{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:OPDJSMRTYV6GSZVKV4FOTI23GX","short_pith_number":"pith:OPDJSMRT","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"},"canonical_sha256":"73c6993233c57c6966aaaf0ae9a35b35d622ddda2b1db7aba5ae49b9a6d22c28","source":{"kind":"arxiv","id":"math/0612645","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612645","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612645v2","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612645","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"OPDJSMRTYV6G","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"OPDJSMRTYV6GSZVK","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"OPDJSMRT","created_at":"2026-06-03T22:06:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:OPDJSMRTYV6GSZVKV4FOTI23GX","target":"record","payload":{"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"},"canonical_sha256":"73c6993233c57c6966aaaf0ae9a35b35d622ddda2b1db7aba5ae49b9a6d22c28","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"},"source_kind":"arxiv","source_id":"math/0612645","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+RuaIsZOAD+oGk5XA9VE5s1WNNRxCPujpAuLdUF9TihHAHqUauTKPkjGVdVhRNtxkKzJet9RZRUOTe0300YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:16:34.011165Z"},"content_sha256":"1216c80ed0630e9308b54f06ce09142e6803fefa9ceb06cd2f84aa8dcb2b7787","schema_version":"1.0","event_id":"sha256:1216c80ed0630e9308b54f06ce09142e6803fefa9ceb06cd2f84aa8dcb2b7787"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:OPDJSMRTYV6GSZVKV4FOTI23GX","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOIkTUcBoG4N6M4HqVnSqWrvqpBFCkdOlkb6+NKXCdgS+kGUDjhBibrsUIW3+i3SU/J5WVwddTbVQOh+LQT2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:16:34.011567Z"},"content_sha256":"85627b3ae4657c38f5cd40fe4cd624f5e09215400db8b1d35b71a33414bc656e","schema_version":"1.0","event_id":"sha256:85627b3ae4657c38f5cd40fe4cd624f5e09215400db8b1d35b71a33414bc656e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/bundle.json","state_url":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T01:16:34Z","links":{"resolver":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX","bundle":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/bundle.json","state":"https://pith.science/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPDJSMRTYV6GSZVKV4FOTI23GX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:OPDJSMRTYV6GSZVKV4FOTI23GX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fe30774c3b1222f9a6e0350a6dbe0b633c57030d0f3d59bca297e8102eb9f7c9","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2006-12-21T14:48:32Z","title_canon_sha256":"aff4f767ae3823b4d077c66a7eb724bb75bee303f038811eb7a3b5cfa0431710"},"schema_version":"1.0","source":{"id":"math/0612645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612645","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612645v2","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612645","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"OPDJSMRTYV6G","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"OPDJSMRTYV6GSZVK","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"OPDJSMRT","created_at":"2026-06-03T22:06:21Z"}],"graph_snapshots":[{"event_id":"sha256:85627b3ae4657c38f5cd40fe4cd624f5e09215400db8b1d35b71a33414bc656e","target":"graph","created_at":"2026-06-03T22:06:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0612645/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Peter Oswald, Tatiana Shingel","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2006-12-21T14:48:32Z","title":"Splitting Methods for SU(N) Loop Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612645","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1216c80ed0630e9308b54f06ce09142e6803fefa9ceb06cd2f84aa8dcb2b7787","target":"record","created_at":"2026-06-03T22:06:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fe30774c3b1222f9a6e0350a6dbe0b633c57030d0f3d59bca297e8102eb9f7c9","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2006-12-21T14:48:32Z","title_canon_sha256":"aff4f767ae3823b4d077c66a7eb724bb75bee303f038811eb7a3b5cfa0431710"},"schema_version":"1.0","source":{"id":"math/0612645","kind":"arxiv","version":2}},"canonical_sha256":"73c6993233c57c6966aaaf0ae9a35b35d622ddda2b1db7aba5ae49b9a6d22c28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73c6993233c57c6966aaaf0ae9a35b35d622ddda2b1db7aba5ae49b9a6d22c28","first_computed_at":"2026-06-03T22:06:21.594797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:21.594797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tS9bV5waSE1sG8fRAlN7UfPmhhNpshbW6XGHYcgrP5AXWKz6F4VDhoGSDnCV+zbwDDlYMODnYP03iB8Kv8rNDQ==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:21.595183Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1216c80ed0630e9308b54f06ce09142e6803fefa9ceb06cd2f84aa8dcb2b7787","sha256:85627b3ae4657c38f5cd40fe4cd624f5e09215400db8b1d35b71a33414bc656e"],"state_sha256":"d6af42a829deae1c5be6bc74f81534d3a780b16b8beccd8d26811e2e2b253f84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDYXRcAXu+fkhzNfdmPWObibicW/byp69y8haSisFXSGJNk3TTTnCW13cx/jZb8WnqAeFba0ts2NrYni5+zACA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:16:34.013600Z","bundle_sha256":"f5cc2523d73bd1b7bc9b14394fdd9cbd76f4921bab9c25da62dd58fa9657e027"}}