{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YKPZURG55JG5MWIQH3TG4VFCTZ","short_pith_number":"pith:YKPZURG5","schema_version":"1.0","canonical_sha256":"c29f9a44ddea4dd659103ee66e54a29e7c4cf0e4fd38984e5e7fea19bbf7f80e","source":{"kind":"arxiv","id":"1109.0348","version":3},"attestation_state":"computed","paper":{"title":"E-Determinants of Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chen Ling, Liqun Qi, Shenglong Hu, Zheng-Hai Huang","submitted_at":"2011-09-02T03:19:03Z","abstract_excerpt":"We generalize the concept of the symmetric hyperdeterminants for symmetric tensors to the E-determinants for general tensors. We show that the E-determinant inherits many properties of the determinant of a matrix. These properties include: solvability of polynomial systems, the E-determinat of the composition of tensors, product formula for the E-determinant of a block tensor, Hadamard's inequality, Gersgrin's inequality and Minikowski's inequality. As a simple application, we show that if the leading coefficient tensor of a polynomial system is a triangular tensor with nonzero diagonal elemen"},"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":"1109.0348","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-02T03:19:03Z","cross_cats_sorted":[],"title_canon_sha256":"92f0d3becfdcc2525553cac23766cc7decc96930452a5a936f6475bd51f5730c","abstract_canon_sha256":"c63f5861743ec3abc3d2901062538a873fcdbd54efbb0593fa1e32781eaea38a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:11.844604Z","signature_b64":"Vv1OWbBrpuDlmZUtOVde0NTBnuVKRziFXmwgocxHBF7DaWEQBXYq1MB9ZZcDKEgO9YQjPjW2JjdqqCT9iUfsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c29f9a44ddea4dd659103ee66e54a29e7c4cf0e4fd38984e5e7fea19bbf7f80e","last_reissued_at":"2026-05-18T02:25:11.844101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:11.844101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"E-Determinants of Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chen Ling, Liqun Qi, Shenglong Hu, Zheng-Hai Huang","submitted_at":"2011-09-02T03:19:03Z","abstract_excerpt":"We generalize the concept of the symmetric hyperdeterminants for symmetric tensors to the E-determinants for general tensors. We show that the E-determinant inherits many properties of the determinant of a matrix. These properties include: solvability of polynomial systems, the E-determinat of the composition of tensors, product formula for the E-determinant of a block tensor, Hadamard's inequality, Gersgrin's inequality and Minikowski's inequality. As a simple application, we show that if the leading coefficient tensor of a polynomial system is a triangular tensor with nonzero diagonal elemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0348","kind":"arxiv","version":3},"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":"1109.0348","created_at":"2026-05-18T02:25:11.844167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.0348v3","created_at":"2026-05-18T02:25:11.844167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0348","created_at":"2026-05-18T02:25:11.844167+00:00"},{"alias_kind":"pith_short_12","alias_value":"YKPZURG55JG5","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YKPZURG55JG5MWIQ","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YKPZURG5","created_at":"2026-05-18T12:26:47.523578+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/YKPZURG55JG5MWIQH3TG4VFCTZ","json":"https://pith.science/pith/YKPZURG55JG5MWIQH3TG4VFCTZ.json","graph_json":"https://pith.science/api/pith-number/YKPZURG55JG5MWIQH3TG4VFCTZ/graph.json","events_json":"https://pith.science/api/pith-number/YKPZURG55JG5MWIQH3TG4VFCTZ/events.json","paper":"https://pith.science/paper/YKPZURG5"},"agent_actions":{"view_html":"https://pith.science/pith/YKPZURG55JG5MWIQH3TG4VFCTZ","download_json":"https://pith.science/pith/YKPZURG55JG5MWIQH3TG4VFCTZ.json","view_paper":"https://pith.science/paper/YKPZURG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.0348&json=true","fetch_graph":"https://pith.science/api/pith-number/YKPZURG55JG5MWIQH3TG4VFCTZ/graph.json","fetch_events":"https://pith.science/api/pith-number/YKPZURG55JG5MWIQH3TG4VFCTZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YKPZURG55JG5MWIQH3TG4VFCTZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YKPZURG55JG5MWIQH3TG4VFCTZ/action/storage_attestation","attest_author":"https://pith.science/pith/YKPZURG55JG5MWIQH3TG4VFCTZ/action/author_attestation","sign_citation":"https://pith.science/pith/YKPZURG55JG5MWIQH3TG4VFCTZ/action/citation_signature","submit_replication":"https://pith.science/pith/YKPZURG55JG5MWIQH3TG4VFCTZ/action/replication_record"}},"created_at":"2026-05-18T02:25:11.844167+00:00","updated_at":"2026-05-18T02:25:11.844167+00:00"}