{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KPNZOLOCMNQI3MEVW7GF5ERBGS","short_pith_number":"pith:KPNZOLOC","canonical_record":{"source":{"id":"1112.6018","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2011-12-27T20:48:03Z","cross_cats_sorted":[],"title_canon_sha256":"1b7a43796bb848c0d5103e20dd9c304f171b9ff119c20133dd065db16e219047","abstract_canon_sha256":"9ece7ff5b53c02f71bad23bc74617cf52ec2405b53b0423df41eef6d5cc96929"},"schema_version":"1.0"},"canonical_sha256":"53db972dc263608db095b7cc5e922134b08f9ba89d88811e2a41d348e819168f","source":{"kind":"arxiv","id":"1112.6018","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6018","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6018v2","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6018","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"KPNZOLOCMNQI","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KPNZOLOCMNQI3MEV","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KPNZOLOC","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KPNZOLOCMNQI3MEVW7GF5ERBGS","target":"record","payload":{"canonical_record":{"source":{"id":"1112.6018","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2011-12-27T20:48:03Z","cross_cats_sorted":[],"title_canon_sha256":"1b7a43796bb848c0d5103e20dd9c304f171b9ff119c20133dd065db16e219047","abstract_canon_sha256":"9ece7ff5b53c02f71bad23bc74617cf52ec2405b53b0423df41eef6d5cc96929"},"schema_version":"1.0"},"canonical_sha256":"53db972dc263608db095b7cc5e922134b08f9ba89d88811e2a41d348e819168f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:26.542252Z","signature_b64":"Ax5CU8ZQphZ+m+AQV/Tgd7kM3Jkv12fOuBnxxo57JF/NDyG4LHFmFb6y/48gVlonmVgfLBKq+KomnOtL6Zz+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53db972dc263608db095b7cc5e922134b08f9ba89d88811e2a41d348e819168f","last_reissued_at":"2026-05-18T04:05:26.541508Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:26.541508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.6018","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":"2026-05-18T04:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3P9vlr0n1bTi+eFX0fNky70EZV3N0VtB9WN6nBxR6e1uUjyPHOEtnfiZX71JUNwheGR6qMxVyJOnM8WwBzyWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:10:35.498095Z"},"content_sha256":"94b89dea05ce8a505fe1fd4d3c5c3f763ba6f31a29e506d4cfebd2bd10480fbe","schema_version":"1.0","event_id":"sha256:94b89dea05ce8a505fe1fd4d3c5c3f763ba6f31a29e506d4cfebd2bd10480fbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KPNZOLOCMNQI3MEVW7GF5ERBGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multilevel quasiseparable matrices in PDE-constrained optimization","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jacek Gondzio, Pavel Zhlobich","submitted_at":"2011-12-27T20:48:03Z","abstract_excerpt":"Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems of saddle-point type. In this paper we propose and develop a novel approach to solving such systems by exploiting so-called quasiseparable matrices. One may think of a usual quasiseparable matrix as of a discrete analog of the Green's function of a one-dimensional differential operator. Nice feature of such matrices is that almost every algorithm which employ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6018","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":""},"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":"2026-05-18T04:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yab8HNzw9I68RfIlmtgE+uZbWZcRX9tS/PlEzX8N1nBL+yJcTZ6fsuzefDUSNxOd6HFD6XsoQCZCKjqfXC6ZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:10:35.498696Z"},"content_sha256":"ae13cb70de955ee81c2798825f0dd546c6d4091ff731f7d5b578a3ab7a73833c","schema_version":"1.0","event_id":"sha256:ae13cb70de955ee81c2798825f0dd546c6d4091ff731f7d5b578a3ab7a73833c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KPNZOLOCMNQI3MEVW7GF5ERBGS/bundle.json","state_url":"https://pith.science/pith/KPNZOLOCMNQI3MEVW7GF5ERBGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KPNZOLOCMNQI3MEVW7GF5ERBGS/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":"2026-06-06T20:10:35Z","links":{"resolver":"https://pith.science/pith/KPNZOLOCMNQI3MEVW7GF5ERBGS","bundle":"https://pith.science/pith/KPNZOLOCMNQI3MEVW7GF5ERBGS/bundle.json","state":"https://pith.science/pith/KPNZOLOCMNQI3MEVW7GF5ERBGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KPNZOLOCMNQI3MEVW7GF5ERBGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KPNZOLOCMNQI3MEVW7GF5ERBGS","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":"9ece7ff5b53c02f71bad23bc74617cf52ec2405b53b0423df41eef6d5cc96929","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2011-12-27T20:48:03Z","title_canon_sha256":"1b7a43796bb848c0d5103e20dd9c304f171b9ff119c20133dd065db16e219047"},"schema_version":"1.0","source":{"id":"1112.6018","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6018","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6018v2","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6018","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"KPNZOLOCMNQI","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KPNZOLOCMNQI3MEV","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KPNZOLOC","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:ae13cb70de955ee81c2798825f0dd546c6d4091ff731f7d5b578a3ab7a73833c","target":"graph","created_at":"2026-05-18T04:05:26Z","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":"Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems of saddle-point type. In this paper we propose and develop a novel approach to solving such systems by exploiting so-called quasiseparable matrices. One may think of a usual quasiseparable matrix as of a discrete analog of the Green's function of a one-dimensional differential operator. Nice feature of such matrices is that almost every algorithm which employ","authors_text":"Jacek Gondzio, Pavel Zhlobich","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2011-12-27T20:48:03Z","title":"Multilevel quasiseparable matrices in PDE-constrained optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6018","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":"sha256:94b89dea05ce8a505fe1fd4d3c5c3f763ba6f31a29e506d4cfebd2bd10480fbe","target":"record","created_at":"2026-05-18T04:05:26Z","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":"9ece7ff5b53c02f71bad23bc74617cf52ec2405b53b0423df41eef6d5cc96929","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2011-12-27T20:48:03Z","title_canon_sha256":"1b7a43796bb848c0d5103e20dd9c304f171b9ff119c20133dd065db16e219047"},"schema_version":"1.0","source":{"id":"1112.6018","kind":"arxiv","version":2}},"canonical_sha256":"53db972dc263608db095b7cc5e922134b08f9ba89d88811e2a41d348e819168f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53db972dc263608db095b7cc5e922134b08f9ba89d88811e2a41d348e819168f","first_computed_at":"2026-05-18T04:05:26.541508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:26.541508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ax5CU8ZQphZ+m+AQV/Tgd7kM3Jkv12fOuBnxxo57JF/NDyG4LHFmFb6y/48gVlonmVgfLBKq+KomnOtL6Zz+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:26.542252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.6018","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94b89dea05ce8a505fe1fd4d3c5c3f763ba6f31a29e506d4cfebd2bd10480fbe","sha256:ae13cb70de955ee81c2798825f0dd546c6d4091ff731f7d5b578a3ab7a73833c"],"state_sha256":"2edf4008273789dca1c2f51848daf2643e8ab4e554678d2df696fd93ac7aecf3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iP8vKYv+Bv+0Lss5I1xDdIfKtVmgQSAL0+KwTz0gIyhajzjZL6nNT7RuWCCjLBnbG57S+T1w2S2vz3fBTYaFBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:10:35.501139Z","bundle_sha256":"9aa92c69b9e7783fd14d40f3edc27a8f38d3ad2e83be067830358e25eb548e9e"}}