{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:3O37F3MUVKQ5B2FY4PFNFO47P6","short_pith_number":"pith:3O37F3MU","schema_version":"1.0","canonical_sha256":"dbb7f2ed94aaa1d0e8b8e3cad2bb9f7fb7094f61f648063b3a45afd7c8035c0e","source":{"kind":"arxiv","id":"2302.14219","version":1},"attestation_state":"computed","paper":{"title":"Approximating Tensor Norms via Sphere Covering: Bridging the Gap Between Primal and Dual","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Jiang, Haodong Hu, Simai He, Zhening Li","submitted_at":"2023-02-28T00:47:33Z","abstract_excerpt":"The matrix spectral and nuclear norms appear in enormous applications. The generalizations of these norms to higher-order tensors is becoming increasingly important but unfortunately they are NP-hard to compute or even approximate. Although the two norms are dual to each other, the best known approximation bound achieved by polynomial-time algorithms for the tensor nuclear norm is worse than that for the tensor spectral norm. In this paper, we bridge this gap by proposing deterministic algorithms with the best bound for both tensor norms. Our methods not only improve the approximation bound fo"},"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":"2302.14219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-28T00:47:33Z","cross_cats_sorted":[],"title_canon_sha256":"d263dce87cf88700e0c36c436734ea4209f8009a94c3056b79c873ba2052e33e","abstract_canon_sha256":"e0f94df06d17eeeae67284ac0ae79301d06221785f158d3bb4d63ac7f2b5b227"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:46:42.206356Z","signature_b64":"8ZQkqdBrm7IVKD1JVoho5WsNqNYolbeuM1VLGkzrwpAwd1Ss94qJoeM42txwuvwQMLy04ISa4h+Pj8ugwWKxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbb7f2ed94aaa1d0e8b8e3cad2bb9f7fb7094f61f648063b3a45afd7c8035c0e","last_reissued_at":"2026-07-05T05:46:42.205851Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:46:42.205851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating Tensor Norms via Sphere Covering: Bridging the Gap Between Primal and Dual","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Jiang, Haodong Hu, Simai He, Zhening Li","submitted_at":"2023-02-28T00:47:33Z","abstract_excerpt":"The matrix spectral and nuclear norms appear in enormous applications. The generalizations of these norms to higher-order tensors is becoming increasingly important but unfortunately they are NP-hard to compute or even approximate. Although the two norms are dual to each other, the best known approximation bound achieved by polynomial-time algorithms for the tensor nuclear norm is worse than that for the tensor spectral norm. In this paper, we bridge this gap by proposing deterministic algorithms with the best bound for both tensor norms. Our methods not only improve the approximation bound fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.14219","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.14219/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2302.14219","created_at":"2026-07-05T05:46:42.205907+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.14219v1","created_at":"2026-07-05T05:46:42.205907+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.14219","created_at":"2026-07-05T05:46:42.205907+00:00"},{"alias_kind":"pith_short_12","alias_value":"3O37F3MUVKQ5","created_at":"2026-07-05T05:46:42.205907+00:00"},{"alias_kind":"pith_short_16","alias_value":"3O37F3MUVKQ5B2FY","created_at":"2026-07-05T05:46:42.205907+00:00"},{"alias_kind":"pith_short_8","alias_value":"3O37F3MU","created_at":"2026-07-05T05:46:42.205907+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.00966","citing_title":"A Framework for Computational Lower Bounds in Nontrivial Norm Approximation","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6","json":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6.json","graph_json":"https://pith.science/api/pith-number/3O37F3MUVKQ5B2FY4PFNFO47P6/graph.json","events_json":"https://pith.science/api/pith-number/3O37F3MUVKQ5B2FY4PFNFO47P6/events.json","paper":"https://pith.science/paper/3O37F3MU"},"agent_actions":{"view_html":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6","download_json":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6.json","view_paper":"https://pith.science/paper/3O37F3MU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.14219&json=true","fetch_graph":"https://pith.science/api/pith-number/3O37F3MUVKQ5B2FY4PFNFO47P6/graph.json","fetch_events":"https://pith.science/api/pith-number/3O37F3MUVKQ5B2FY4PFNFO47P6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6/action/storage_attestation","attest_author":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6/action/author_attestation","sign_citation":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6/action/citation_signature","submit_replication":"https://pith.science/pith/3O37F3MUVKQ5B2FY4PFNFO47P6/action/replication_record"}},"created_at":"2026-07-05T05:46:42.205907+00:00","updated_at":"2026-07-05T05:46:42.205907+00:00"}