{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2SL7SJZB2VBD4X665EYEZOQZZQ","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":"42564b9acb3c41f3bda63e49c3c449ceaff4e075126d1aadd65d43c8a5995b60","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-08-09T10:42:43Z","title_canon_sha256":"a436491e0f94763e4616f44cde320de9d99631fd9151eeb67403b57a5e1cad08"},"schema_version":"1.0","source":{"id":"1208.1869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1869","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1869v1","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1869","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"pith_short_12","alias_value":"2SL7SJZB2VBD","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2SL7SJZB2VBD4X66","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2SL7SJZB","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:398f448de915864cf59420ee7430837acdbaaed2f457f8a2a5a239955b03cff3","target":"graph","created_at":"2026-05-18T03:49:09Z","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"},"paper":{"abstract_excerpt":"We here specialize the standard matrix-valued polynomial interpolation to the case where on the imaginary axis the interpolating polynomials admit various symmetries: Positive semidefinite, Skew-Hermitian, $J$-Hermitian, Hamiltonian and others. The procedure is comprized of three stages, illustrated through the case where on $i\\R$ the interpolating polynomials are to be positive semidefinite. We first, on the expense of doubling the degree, obtain a minimal degree interpolating polynomial $P(s)$ which on $i\\R$ is Hermitian. Then we find all polynomials $\\Psi(s)$, vanishing at the interpolation","authors_text":"Daniel Alpay, Izchak Lewkowicz","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-08-09T10:42:43Z","title":"Interpolation by polynomials with symmetries on the imaginary axis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1869","kind":"arxiv","version":1},"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:b67777c7795b1edab4c990b2fb46f203dfaf18e6454e5368a12e4bf13fbfe036","target":"record","created_at":"2026-05-18T03:49:09Z","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":"42564b9acb3c41f3bda63e49c3c449ceaff4e075126d1aadd65d43c8a5995b60","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-08-09T10:42:43Z","title_canon_sha256":"a436491e0f94763e4616f44cde320de9d99631fd9151eeb67403b57a5e1cad08"},"schema_version":"1.0","source":{"id":"1208.1869","kind":"arxiv","version":1}},"canonical_sha256":"d497f92721d5423e5fdee9304cba19cc1e7e638844ab036d6ac141eb5195ae5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d497f92721d5423e5fdee9304cba19cc1e7e638844ab036d6ac141eb5195ae5b","first_computed_at":"2026-05-18T03:49:09.792672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:09.792672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nrwuVfI/tjBEGeTqnnmbq5gfR5CvK7TYRfPOD8xC3ILFXPkzj0lKph1SQyeSj18zckbvCau5FNP5jRfFAtptBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:09.793177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b67777c7795b1edab4c990b2fb46f203dfaf18e6454e5368a12e4bf13fbfe036","sha256:398f448de915864cf59420ee7430837acdbaaed2f457f8a2a5a239955b03cff3"],"state_sha256":"6289b53ee04083c36a90f1f66591fb4f368fefda8c8d0887771aa75c1d661000"}