{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4376JMSK5D5RQCDRQHOYQCZ5YB","short_pith_number":"pith:4376JMSK","canonical_record":{"source":{"id":"1402.2018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-02-10T02:20:09Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"f83f658c5a26d711000090e8f2a5cec3f54f096df95a12138af7f1813e4ebf43","abstract_canon_sha256":"583ccd1305252588b7d834e1b6a80c95d81e7fd728cd2f98c29f1621a73982f1"},"schema_version":"1.0"},"canonical_sha256":"e6ffe4b24ae8fb18087181dd880b3dc042c6ce05e27c330e40a3669f21f22370","source":{"kind":"arxiv","id":"1402.2018","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2018","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2018v1","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2018","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"4376JMSK5D5R","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"4376JMSK5D5RQCDR","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"4376JMSK","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4376JMSK5D5RQCDRQHOYQCZ5YB","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-02-10T02:20:09Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"f83f658c5a26d711000090e8f2a5cec3f54f096df95a12138af7f1813e4ebf43","abstract_canon_sha256":"583ccd1305252588b7d834e1b6a80c95d81e7fd728cd2f98c29f1621a73982f1"},"schema_version":"1.0"},"canonical_sha256":"e6ffe4b24ae8fb18087181dd880b3dc042c6ce05e27c330e40a3669f21f22370","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:46.056513Z","signature_b64":"En+2VtqlvORyitlvqa9VXLdLSkVvboGQFdYSPUpU7BiYnbaGkuY3dcPXnT5Lzx3KTt3MsjQhwTZPvfHII0mvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6ffe4b24ae8fb18087181dd880b3dc042c6ce05e27c330e40a3669f21f22370","last_reissued_at":"2026-05-18T01:44:46.055851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:46.055851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2018","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":"2026-05-18T01:44:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R2R+hYGRo+7uSKJThbITCO7V/MtkRhWmEHtXEXAWwOqusfSCKbnqB5M+z6QmgY6YuE7fKY0ZYtxOmBQtALYRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:46:40.709019Z"},"content_sha256":"16fa695e8f4c2fef75c7825f6beee11fdbae9a772b6011e255a2482520d6b324","schema_version":"1.0","event_id":"sha256:16fa695e8f4c2fef75c7825f6beee11fdbae9a772b6011e255a2482520d6b324"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4376JMSK5D5RQCDRQHOYQCZ5YB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.NA","authors_text":"Adrian Sandu, Ionel M. Navon, R\\u{a}zvan \\c{S}tef\\u{a}nescu","submitted_at":"2014-02-10T02:20:09Z","abstract_excerpt":"This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2018","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":"2026-05-18T01:44:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yt+5Om8mZhnSXS7s7iPEk6br2lZpBJyNi+8rC+im1JUmxK86UoTG0jAF38NG8Tn//NPhP0g3cSq/B09MZvOMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:46:40.709376Z"},"content_sha256":"ee9b58ddd9eb411c131c16a2d0a50fa3f591622ba68cac6e55ac27744c97e687","schema_version":"1.0","event_id":"sha256:ee9b58ddd9eb411c131c16a2d0a50fa3f591622ba68cac6e55ac27744c97e687"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4376JMSK5D5RQCDRQHOYQCZ5YB/bundle.json","state_url":"https://pith.science/pith/4376JMSK5D5RQCDRQHOYQCZ5YB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4376JMSK5D5RQCDRQHOYQCZ5YB/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":"2026-06-26T20:46:40Z","links":{"resolver":"https://pith.science/pith/4376JMSK5D5RQCDRQHOYQCZ5YB","bundle":"https://pith.science/pith/4376JMSK5D5RQCDRQHOYQCZ5YB/bundle.json","state":"https://pith.science/pith/4376JMSK5D5RQCDRQHOYQCZ5YB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4376JMSK5D5RQCDRQHOYQCZ5YB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4376JMSK5D5RQCDRQHOYQCZ5YB","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":"583ccd1305252588b7d834e1b6a80c95d81e7fd728cd2f98c29f1621a73982f1","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-02-10T02:20:09Z","title_canon_sha256":"f83f658c5a26d711000090e8f2a5cec3f54f096df95a12138af7f1813e4ebf43"},"schema_version":"1.0","source":{"id":"1402.2018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2018","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2018v1","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2018","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"4376JMSK5D5R","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"4376JMSK5D5RQCDR","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"4376JMSK","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:ee9b58ddd9eb411c131c16a2d0a50fa3f591622ba68cac6e55ac27744c97e687","target":"graph","created_at":"2026-05-18T01:44:46Z","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":"This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once t","authors_text":"Adrian Sandu, Ionel M. Navon, R\\u{a}zvan \\c{S}tef\\u{a}nescu","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-02-10T02:20:09Z","title":"Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2018","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":"sha256:16fa695e8f4c2fef75c7825f6beee11fdbae9a772b6011e255a2482520d6b324","target":"record","created_at":"2026-05-18T01:44:46Z","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":"583ccd1305252588b7d834e1b6a80c95d81e7fd728cd2f98c29f1621a73982f1","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-02-10T02:20:09Z","title_canon_sha256":"f83f658c5a26d711000090e8f2a5cec3f54f096df95a12138af7f1813e4ebf43"},"schema_version":"1.0","source":{"id":"1402.2018","kind":"arxiv","version":1}},"canonical_sha256":"e6ffe4b24ae8fb18087181dd880b3dc042c6ce05e27c330e40a3669f21f22370","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6ffe4b24ae8fb18087181dd880b3dc042c6ce05e27c330e40a3669f21f22370","first_computed_at":"2026-05-18T01:44:46.055851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:46.055851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"En+2VtqlvORyitlvqa9VXLdLSkVvboGQFdYSPUpU7BiYnbaGkuY3dcPXnT5Lzx3KTt3MsjQhwTZPvfHII0mvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:46.056513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16fa695e8f4c2fef75c7825f6beee11fdbae9a772b6011e255a2482520d6b324","sha256:ee9b58ddd9eb411c131c16a2d0a50fa3f591622ba68cac6e55ac27744c97e687"],"state_sha256":"e545be7bc11471706b03ef9a81252977c5d8c6ef55d7f27eb78a6f989fee2e02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MoNvqepdp3Kh0365liNrgl8UVU4uKa7/sgSR9bTjOjumok/T2Xk2cwRtI1wLoc4wPdwEoKaW//Xp1Ogt44n2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T20:46:40.711217Z","bundle_sha256":"7230727bd25ffb468e3b2b612ea8501c6fb028876876233a42f3204e5946fa49"}}