{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:II3R5LMSD6OLMCZAQDRJTGAYX2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aaf2d9b8d60fb5f816d6ae61868ed18af92705fa95c4430723fff87485b69be8","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-25T05:55:01Z","title_canon_sha256":"64a393324b788e44b69b644c268228ac49d066124be56ef61f5463e66856b856"},"schema_version":"1.0","source":{"id":"1408.5664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5664","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5664v2","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5664","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"pith_short_12","alias_value":"II3R5LMSD6OL","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"II3R5LMSD6OLMCZA","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"II3R5LMS","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:76c7940418fa82130d380b74f115bc368580ec6156a3c761a07972e5468e7b70","target":"graph","created_at":"2026-05-18T01:31:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Jiawang Nie","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-25T05:55:01Z","title":"Generating Polynomials and Symmetric Tensor Decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5664","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:04906c5e809d24abc6905a516b003a9ed5362420776b8633a8651827ecb4f742","target":"record","created_at":"2026-05-18T01:31:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aaf2d9b8d60fb5f816d6ae61868ed18af92705fa95c4430723fff87485b69be8","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-25T05:55:01Z","title_canon_sha256":"64a393324b788e44b69b644c268228ac49d066124be56ef61f5463e66856b856"},"schema_version":"1.0","source":{"id":"1408.5664","kind":"arxiv","version":2}},"canonical_sha256":"42371ead921f9cb60b2080e2999818bebd6ff07937d23f042a7656e501dffd69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42371ead921f9cb60b2080e2999818bebd6ff07937d23f042a7656e501dffd69","first_computed_at":"2026-05-18T01:31:11.777239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:11.777239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sV+lYlB5yYPqMolBOOkbPbLa1Q6M7IqGbju3+lR0LJ71eqojh6vt9LgsZHS0OiGetw1o1UxMhOuWYzQc0fTyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:11.777741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04906c5e809d24abc6905a516b003a9ed5362420776b8633a8651827ecb4f742","sha256:76c7940418fa82130d380b74f115bc368580ec6156a3c761a07972e5468e7b70"],"state_sha256":"2db6ad3b46d34a013216d6b13623a75a087ff3abc95f545c57511a2383a9047e"}