QTDUPMZLRDKB/action/author_attestation","sign_citation":"https://pith.science/pith/Q3YZYXCAZG5XS2QTDUPMZLRDKB/action/citation_signature","submit_replication":"https://pith.science/pith/Q3YZYXCAZG5XS2QTDUPMZLRDKB/action/replication_record"}},"created_at":"2026-05-18T02:43:45.296969+00:00","updated_at":"2026-05-18T02:43:45.296969+00:00"}