{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:LCRNKK7C66EWUAHXMP6JFZ6XGU","short_pith_number":"pith:LCRNKK7C","schema_version":"1.0","canonical_sha256":"58a2d52be2f7896a00f763fc92e7d7350db80d56be85a011d145c67f46bb4066","source":{"kind":"arxiv","id":"1012.3281","version":1},"attestation_state":"computed","paper":{"title":"Canonical lossless state-space systems: Staircase forms and the Schur algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bernard Hanzon, Martine Olivi (INRIA Sophia Antipolis), Ralf L.M. Peeters","submitted_at":"2010-12-15T11:09:56Z","abstract_excerpt":"A new finite atlas of overlapping balanced canonical forms for multivariate discrete-time lossless systems is presented. The canonical forms have the property that the controllability matrix is positive upper triangular up to a suitable permutation of its columns. This is a generalization of a similar balanced canonical form for continuous-time lossless systems. It is shown that this atlas is in fact a finite sub-atlas of the infinite atlas of overlapping balanced canonical forms for lossless systems that is associated with the tangential Schur algorithm; such canonical forms satisfy certain i"},"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":"1012.3281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-12-15T11:09:56Z","cross_cats_sorted":[],"title_canon_sha256":"df24bc508d66edcc02f764949119df21e54eb39b05946d52c6e857ef968f2343","abstract_canon_sha256":"b86aaaac39510510fc08a0c691d0c445e957de7d1056d33e6d552a7968dbade7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:17.313525Z","signature_b64":"57UogoOaP8UHkoZgk4ap3X90zzId54n2w1TJz6GDpvxHxBY0mjwJUI8/5B/fdjQwXfQIDmpLmYhOKx4nbQ9lBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58a2d52be2f7896a00f763fc92e7d7350db80d56be85a011d145c67f46bb4066","last_reissued_at":"2026-05-18T04:33:17.312806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:17.312806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical lossless state-space systems: Staircase forms and the Schur algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bernard Hanzon, Martine Olivi (INRIA Sophia Antipolis), Ralf L.M. Peeters","submitted_at":"2010-12-15T11:09:56Z","abstract_excerpt":"A new finite atlas of overlapping balanced canonical forms for multivariate discrete-time lossless systems is presented. The canonical forms have the property that the controllability matrix is positive upper triangular up to a suitable permutation of its columns. This is a generalization of a similar balanced canonical form for continuous-time lossless systems. It is shown that this atlas is in fact a finite sub-atlas of the infinite atlas of overlapping balanced canonical forms for lossless systems that is associated with the tangential Schur algorithm; such canonical forms satisfy certain i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3281","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":"1012.3281","created_at":"2026-05-18T04:33:17.312929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.3281v1","created_at":"2026-05-18T04:33:17.312929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3281","created_at":"2026-05-18T04:33:17.312929+00:00"},{"alias_kind":"pith_short_12","alias_value":"LCRNKK7C66EW","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"LCRNKK7C66EWUAHX","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"LCRNKK7C","created_at":"2026-05-18T12:26:10.704358+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/LCRNKK7C66EWUAHXMP6JFZ6XGU","json":"https://pith.science/pith/LCRNKK7C66EWUAHXMP6JFZ6XGU.json","graph_json":"https://pith.science/api/pith-number/LCRNKK7C66EWUAHXMP6JFZ6XGU/graph.json","events_json":"https://pith.science/api/pith-number/LCRNKK7C66EWUAHXMP6JFZ6XGU/events.json","paper":"https://pith.science/paper/LCRNKK7C"},"agent_actions":{"view_html":"https://pith.science/pith/LCRNKK7C66EWUAHXMP6JFZ6XGU","download_json":"https://pith.science/pith/LCRNKK7C66EWUAHXMP6JFZ6XGU.json","view_paper":"https://pith.science/paper/LCRNKK7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.3281&json=true","fetch_graph":"https://pith.science/api/pith-number/LCRNKK7C66EWUAHXMP6JFZ6XGU/graph.json","fetch_events":"https://pith.science/api/pith-number/LCRNKK7C66EWUAHXMP6JFZ6XGU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LCRNKK7C66EWUAHXMP6JFZ6XGU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LCRNKK7C66EWUAHXMP6JFZ6XGU/action/storage_attestation","attest_author":"https://pith.science/pith/LCRNKK7C66EWUAHXMP6JFZ6XGU/action/author_attestation","sign_citation":"https://pith.science/pith/LCRNKK7C66EWUAHXMP6JFZ6XGU/action/citation_signature","submit_replication":"https://pith.science/pith/LCRNKK7C66EWUAHXMP6JFZ6XGU/action/replication_record"}},"created_at":"2026-05-18T04:33:17.312929+00:00","updated_at":"2026-05-18T04:33:17.312929+00:00"}