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Denote by $\\text{Sym}(V)$ and $\\text{Skew-Sym}(V)$ the subspaces of symmetric and skew-symmetric tensors of a subspace $V$ of $W\\otimes W$, respectively. In this paper we show that if $V$ is generated by tensors with tensor rank 1, $V=\\text{Sym}(V)\\oplus\\text{Skew-Sym}(V)$ and $W$ is the smallest vector space such that $V\\subset W\\otimes W$ then $\\dim(\\text{Sym}(V))\\geq\\max\\{\\frac{2\\dim(\\text{Skew-Sym}(V))}{\\dim(W)}, \\frac{\\dim(W)}{2}\\}$.\n  This result has a straightforward application to the separabi","authors_text":"Daniel Cariello","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-09-22T17:26:18Z","title":"A gap for PPT entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07079","kind":"arxiv","version":1},"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":"sha256:66b188323d8186a5696388d4719e31dd97cd44857b1cdee0edc40ad9d4d539f0","target":"record","created_at":"2026-05-18T00:10:48Z","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":"35c399acc170e8ba894c01c030dfb19e9e318bc55bf5a35db0370f1a968563d2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-09-22T17:26:18Z","title_canon_sha256":"cd8164854f1b625f73c6692d5e229e3af84bbd183cad792c26fe6ac78086baa4"},"schema_version":"1.0","source":{"id":"1609.07079","kind":"arxiv","version":1}},"canonical_sha256":"037da5e8b521f6837166aaa4a8e3b354eaac5a672cf0051b5168e957c8a36819","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"037da5e8b521f6837166aaa4a8e3b354eaac5a672cf0051b5168e957c8a36819","first_computed_at":"2026-05-18T00:10:48.063210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:48.063210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TOc7qlRNJa5SjXnf7pQp9iSWCH7nMtXuGmvNf2KK3VCHUDsfdfyVhn/O4ivQwD/Feo6J2aRQZ3jtqCNo1xFgAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:48.063752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07079","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66b188323d8186a5696388d4719e31dd97cd44857b1cdee0edc40ad9d4d539f0","sha256:3dc822e7fbc4570c5d62b5ce439f118b58490d6d8dbdce8e79674c32a768f0eb"],"state_sha256":"207cf60b381a898f42e8fbaaa0be400f69c42e7344d3acda67a0a50cd9c973e1"}