{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:C432S33V6GXZO6KBTTFTJEADGQ","short_pith_number":"pith:C432S33V","schema_version":"1.0","canonical_sha256":"1737a96f75f1af9779419ccb34900334018721c53665f4991b2ecf82f4022908","source":{"kind":"arxiv","id":"1705.01576","version":1},"attestation_state":"computed","paper":{"title":"Fourth-order Tensors with Multidimensional Discrete Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.NA","authors_text":"Xiaodong Wang, Xiao-Yang Liu","submitted_at":"2017-05-03T18:44:31Z","abstract_excerpt":"The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to the development of multilinear modeling tools and efficient algorithms. In this paper, we build a novel multilinear tensor space that supports useful algorithms such as SVD and QR, while generalizing the matrix space to fourth-order tensors was believed to be challenging. Specifically, given any multidimensional discrete transform, we show that fourth-order"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.01576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-05-03T18:44:31Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7bc907ef7212a284ee29a28a2ed25a43a264c07119a20e919c98dffa0c4b7ab0","abstract_canon_sha256":"1823f26acfeab444a0301deb3485372949f00e5307e93ec612f89de4c735930e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:04.623748Z","signature_b64":"ZDPNMQSIqrYwM6YtQfy8UcDNW8e6nX7rEZC1gHoesRd1Oeqxb9g0+A9jxdXFT6mddb5yFG5c5HF3N/66Z3QxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1737a96f75f1af9779419ccb34900334018721c53665f4991b2ecf82f4022908","last_reissued_at":"2026-05-18T00:45:04.623409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:04.623409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fourth-order Tensors with Multidimensional Discrete Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.NA","authors_text":"Xiaodong Wang, Xiao-Yang Liu","submitted_at":"2017-05-03T18:44:31Z","abstract_excerpt":"The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to the development of multilinear modeling tools and efficient algorithms. In this paper, we build a novel multilinear tensor space that supports useful algorithms such as SVD and QR, while generalizing the matrix space to fourth-order tensors was believed to be challenging. Specifically, given any multidimensional discrete transform, we show that fourth-order"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01576","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.01576","created_at":"2026-05-18T00:45:04.623464+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.01576v1","created_at":"2026-05-18T00:45:04.623464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01576","created_at":"2026-05-18T00:45:04.623464+00:00"},{"alias_kind":"pith_short_12","alias_value":"C432S33V6GXZ","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"C432S33V6GXZO6KB","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"C432S33V","created_at":"2026-05-18T12:31:08.081275+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ","json":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ.json","graph_json":"https://pith.science/api/pith-number/C432S33V6GXZO6KBTTFTJEADGQ/graph.json","events_json":"https://pith.science/api/pith-number/C432S33V6GXZO6KBTTFTJEADGQ/events.json","paper":"https://pith.science/paper/C432S33V"},"agent_actions":{"view_html":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ","download_json":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ.json","view_paper":"https://pith.science/paper/C432S33V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.01576&json=true","fetch_graph":"https://pith.science/api/pith-number/C432S33V6GXZO6KBTTFTJEADGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/C432S33V6GXZO6KBTTFTJEADGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ/action/storage_attestation","attest_author":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ/action/author_attestation","sign_citation":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ/action/citation_signature","submit_replication":"https://pith.science/pith/C432S33V6GXZO6KBTTFTJEADGQ/action/replication_record"}},"created_at":"2026-05-18T00:45:04.623464+00:00","updated_at":"2026-05-18T00:45:04.623464+00:00"}