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We prove that\n  $$\n  \\sigma_1^2+\\dots+\\sigma_{n-1}^2+\\sigma_{n+1}^2+\\dots+\\sigma_{N}^2\\leq (N-2)\\|\\mathcal T\\|^2 + \\sigma_n^2,\\quad n=1,\\dots,N, \\qquad\\qquad (1)\n  $$ where $\\|\\cdot\\|$ denotes the Frobenius norm. We also show that at least for the cubic tensors the inverse problem always has a solution. Namely, for each $\\sigma_1,\\dots,\\sigma_N$ that satisfy (1) and the trivial inequalities $\\sigma_1\\geq \\frac{1}{\\sqrt{I}}\\|\\mathcal T\\|,\\dots, \\sigma_N\\geq \\frac{1}{\\sqrt"},"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":"1612.03751","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-12-12T15:42:14Z","cross_cats_sorted":[],"title_canon_sha256":"759652fbdb5d8d0eda776130c03f09707e4c5628908430a70f1cc87d0dbfd5dc","abstract_canon_sha256":"fbc69b0f15c7ad1f048678ba8bb4049a501e0e9fc61cf1330f02c728cbd9b9c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:10.595270Z","signature_b64":"Wp7TCK553hXKOdT5PDCpG/VpM1FRBXwTgCC700G1gLNFLuBrpNwKdXJZBlLpsNoal9jCcSooGmx002ep5/qXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23ece8629833cf37661f64105854840a1637ac43f04b386f24c4e91117172391","last_reissued_at":"2026-05-18T00:15:10.594504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:10.594504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the largest multilinear singular values of higher-order tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Alwin Stegeman, Ignat Domanov, Lieven De Lathauwer","submitted_at":"2016-12-12T15:42:14Z","abstract_excerpt":"Let $\\sigma_n$ denote the largest mode-$n$ multilinear singular value of an $I_1\\times\\dots \\times I_N$ tensor $\\mathcal T$. We prove that\n  $$\n  \\sigma_1^2+\\dots+\\sigma_{n-1}^2+\\sigma_{n+1}^2+\\dots+\\sigma_{N}^2\\leq (N-2)\\|\\mathcal T\\|^2 + \\sigma_n^2,\\quad n=1,\\dots,N, \\qquad\\qquad (1)\n  $$ where $\\|\\cdot\\|$ denotes the Frobenius norm. We also show that at least for the cubic tensors the inverse problem always has a solution. Namely, for each $\\sigma_1,\\dots,\\sigma_N$ that satisfy (1) and the trivial inequalities $\\sigma_1\\geq \\frac{1}{\\sqrt{I}}\\|\\mathcal T\\|,\\dots, \\sigma_N\\geq \\frac{1}{\\sqrt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03751","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.03751","created_at":"2026-05-18T00:15:10.594626+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.03751v2","created_at":"2026-05-18T00:15:10.594626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03751","created_at":"2026-05-18T00:15:10.594626+00:00"},{"alias_kind":"pith_short_12","alias_value":"EPWOQYUYGPHT","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EPWOQYUYGPHTOZQ7","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EPWOQYUY","created_at":"2026-05-18T12:30:12.583610+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/EPWOQYUYGPHTOZQ7MQIFQVEEBI","json":"https://pith.science/pith/EPWOQYUYGPHTOZQ7MQIFQVEEBI.json","graph_json":"https://pith.science/api/pith-number/EPWOQYUYGPHTOZQ7MQIFQVEEBI/graph.json","events_json":"https://pith.science/api/pith-number/EPWOQYUYGPHTOZQ7MQIFQVEEBI/events.json","paper":"https://pith.science/paper/EPWOQYUY"},"agent_actions":{"view_html":"https://pith.science/pith/EPWOQYUYGPHTOZQ7MQIFQVEEBI","download_json":"https://pith.science/pith/EPWOQYUYGPHTOZQ7MQIFQVEEBI.json","view_paper":"https://pith.science/paper/EPWOQYUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.03751&json=true","fetch_graph":"https://pith.science/api/pith-number/EPWOQYUYGPHTOZQ7MQIFQVEEBI/graph.json","fetch_events":"https://pith.science/api/pith-number/EPWOQYUYGPHTOZQ7MQIFQVEEBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EPWOQYUYGPHTOZQ7MQIFQVEEBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EPWOQYUYGPHTOZQ7MQIFQVEEBI/action/storage_attestation","attest_author":"https://pith.science/pith/EPWOQYUYGPHTOZQ7MQIFQVEEBI/action/author_attestation","sign_citation":"https://pith.science/pith/EPWOQYUYGPHTOZQ7MQIFQVEEBI/action/citation_signature","submit_replication":"https://pith.science/pith/EPWOQYUYGPHTOZQ7MQIFQVEEBI/action/replication_record"}},"created_at":"2026-05-18T00:15:10.594626+00:00","updated_at":"2026-05-18T00:15:10.594626+00:00"}