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We prove that, if $T$ is an operator in $\\mathcal{B}(H)$ that generates an unital $C^*$-algebra $\\mathcal{A}$ then $\\{T,T^*T,TT^*\\}$ is a hyperrigid generator for $\\mathcal{A}$. As a corollary it follows that, if $T\\in \\mathcal{B}(H)$ is normal then $\\{T,TT^*\\}$ is hyperrigid generator for the unital $C^*$-algebra generated by $T$ and if $T\\in \\mathcal{B}(H)$ is unitary then $\\{T\\}$ is hyp"},"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":"1812.08574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-12-20T14:04:27Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"816c0bc248c251b74cc875b603d409621f86fed9769dc1666880337730e2de8a","abstract_canon_sha256":"b5e156ae559578152e7a820cd02b52b8e1b1d73db0b925faee49883457f5a647"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:49.604024Z","signature_b64":"bfxm0YuCk74FHWELLU1UY+lC444U/H9PkI3N3Ma4cH2kEFe9+FLhdV65L82yyT+SbXXDA0UVcMOFx+bAA3mCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5c58ffe32bd19f94f22fa35571043e01730f02e210942953c9e29170b0d49b1","last_reissued_at":"2026-05-17T23:57:49.603414Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:49.603414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hyperrigid generators in C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"P. Shankar","submitted_at":"2018-12-20T14:04:27Z","abstract_excerpt":"In this article, we show that, if $S\\in \\mathcal{B}(H)$ is irreducible and essential unitary, then $\\{S,SS^*\\}$ is a hyperrigid generator for the unital $C^*$-algebra $\\mathcal{T}$ generated by $\\{S,SS^*\\}$. We prove that, if $T$ is an operator in $\\mathcal{B}(H)$ that generates an unital $C^*$-algebra $\\mathcal{A}$ then $\\{T,T^*T,TT^*\\}$ is a hyperrigid generator for $\\mathcal{A}$. As a corollary it follows that, if $T\\in \\mathcal{B}(H)$ is normal then $\\{T,TT^*\\}$ is hyperrigid generator for the unital $C^*$-algebra generated by $T$ and if $T\\in \\mathcal{B}(H)$ is unitary then $\\{T\\}$ is hyp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08574","kind":"arxiv","version":1},"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":"1812.08574","created_at":"2026-05-17T23:57:49.603504+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.08574v1","created_at":"2026-05-17T23:57:49.603504+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08574","created_at":"2026-05-17T23:57:49.603504+00:00"},{"alias_kind":"pith_short_12","alias_value":"YXCY77RSXUM7","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YXCY77RSXUM7STZC","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YXCY77RS","created_at":"2026-05-18T12:33:04.347982+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/YXCY77RSXUM7STZC7I2VOECD4A","json":"https://pith.science/pith/YXCY77RSXUM7STZC7I2VOECD4A.json","graph_json":"https://pith.science/api/pith-number/YXCY77RSXUM7STZC7I2VOECD4A/graph.json","events_json":"https://pith.science/api/pith-number/YXCY77RSXUM7STZC7I2VOECD4A/events.json","paper":"https://pith.science/paper/YXCY77RS"},"agent_actions":{"view_html":"https://pith.science/pith/YXCY77RSXUM7STZC7I2VOECD4A","download_json":"https://pith.science/pith/YXCY77RSXUM7STZC7I2VOECD4A.json","view_paper":"https://pith.science/paper/YXCY77RS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.08574&json=true","fetch_graph":"https://pith.science/api/pith-number/YXCY77RSXUM7STZC7I2VOECD4A/graph.json","fetch_events":"https://pith.science/api/pith-number/YXCY77RSXUM7STZC7I2VOECD4A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YXCY77RSXUM7STZC7I2VOECD4A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YXCY77RSXUM7STZC7I2VOECD4A/action/storage_attestation","attest_author":"https://pith.science/pith/YXCY77RSXUM7STZC7I2VOECD4A/action/author_attestation","sign_citation":"https://pith.science/pith/YXCY77RSXUM7STZC7I2VOECD4A/action/citation_signature","submit_replication":"https://pith.science/pith/YXCY77RSXUM7STZC7I2VOECD4A/action/replication_record"}},"created_at":"2026-05-17T23:57:49.603504+00:00","updated_at":"2026-05-17T23:57:49.603504+00:00"}