{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:II3R5LMSD6OLMCZAQDRJTGAYX2","short_pith_number":"pith:II3R5LMS","schema_version":"1.0","canonical_sha256":"42371ead921f9cb60b2080e2999818bebd6ff07937d23f042a7656e501dffd69","source":{"kind":"arxiv","id":"1408.5664","version":2},"attestation_state":"computed","paper":{"title":"Generating Polynomials and Symmetric Tensor Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NA","authors_text":"Jiawang Nie","submitted_at":"2014-08-25T05:55:01Z","abstract_excerpt":"This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial. The homogenization of a generating polynomial belongs to the apolar ideal of the tensor. A symmetric tensor decomposition can be determined by a set of generating polynomials, which can be represented by a matrix. We call it a generating matrix. Generally, a symmetric tensor decomposition can be determined by a generating matrix satisfying certain conditions"},"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":"1408.5664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-25T05:55:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"64a393324b788e44b69b644c268228ac49d066124be56ef61f5463e66856b856","abstract_canon_sha256":"aaf2d9b8d60fb5f816d6ae61868ed18af92705fa95c4430723fff87485b69be8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:11.777741Z","signature_b64":"sV+lYlB5yYPqMolBOOkbPbLa1Q6M7IqGbju3+lR0LJ71eqojh6vt9LgsZHS0OiGetw1o1UxMhOuWYzQc0fTyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42371ead921f9cb60b2080e2999818bebd6ff07937d23f042a7656e501dffd69","last_reissued_at":"2026-05-18T01:31:11.777239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:11.777239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generating Polynomials and Symmetric Tensor Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NA","authors_text":"Jiawang Nie","submitted_at":"2014-08-25T05:55:01Z","abstract_excerpt":"This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial. The homogenization of a generating polynomial belongs to the apolar ideal of the tensor. A symmetric tensor decomposition can be determined by a set of generating polynomials, which can be represented by a matrix. We call it a generating matrix. Generally, a symmetric tensor decomposition can be determined by a generating matrix satisfying certain conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5664","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":"1408.5664","created_at":"2026-05-18T01:31:11.777327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.5664v2","created_at":"2026-05-18T01:31:11.777327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5664","created_at":"2026-05-18T01:31:11.777327+00:00"},{"alias_kind":"pith_short_12","alias_value":"II3R5LMSD6OL","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"II3R5LMSD6OLMCZA","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"II3R5LMS","created_at":"2026-05-18T12:28:33.132498+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/II3R5LMSD6OLMCZAQDRJTGAYX2","json":"https://pith.science/pith/II3R5LMSD6OLMCZAQDRJTGAYX2.json","graph_json":"https://pith.science/api/pith-number/II3R5LMSD6OLMCZAQDRJTGAYX2/graph.json","events_json":"https://pith.science/api/pith-number/II3R5LMSD6OLMCZAQDRJTGAYX2/events.json","paper":"https://pith.science/paper/II3R5LMS"},"agent_actions":{"view_html":"https://pith.science/pith/II3R5LMSD6OLMCZAQDRJTGAYX2","download_json":"https://pith.science/pith/II3R5LMSD6OLMCZAQDRJTGAYX2.json","view_paper":"https://pith.science/paper/II3R5LMS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.5664&json=true","fetch_graph":"https://pith.science/api/pith-number/II3R5LMSD6OLMCZAQDRJTGAYX2/graph.json","fetch_events":"https://pith.science/api/pith-number/II3R5LMSD6OLMCZAQDRJTGAYX2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/II3R5LMSD6OLMCZAQDRJTGAYX2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/II3R5LMSD6OLMCZAQDRJTGAYX2/action/storage_attestation","attest_author":"https://pith.science/pith/II3R5LMSD6OLMCZAQDRJTGAYX2/action/author_attestation","sign_citation":"https://pith.science/pith/II3R5LMSD6OLMCZAQDRJTGAYX2/action/citation_signature","submit_replication":"https://pith.science/pith/II3R5LMSD6OLMCZAQDRJTGAYX2/action/replication_record"}},"created_at":"2026-05-18T01:31:11.777327+00:00","updated_at":"2026-05-18T01:31:11.777327+00:00"}