{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:OPDJSMRTYV6GSZVKV4FOTI23GX","short_pith_number":"pith:OPDJSMRT","schema_version":"1.0","canonical_sha256":"73c6993233c57c6966aaaf0ae9a35b35d622ddda2b1db7aba5ae49b9a6d22c28","source":{"kind":"arxiv","id":"math/0612645","version":2},"attestation_state":"computed","paper":{"title":"Splitting Methods for SU(N) Loop Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Peter Oswald, Tatiana Shingel","submitted_at":"2006-12-21T14:48:32Z","abstract_excerpt":"The problem of finding the correct asymptotic rate of approximation by polynomial loops in dependence of the smoothness of the elements of a loop group seems not well-understood in general. For matrix Lie groups such as SU(N), it can be viewed as a problem of nonlinearly constrained trigonometric approximation. Motivated by applications to optical FIR filter design and control, we present some initial results for the case of SU(N)-loops, N>1. In particular, using representations via the exponential map and ideas from splitting methods, we prove that the best approximation of an SU(N)-loop belo"},"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":"math/0612645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2006-12-21T14:48:32Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"aff4f767ae3823b4d077c66a7eb724bb75bee303f038811eb7a3b5cfa0431710","abstract_canon_sha256":"fe30774c3b1222f9a6e0350a6dbe0b633c57030d0f3d59bca297e8102eb9f7c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:21.595183Z","signature_b64":"tS9bV5waSE1sG8fRAlN7UfPmhhNpshbW6XGHYcgrP5AXWKz6F4VDhoGSDnCV+zbwDDlYMODnYP03iB8Kv8rNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73c6993233c57c6966aaaf0ae9a35b35d622ddda2b1db7aba5ae49b9a6d22c28","last_reissued_at":"2026-06-03T22:06:21.594797Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:21.594797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Splitting Methods for SU(N) Loop Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Peter Oswald, Tatiana Shingel","submitted_at":"2006-12-21T14:48:32Z","abstract_excerpt":"The problem of finding the correct asymptotic rate of approximation by polynomial loops in dependence of the smoothness of the elements of a loop group seems not well-understood in general. For matrix Lie groups such as SU(N), it can be viewed as a problem of nonlinearly constrained trigonometric approximation. Motivated by applications to optical FIR filter design and control, we present some initial results for the case of SU(N)-loops, N>1. In particular, using representations via the exponential map and ideas from splitting methods, we prove that the best approximation of an SU(N)-loop belo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612645","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0612645/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0612645","created_at":"2026-06-03T22:06:21.594862+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0612645v2","created_at":"2026-06-03T22:06:21.594862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612645","created_at":"2026-06-03T22:06:21.594862+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPDJSMRTYV6G","created_at":"2026-06-03T22:06:21.594862+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPDJSMRTYV6GSZVK","created_at":"2026-06-03T22:06:21.594862+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPDJSMRT","created_at":"2026-06-03T22:06:21.594862+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/OPDJSMRTYV6GSZVKV4FOTI23GX","json":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX.json","graph_json":"https://pith.science/api/pith-number/OPDJSMRTYV6GSZVKV4FOTI23GX/graph.json","events_json":"https://pith.science/api/pith-number/OPDJSMRTYV6GSZVKV4FOTI23GX/events.json","paper":"https://pith.science/paper/OPDJSMRT"},"agent_actions":{"view_html":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX","download_json":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX.json","view_paper":"https://pith.science/paper/OPDJSMRT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0612645&json=true","fetch_graph":"https://pith.science/api/pith-number/OPDJSMRTYV6GSZVKV4FOTI23GX/graph.json","fetch_events":"https://pith.science/api/pith-number/OPDJSMRTYV6GSZVKV4FOTI23GX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/action/storage_attestation","attest_author":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/action/author_attestation","sign_citation":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/action/citation_signature","submit_replication":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/action/replication_record"}},"created_at":"2026-06-03T22:06:21.594862+00:00","updated_at":"2026-06-03T22:06:21.594862+00:00"}