{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:OZUFVBBM4XXZIG6G33FKPLS5EC","short_pith_number":"pith:OZUFVBBM","schema_version":"1.0","canonical_sha256":"76685a842ce5ef941bc6decaa7ae5d20843d49ef9be607c308b3131e8aef2952","source":{"kind":"arxiv","id":"0901.3706","version":2},"attestation_state":"computed","paper":{"title":"Symmetric tensor decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.SC","authors_text":"Bernard Mourrain (INRIA Sophia Antipolis), Elias Tsigaridas (INRIA Sophia Antipolis), Jerome Brachat (INRIA Sophia Antipolis), Pierre Comon (I3S)","submitted_at":"2009-01-23T16:21:18Z","abstract_excerpt":"We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables of total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. "},"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":"0901.3706","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-23T16:21:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"98e30cba65459a9f8ea655f74f950b00e53b2e9f8ce054b96069decc0afb7749","abstract_canon_sha256":"532948d01cd9c9831f19f8f5e880bb5eeab8b49636b5516591a6a439d400dfd7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:46.362826Z","signature_b64":"YTJPzhIxDGVQc9IoC6eVS5pZ5H5shZ16tGhmo2DvkoSEEKK1QWJkOLBIGTIBd3ZI7uCghVrBcwgSbh0hTnMHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76685a842ce5ef941bc6decaa7ae5d20843d49ef9be607c308b3131e8aef2952","last_reissued_at":"2026-05-18T04:34:46.362253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:46.362253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric tensor decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.SC","authors_text":"Bernard Mourrain (INRIA Sophia Antipolis), Elias Tsigaridas (INRIA Sophia Antipolis), Jerome Brachat (INRIA Sophia Antipolis), Pierre Comon (I3S)","submitted_at":"2009-01-23T16:21:18Z","abstract_excerpt":"We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables of total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3706","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":"0901.3706","created_at":"2026-05-18T04:34:46.362359+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.3706v2","created_at":"2026-05-18T04:34:46.362359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3706","created_at":"2026-05-18T04:34:46.362359+00:00"},{"alias_kind":"pith_short_12","alias_value":"OZUFVBBM4XXZ","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"OZUFVBBM4XXZIG6G","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"OZUFVBBM","created_at":"2026-05-18T12:26:01.383474+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/OZUFVBBM4XXZIG6G33FKPLS5EC","json":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC.json","graph_json":"https://pith.science/api/pith-number/OZUFVBBM4XXZIG6G33FKPLS5EC/graph.json","events_json":"https://pith.science/api/pith-number/OZUFVBBM4XXZIG6G33FKPLS5EC/events.json","paper":"https://pith.science/paper/OZUFVBBM"},"agent_actions":{"view_html":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC","download_json":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC.json","view_paper":"https://pith.science/paper/OZUFVBBM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.3706&json=true","fetch_graph":"https://pith.science/api/pith-number/OZUFVBBM4XXZIG6G33FKPLS5EC/graph.json","fetch_events":"https://pith.science/api/pith-number/OZUFVBBM4XXZIG6G33FKPLS5EC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/action/storage_attestation","attest_author":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/action/author_attestation","sign_citation":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/action/citation_signature","submit_replication":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/action/replication_record"}},"created_at":"2026-05-18T04:34:46.362359+00:00","updated_at":"2026-05-18T04:34:46.362359+00:00"}