{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NP7HCE53653SLUKPYKNFFOMLVI","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":"449d93438fe09857e570df8f90938be6683d5cb017b9f7aedd0682800b518530","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-04-14T03:45:27Z","title_canon_sha256":"9f93b0662ff9557d986c63da1643cc9d76cd84c4b608c76133ab4a18d36f958f"},"schema_version":"1.0","source":{"id":"1504.03414","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03414","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03414v4","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03414","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"pith_short_12","alias_value":"NP7HCE53653S","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NP7HCE53653SLUKP","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NP7HCE53","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:823de30e32799c16b5baa6e4fe61c69db8fabee445e43b10ac59cd62192b3958","target":"graph","created_at":"2026-05-18T01:30:34Z","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":"In this paper, we examine structured tensors which have sum-of-squares (SOS) tensor decomposition, and study the SOS-rank of SOS tensor decomposition. We first show that several classes of even order symmetric structured tensors available in the literature have SOS tensor decomposition. These include positive Cauchy tensors, weakly diagonally dominated tensors, $B_0$-tensors, double $B$-tensors, quasi-double $B_0$-tensors, $MB_0$-tensors, $H$-tensors, absolute tensors of positive semi-definite $Z$-tensors and extended $Z$-tensors. We also examine the SOS-rank of SOS tensor decomposition and th","authors_text":"Guoyin Li, Haibin Chen, Liqun Qi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-04-14T03:45:27Z","title":"SOS Tensor Decomposition: Theory and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03414","kind":"arxiv","version":4},"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":"sha256:7cdb6f5100f2148521ed420924c889b203b74562d55587c9f725c4d2a076d625","target":"record","created_at":"2026-05-18T01:30:34Z","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":"449d93438fe09857e570df8f90938be6683d5cb017b9f7aedd0682800b518530","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-04-14T03:45:27Z","title_canon_sha256":"9f93b0662ff9557d986c63da1643cc9d76cd84c4b608c76133ab4a18d36f958f"},"schema_version":"1.0","source":{"id":"1504.03414","kind":"arxiv","version":4}},"canonical_sha256":"6bfe7113bbf77725d14fc29a52b98baa26de72337c1b667dc8a7b2d8a36d888c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bfe7113bbf77725d14fc29a52b98baa26de72337c1b667dc8a7b2d8a36d888c","first_computed_at":"2026-05-18T01:30:34.686746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:34.686746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nCngQ+W81zBEGsClx92rCtr5tjaFrfpLstpEU7xp85k8MAGDKps3POpYRFsJUHNuhJ7EmdRygmzTxe0yfE6PDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:34.687532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03414","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cdb6f5100f2148521ed420924c889b203b74562d55587c9f725c4d2a076d625","sha256:823de30e32799c16b5baa6e4fe61c69db8fabee445e43b10ac59cd62192b3958"],"state_sha256":"b6864bd14ed716e099a7e1eee59a470a7aec491616980208bf725a7a6a0b3663"}