{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:A2FUJA7TGR5IKHOJZWDG2DI5VU","short_pith_number":"pith:A2FUJA7T","canonical_record":{"source":{"id":"1312.3976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-13T22:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"49caf1d87d005c49443b3978ca328aef879583715853bc90e0cb38bd04d8cba2","abstract_canon_sha256":"b16d627ed6f67d7ab0d037aed7294a3cea50f398c3318faea78c4fb0d0ac987e"},"schema_version":"1.0"},"canonical_sha256":"068b4483f3347a851dc9cd866d0d1dad3f58163ed923ebd5c68ea7a8b91358b7","source":{"kind":"arxiv","id":"1312.3976","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3976","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3976v1","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3976","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"A2FUJA7TGR5I","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A2FUJA7TGR5IKHOJ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A2FUJA7T","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:A2FUJA7TGR5IKHOJZWDG2DI5VU","target":"record","payload":{"canonical_record":{"source":{"id":"1312.3976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-13T22:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"49caf1d87d005c49443b3978ca328aef879583715853bc90e0cb38bd04d8cba2","abstract_canon_sha256":"b16d627ed6f67d7ab0d037aed7294a3cea50f398c3318faea78c4fb0d0ac987e"},"schema_version":"1.0"},"canonical_sha256":"068b4483f3347a851dc9cd866d0d1dad3f58163ed923ebd5c68ea7a8b91358b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:36.395859Z","signature_b64":"rAEtS7QJvAy9I19KKsCWSKKB8kbIrGJASAgAIAaIJV3xuEfQvBkvm2mx6gDc6vyB3DNvPvAI4fi276LEBsymAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"068b4483f3347a851dc9cd866d0d1dad3f58163ed923ebd5c68ea7a8b91358b7","last_reissued_at":"2026-05-18T03:04:36.395119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:36.395119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.3976","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rXK3buaz/eQo2UJ368clfOetRF3gCmDLLp8LTCcD33keL9/hXx4iZPlpaEG/+N2/CinU2+lG1DByR5ZGsXzHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:15:27.014048Z"},"content_sha256":"7094e9ad3ccfbb60c16e73af1ab7424cd3ffc49340dd3fce40358124befe9ee7","schema_version":"1.0","event_id":"sha256:7094e9ad3ccfbb60c16e73af1ab7424cd3ffc49340dd3fce40358124befe9ee7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:A2FUJA7TGR5IKHOJZWDG2DI5VU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Randomized Proper Orthogonal Decomposition Technique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dan Yu, Suman Chakravorty","submitted_at":"2013-12-13T22:52:25Z","abstract_excerpt":"In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced order models by randomly choosing a subset of the inputs/outputs of the system to construct a suitable small sized Hankel matrix from the full Hankel matrix. It is shown that the RPOD technique is computationally orders of magnitude cheaper when compared to techniques such as the Eigensystem Realization algorithm (ERA)/Balanced POD (BPOD) while obtaining the sam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3976","kind":"arxiv","version":1},"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":"2026-05-18T03:04:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avUFqEc7fpz7Dvq3Pwekqxw+EKss5Nhv4qIp7Z8YASFBiLB3dF1tXSN/HCehBLzLMpjeXpvD4u6uyrg+b7buDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:15:27.014795Z"},"content_sha256":"200ccbd2e2ecb61c7d1ef31ce7e6fcd41080e12fb2438d786ced7701adbb8e14","schema_version":"1.0","event_id":"sha256:200ccbd2e2ecb61c7d1ef31ce7e6fcd41080e12fb2438d786ced7701adbb8e14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A2FUJA7TGR5IKHOJZWDG2DI5VU/bundle.json","state_url":"https://pith.science/pith/A2FUJA7TGR5IKHOJZWDG2DI5VU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A2FUJA7TGR5IKHOJZWDG2DI5VU/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":"2026-05-22T03:15:27Z","links":{"resolver":"https://pith.science/pith/A2FUJA7TGR5IKHOJZWDG2DI5VU","bundle":"https://pith.science/pith/A2FUJA7TGR5IKHOJZWDG2DI5VU/bundle.json","state":"https://pith.science/pith/A2FUJA7TGR5IKHOJZWDG2DI5VU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A2FUJA7TGR5IKHOJZWDG2DI5VU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:A2FUJA7TGR5IKHOJZWDG2DI5VU","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":"b16d627ed6f67d7ab0d037aed7294a3cea50f398c3318faea78c4fb0d0ac987e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-13T22:52:25Z","title_canon_sha256":"49caf1d87d005c49443b3978ca328aef879583715853bc90e0cb38bd04d8cba2"},"schema_version":"1.0","source":{"id":"1312.3976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3976","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3976v1","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3976","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"A2FUJA7TGR5I","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A2FUJA7TGR5IKHOJ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A2FUJA7T","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:200ccbd2e2ecb61c7d1ef31ce7e6fcd41080e12fb2438d786ced7701adbb8e14","target":"graph","created_at":"2026-05-18T03:04:36Z","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":"In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced order models by randomly choosing a subset of the inputs/outputs of the system to construct a suitable small sized Hankel matrix from the full Hankel matrix. It is shown that the RPOD technique is computationally orders of magnitude cheaper when compared to techniques such as the Eigensystem Realization algorithm (ERA)/Balanced POD (BPOD) while obtaining the sam","authors_text":"Dan Yu, Suman Chakravorty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-13T22:52:25Z","title":"A Randomized Proper Orthogonal Decomposition Technique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3976","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":"sha256:7094e9ad3ccfbb60c16e73af1ab7424cd3ffc49340dd3fce40358124befe9ee7","target":"record","created_at":"2026-05-18T03:04:36Z","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":"b16d627ed6f67d7ab0d037aed7294a3cea50f398c3318faea78c4fb0d0ac987e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-13T22:52:25Z","title_canon_sha256":"49caf1d87d005c49443b3978ca328aef879583715853bc90e0cb38bd04d8cba2"},"schema_version":"1.0","source":{"id":"1312.3976","kind":"arxiv","version":1}},"canonical_sha256":"068b4483f3347a851dc9cd866d0d1dad3f58163ed923ebd5c68ea7a8b91358b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"068b4483f3347a851dc9cd866d0d1dad3f58163ed923ebd5c68ea7a8b91358b7","first_computed_at":"2026-05-18T03:04:36.395119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:36.395119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rAEtS7QJvAy9I19KKsCWSKKB8kbIrGJASAgAIAaIJV3xuEfQvBkvm2mx6gDc6vyB3DNvPvAI4fi276LEBsymAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:36.395859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7094e9ad3ccfbb60c16e73af1ab7424cd3ffc49340dd3fce40358124befe9ee7","sha256:200ccbd2e2ecb61c7d1ef31ce7e6fcd41080e12fb2438d786ced7701adbb8e14"],"state_sha256":"5cf92bd7516c5286b96bd4ced73f9e044fd16dadd9a0763967348d563fa1f4a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14KxEqYm9nXORfZruGu/d9L+0qUnBkaYYnOvkWfWeZsnOw0yFdSiNqz+pKwCVA1jyIBKRnstDiPYEpxOO2OcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T03:15:27.018442Z","bundle_sha256":"2b82bdb6c3f284a45ada3824cd7f1bbfd47e11747e12b86b525abf557c1912dc"}}