{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:W3C4CKLD5NFKOYVWDJQPBG2NCR","short_pith_number":"pith:W3C4CKLD","canonical_record":{"source":{"id":"2505.03057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-05T22:39:27Z","cross_cats_sorted":["cs.NA","cs.SY","eess.SY","math.DS","math.OC"],"title_canon_sha256":"58e520b2acca4578b8d4aebe68de829164d3c455117cfd56d7de46840c4b876e","abstract_canon_sha256":"af2ebacba8f3d4b82e41a68ef2aad78d96835920746327953f4d55b64400783f"},"schema_version":"1.0"},"canonical_sha256":"b6c5c12963eb4aa762b61a60f09b4d146bc43073fe48010c27220da92d305872","source":{"kind":"arxiv","id":"2505.03057","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.03057","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"2505.03057v2","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.03057","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"W3C4CKLD5NFK","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"pith_short_16","alias_value":"W3C4CKLD5NFKOYVW","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"pith_short_8","alias_value":"W3C4CKLD","created_at":"2026-06-04T00:06:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:W3C4CKLD5NFKOYVWDJQPBG2NCR","target":"record","payload":{"canonical_record":{"source":{"id":"2505.03057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-05T22:39:27Z","cross_cats_sorted":["cs.NA","cs.SY","eess.SY","math.DS","math.OC"],"title_canon_sha256":"58e520b2acca4578b8d4aebe68de829164d3c455117cfd56d7de46840c4b876e","abstract_canon_sha256":"af2ebacba8f3d4b82e41a68ef2aad78d96835920746327953f4d55b64400783f"},"schema_version":"1.0"},"canonical_sha256":"b6c5c12963eb4aa762b61a60f09b4d146bc43073fe48010c27220da92d305872","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T00:06:42.897016Z","signature_b64":"+qE5oaujyDwUMJyoJ8b/r9Z60A6w2k7WJuzoWCpqdGB45yJ/9D9LqvjJUeA6EwNWgHAYX3EFy8i6DohbzofvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6c5c12963eb4aa762b61a60f09b4d146bc43073fe48010c27220da92d305872","last_reissued_at":"2026-06-04T00:06:42.896478Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T00:06:42.896478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.03057","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":"2026-06-04T00:06:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tF0na5PwC9VssKml9zd+P3S08SdRtCpVDYM9T9fjTul6CZm6XXSwg/p5hPGVvMhwB/FidRoIoTghkrqXEdXRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:43:25.166766Z"},"content_sha256":"d7333dcf2ab855bbdd752890a3c4ca2a611c48fe1992db8e7508ca98016033a2","schema_version":"1.0","event_id":"sha256:d7333dcf2ab855bbdd752890a3c4ca2a611c48fe1992db8e7508ca98016033a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:W3C4CKLD5NFKOYVWDJQPBG2NCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","cs.SY","eess.SY","math.DS","math.OC"],"primary_cat":"math.NA","authors_text":"Igor Pontes Duff, Ion Victor Gosea, Sean Reiter, Serkan Gugercin","submitted_at":"2025-05-05T22:39:27Z","abstract_excerpt":"This paper addresses the $\\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive interpolatory first-order optimality conditions for the linear quadratic-output $\\mathcal{H}_2$ minimization problem. These conditions correspond to the mixed-multipoint tangential interpolation of the full-order linear- and quadratic-output transfer functions, and generalize the Meier-Luenberger optimality framework for the $\\mathcal{H}_2$-optimal model reduction of lin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03057","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/2505.03057/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":"2026-06-04T00:06:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HHrVayspJcmV9p8PQlIJ76XnZP57GxL5NkOqyQ4bODxFMq9T3aZI6KdtxN5CVTothJsXWFZEbqMH9l6nkLHfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:43:25.167153Z"},"content_sha256":"dfd72ca89f35b790548154b8ef5bcf45f29d803c178704046670ada5c5a8263e","schema_version":"1.0","event_id":"sha256:dfd72ca89f35b790548154b8ef5bcf45f29d803c178704046670ada5c5a8263e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3C4CKLD5NFKOYVWDJQPBG2NCR/bundle.json","state_url":"https://pith.science/pith/W3C4CKLD5NFKOYVWDJQPBG2NCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3C4CKLD5NFKOYVWDJQPBG2NCR/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":"2026-06-05T16:43:25Z","links":{"resolver":"https://pith.science/pith/W3C4CKLD5NFKOYVWDJQPBG2NCR","bundle":"https://pith.science/pith/W3C4CKLD5NFKOYVWDJQPBG2NCR/bundle.json","state":"https://pith.science/pith/W3C4CKLD5NFKOYVWDJQPBG2NCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3C4CKLD5NFKOYVWDJQPBG2NCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:W3C4CKLD5NFKOYVWDJQPBG2NCR","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":"af2ebacba8f3d4b82e41a68ef2aad78d96835920746327953f4d55b64400783f","cross_cats_sorted":["cs.NA","cs.SY","eess.SY","math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-05T22:39:27Z","title_canon_sha256":"58e520b2acca4578b8d4aebe68de829164d3c455117cfd56d7de46840c4b876e"},"schema_version":"1.0","source":{"id":"2505.03057","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.03057","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"2505.03057v2","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.03057","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"W3C4CKLD5NFK","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"pith_short_16","alias_value":"W3C4CKLD5NFKOYVW","created_at":"2026-06-04T00:06:42Z"},{"alias_kind":"pith_short_8","alias_value":"W3C4CKLD","created_at":"2026-06-04T00:06:42Z"}],"graph_snapshots":[{"event_id":"sha256:dfd72ca89f35b790548154b8ef5bcf45f29d803c178704046670ada5c5a8263e","target":"graph","created_at":"2026-06-04T00:06:42Z","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/2505.03057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper addresses the $\\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive interpolatory first-order optimality conditions for the linear quadratic-output $\\mathcal{H}_2$ minimization problem. These conditions correspond to the mixed-multipoint tangential interpolation of the full-order linear- and quadratic-output transfer functions, and generalize the Meier-Luenberger optimality framework for the $\\mathcal{H}_2$-optimal model reduction of lin","authors_text":"Igor Pontes Duff, Ion Victor Gosea, Sean Reiter, Serkan Gugercin","cross_cats":["cs.NA","cs.SY","eess.SY","math.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03057","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:d7333dcf2ab855bbdd752890a3c4ca2a611c48fe1992db8e7508ca98016033a2","target":"record","created_at":"2026-06-04T00:06:42Z","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":"af2ebacba8f3d4b82e41a68ef2aad78d96835920746327953f4d55b64400783f","cross_cats_sorted":["cs.NA","cs.SY","eess.SY","math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-05T22:39:27Z","title_canon_sha256":"58e520b2acca4578b8d4aebe68de829164d3c455117cfd56d7de46840c4b876e"},"schema_version":"1.0","source":{"id":"2505.03057","kind":"arxiv","version":2}},"canonical_sha256":"b6c5c12963eb4aa762b61a60f09b4d146bc43073fe48010c27220da92d305872","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6c5c12963eb4aa762b61a60f09b4d146bc43073fe48010c27220da92d305872","first_computed_at":"2026-06-04T00:06:42.896478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T00:06:42.896478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+qE5oaujyDwUMJyoJ8b/r9Z60A6w2k7WJuzoWCpqdGB45yJ/9D9LqvjJUeA6EwNWgHAYX3EFy8i6DohbzofvDA==","signature_status":"signed_v1","signed_at":"2026-06-04T00:06:42.897016Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.03057","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7333dcf2ab855bbdd752890a3c4ca2a611c48fe1992db8e7508ca98016033a2","sha256:dfd72ca89f35b790548154b8ef5bcf45f29d803c178704046670ada5c5a8263e"],"state_sha256":"f70a14d472983e21d5636c644830158e2bc4baa5edad365b0e25679321838752"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOElP7uHddMomvlDXzQiDX+OZtFinsN+cjdy15a+1ne9q8Mz4xwqcbS/4p9AgfeGZKntyCftJaE8ok1nWn1jBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:43:25.169269Z","bundle_sha256":"1ac0f2575c6407a6da9520a0030998959576af6ea2c58c287161dab901748b54"}}