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In this paper, we have constructed a functional model and produced a complete unitary invariant for a pure tetrablock contraction. In this construction, the fundamental operators, which are the unique solutions of the operator equations $$ A-B^*P = D_PX_1D_P \\text{and} B-A^*P=D_PX_2D_P, \\text{where $X_1,X_2 \\in"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.0322","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-02T04:11:27Z","cross_cats_sorted":[],"title_canon_sha256":"80b044b565240ae2255570bde3940d3bc4d75569257f703120d3a3ae994601d0","abstract_canon_sha256":"ea9e7bf9f1baad56d891d90d8e2d5964a4a2428972477ed4461ae1c25c45c628"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:50.213546Z","signature_b64":"LUjKsHvjJB88FPo6oQq1NEYGOGohWCbDQvLgPKwjof/6Qx26D3/BtIsAqzJeKTEPz9F+TNgqifsjadJ0dfhlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae22c7b4696bf8fc204a7a396f6564c4f57f589df0d04820a99d08456cbb8a89","last_reissued_at":"2026-05-18T01:12:50.213207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:50.213207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Tetrablock Contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haripada Sau","submitted_at":"2013-12-02T04:11:27Z","abstract_excerpt":"A commuting triple of operators $(A,B,P)$ on a Hilbert space $\\mathcal{H}$ is called a tetrablock contraction if the closure of the set $$ E = \\{\\underline{x}=(x_1,x_2,x_3)\\in \\mathbb{C}^3:\n  1-x_1z-x_2w+x_3zw \\neq 0 \\text{whenever}|z| \\leq 1\\text{and}|w| \\leq 1 \\} $$ is a spectral set. In this paper, we have constructed a functional model and produced a complete unitary invariant for a pure tetrablock contraction. In this construction, the fundamental operators, which are the unique solutions of the operator equations $$ A-B^*P = D_PX_1D_P \\text{and} B-A^*P=D_PX_2D_P, \\text{where $X_1,X_2 \\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0322","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":"1312.0322","created_at":"2026-05-18T01:12:50.213260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0322v2","created_at":"2026-05-18T01:12:50.213260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0322","created_at":"2026-05-18T01:12:50.213260+00:00"},{"alias_kind":"pith_short_12","alias_value":"VYRMPNDJNP4P","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VYRMPNDJNP4PYICK","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VYRMPNDJ","created_at":"2026-05-18T12:28:04.890932+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/VYRMPNDJNP4PYICKPI4W6ZLEYT","json":"https://pith.science/pith/VYRMPNDJNP4PYICKPI4W6ZLEYT.json","graph_json":"https://pith.science/api/pith-number/VYRMPNDJNP4PYICKPI4W6ZLEYT/graph.json","events_json":"https://pith.science/api/pith-number/VYRMPNDJNP4PYICKPI4W6ZLEYT/events.json","paper":"https://pith.science/paper/VYRMPNDJ"},"agent_actions":{"view_html":"https://pith.science/pith/VYRMPNDJNP4PYICKPI4W6ZLEYT","download_json":"https://pith.science/pith/VYRMPNDJNP4PYICKPI4W6ZLEYT.json","view_paper":"https://pith.science/paper/VYRMPNDJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0322&json=true","fetch_graph":"https://pith.science/api/pith-number/VYRMPNDJNP4PYICKPI4W6ZLEYT/graph.json","fetch_events":"https://pith.science/api/pith-number/VYRMPNDJNP4PYICKPI4W6ZLEYT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VYRMPNDJNP4PYICKPI4W6ZLEYT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VYRMPNDJNP4PYICKPI4W6ZLEYT/action/storage_attestation","attest_author":"https://pith.science/pith/VYRMPNDJNP4PYICKPI4W6ZLEYT/action/author_attestation","sign_citation":"https://pith.science/pith/VYRMPNDJNP4PYICKPI4W6ZLEYT/action/citation_signature","submit_replication":"https://pith.science/pith/VYRMPNDJNP4PYICKPI4W6ZLEYT/action/replication_record"}},"created_at":"2026-05-18T01:12:50.213260+00:00","updated_at":"2026-05-18T01:12:50.213260+00:00"}