{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:C5H5VKLRSDP5UVHIY7CJ6LTITK","short_pith_number":"pith:C5H5VKLR","schema_version":"1.0","canonical_sha256":"174fdaa97190dfda54e8c7c49f2e689abf6082d23feca543a6e6f110674f947d","source":{"kind":"arxiv","id":"1111.2435","version":1},"attestation_state":"computed","paper":{"title":"A Simple Algorithm for Constructing all Real Hessenberg Unitary Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Janet C. Tremain","submitted_at":"2011-11-10T10:01:48Z","abstract_excerpt":"Unitary matrices which are zero below the secondary diagonal (Hessenberg unitary matrices) have many uses in analysis. Given a set of needed conditions on a unitary matrix, this algorithm will give the sparsest unitary matrix. We give an algorithm for constructing all real Hessenberg unitary matrices. The $n\\times n$ unitary matrices given by the algorithm have $n-1$ variables which can be chosen to give additional properties needed for a particular application."},"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":"1111.2435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-11-10T10:01:48Z","cross_cats_sorted":[],"title_canon_sha256":"7831e5a13c8b72dcad786c3070aade672b7b550138560b252a57e06c6b88144b","abstract_canon_sha256":"049e284afcae4215c2ac3784c373ae1bd59be48c208156b0dbb959f1a9e568e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:34.180048Z","signature_b64":"pbaHiRxr0YbEWFSvP7EhwG8wPLIJZisAKWFUAXEpv5DOUbkCGoVSVWAJk8Sjkno6UsR44dpFVMG84+jDxVQ3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"174fdaa97190dfda54e8c7c49f2e689abf6082d23feca543a6e6f110674f947d","last_reissued_at":"2026-05-18T04:08:34.179396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:34.179396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Simple Algorithm for Constructing all Real Hessenberg Unitary Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Janet C. Tremain","submitted_at":"2011-11-10T10:01:48Z","abstract_excerpt":"Unitary matrices which are zero below the secondary diagonal (Hessenberg unitary matrices) have many uses in analysis. Given a set of needed conditions on a unitary matrix, this algorithm will give the sparsest unitary matrix. We give an algorithm for constructing all real Hessenberg unitary matrices. The $n\\times n$ unitary matrices given by the algorithm have $n-1$ variables which can be chosen to give additional properties needed for a particular application."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2435","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":"1111.2435","created_at":"2026-05-18T04:08:34.179502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.2435v1","created_at":"2026-05-18T04:08:34.179502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2435","created_at":"2026-05-18T04:08:34.179502+00:00"},{"alias_kind":"pith_short_12","alias_value":"C5H5VKLRSDP5","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C5H5VKLRSDP5UVHI","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C5H5VKLR","created_at":"2026-05-18T12:26:24.575870+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/C5H5VKLRSDP5UVHIY7CJ6LTITK","json":"https://pith.science/pith/C5H5VKLRSDP5UVHIY7CJ6LTITK.json","graph_json":"https://pith.science/api/pith-number/C5H5VKLRSDP5UVHIY7CJ6LTITK/graph.json","events_json":"https://pith.science/api/pith-number/C5H5VKLRSDP5UVHIY7CJ6LTITK/events.json","paper":"https://pith.science/paper/C5H5VKLR"},"agent_actions":{"view_html":"https://pith.science/pith/C5H5VKLRSDP5UVHIY7CJ6LTITK","download_json":"https://pith.science/pith/C5H5VKLRSDP5UVHIY7CJ6LTITK.json","view_paper":"https://pith.science/paper/C5H5VKLR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.2435&json=true","fetch_graph":"https://pith.science/api/pith-number/C5H5VKLRSDP5UVHIY7CJ6LTITK/graph.json","fetch_events":"https://pith.science/api/pith-number/C5H5VKLRSDP5UVHIY7CJ6LTITK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C5H5VKLRSDP5UVHIY7CJ6LTITK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C5H5VKLRSDP5UVHIY7CJ6LTITK/action/storage_attestation","attest_author":"https://pith.science/pith/C5H5VKLRSDP5UVHIY7CJ6LTITK/action/author_attestation","sign_citation":"https://pith.science/pith/C5H5VKLRSDP5UVHIY7CJ6LTITK/action/citation_signature","submit_replication":"https://pith.science/pith/C5H5VKLRSDP5UVHIY7CJ6LTITK/action/replication_record"}},"created_at":"2026-05-18T04:08:34.179502+00:00","updated_at":"2026-05-18T04:08:34.179502+00:00"}