{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KGUXBYRPUXQTKUGMQFXGB3YDKY","short_pith_number":"pith:KGUXBYRP","schema_version":"1.0","canonical_sha256":"51a970e22fa5e13550cc816e60ef03561017e32afdacd4b72b85d19feb818f89","source":{"kind":"arxiv","id":"1606.01766","version":1},"attestation_state":"computed","paper":{"title":"Symmetric and skew-symmetric block-Kronecker linearizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Heike Fa{\\ss}bender, Javier Perez, Nikta Shayanfar","submitted_at":"2016-06-06T14:42:11Z","abstract_excerpt":"Many applications give rise to structured matrix polynomials. The problem of constructing structure-preserving strong linearizations of structured matrix polynomials is revisited in this work and in the forthcoming ones \\cite{PartII,PartIII}. With the purpose of providing a much simpler framework for structure-preserving linearizations for symmetric and skew-symmetric matrix polynomial than the one based on Fiedler pencils with repetition, we introduce in this work the families of (modified) symmetric and skew-symmetric block Kronecker pencils. These families provide a large arena of structure"},"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":"1606.01766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-06T14:42:11Z","cross_cats_sorted":[],"title_canon_sha256":"7a00b6b4ea98de5349b4f068f1d4f4084d5bfa2c94b722f178a0782aff8cd9b0","abstract_canon_sha256":"7da096f2dc6bce613266f2437bd7c98d4b740730201aa55bb03f23b4c101f774"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:53.626006Z","signature_b64":"qcmcClhifjrJ0+V1PN6Ric7HubgFL9dH49nQ8/2un1ypN5x48GskH8xVpO4bsVks7PqnztWt6BVdQ1HyRw1XCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51a970e22fa5e13550cc816e60ef03561017e32afdacd4b72b85d19feb818f89","last_reissued_at":"2026-05-18T01:12:53.625636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:53.625636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric and skew-symmetric block-Kronecker linearizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Heike Fa{\\ss}bender, Javier Perez, Nikta Shayanfar","submitted_at":"2016-06-06T14:42:11Z","abstract_excerpt":"Many applications give rise to structured matrix polynomials. The problem of constructing structure-preserving strong linearizations of structured matrix polynomials is revisited in this work and in the forthcoming ones \\cite{PartII,PartIII}. With the purpose of providing a much simpler framework for structure-preserving linearizations for symmetric and skew-symmetric matrix polynomial than the one based on Fiedler pencils with repetition, we introduce in this work the families of (modified) symmetric and skew-symmetric block Kronecker pencils. These families provide a large arena of structure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01766","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":"1606.01766","created_at":"2026-05-18T01:12:53.625698+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01766v1","created_at":"2026-05-18T01:12:53.625698+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01766","created_at":"2026-05-18T01:12:53.625698+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGUXBYRPUXQT","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGUXBYRPUXQTKUGM","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGUXBYRP","created_at":"2026-05-18T12:30:25.849896+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/KGUXBYRPUXQTKUGMQFXGB3YDKY","json":"https://pith.science/pith/KGUXBYRPUXQTKUGMQFXGB3YDKY.json","graph_json":"https://pith.science/api/pith-number/KGUXBYRPUXQTKUGMQFXGB3YDKY/graph.json","events_json":"https://pith.science/api/pith-number/KGUXBYRPUXQTKUGMQFXGB3YDKY/events.json","paper":"https://pith.science/paper/KGUXBYRP"},"agent_actions":{"view_html":"https://pith.science/pith/KGUXBYRPUXQTKUGMQFXGB3YDKY","download_json":"https://pith.science/pith/KGUXBYRPUXQTKUGMQFXGB3YDKY.json","view_paper":"https://pith.science/paper/KGUXBYRP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01766&json=true","fetch_graph":"https://pith.science/api/pith-number/KGUXBYRPUXQTKUGMQFXGB3YDKY/graph.json","fetch_events":"https://pith.science/api/pith-number/KGUXBYRPUXQTKUGMQFXGB3YDKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGUXBYRPUXQTKUGMQFXGB3YDKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGUXBYRPUXQTKUGMQFXGB3YDKY/action/storage_attestation","attest_author":"https://pith.science/pith/KGUXBYRPUXQTKUGMQFXGB3YDKY/action/author_attestation","sign_citation":"https://pith.science/pith/KGUXBYRPUXQTKUGMQFXGB3YDKY/action/citation_signature","submit_replication":"https://pith.science/pith/KGUXBYRPUXQTKUGMQFXGB3YDKY/action/replication_record"}},"created_at":"2026-05-18T01:12:53.625698+00:00","updated_at":"2026-05-18T01:12:53.625698+00:00"}