{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:J4LKERMIZNJMP4XMTSSXAIBADU","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":"4a958a7c72f1084f96e2b7ce21beea71854ae5a10d926f2eb36030a88021ddec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-01-28T01:28:55Z","title_canon_sha256":"25d95cf2df4bfce6404dde7f968af630c2f25527052f967e09ede1bc0eaa0fca"},"schema_version":"1.0","source":{"id":"1901.09480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09480","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09480v1","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09480","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"J4LKERMIZNJM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"J4LKERMIZNJMP4XM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"J4LKERMI","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:cecd245a437aa717bb414548e563b4425d5bde1caeed838c85dc1f0e8a3a23a2","target":"graph","created_at":"2026-05-17T23:55:24Z","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":"$ \\newcommand{\\schs}{\\scriptstyle{\\mathsf{S}}_1} $For all $n \\ge 1$, we give an explicit construction of $m \\times m$ matrices $A_1,\\ldots,A_n$ with $m = 2^{\\lfloor n/2 \\rfloor}$ such that for any $d$ and $d \\times d$ matrices $A'_1,\\ldots,A'_n$ that satisfy \\[ \\|A'_i-A'_j\\|_{\\schs} \\,\\leq\\, \\|A_i-A_j\\|_{\\schs}\\,\\leq\\, (1+\\delta) \\|A'_i-A'_j\\|_{\\schs} \\] for all $i,j\\in\\{1,\\ldots,n\\}$ and small enough $\\delta = O(n^{-c})$, where $c> 0$ is a universal constant, it must be the case that $d \\ge 2^{\\lfloor n/2\\rfloor -1}$. This stands in contrast to the metric theory of commutative $\\ell_p$ spaces","authors_text":"Oded Regev, Thomas Vidick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-01-28T01:28:55Z","title":"Bounds on Dimension Reduction in the Nuclear Norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09480","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":"sha256:524065244f13bc5fe462f424e4482ce21e853f21bf6b429836a998d62640ab43","target":"record","created_at":"2026-05-17T23:55:24Z","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":"4a958a7c72f1084f96e2b7ce21beea71854ae5a10d926f2eb36030a88021ddec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-01-28T01:28:55Z","title_canon_sha256":"25d95cf2df4bfce6404dde7f968af630c2f25527052f967e09ede1bc0eaa0fca"},"schema_version":"1.0","source":{"id":"1901.09480","kind":"arxiv","version":1}},"canonical_sha256":"4f16a24588cb52c7f2ec9ca57020201d0a67fe4ad3a8f3b028b96bd2f783f2e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f16a24588cb52c7f2ec9ca57020201d0a67fe4ad3a8f3b028b96bd2f783f2e8","first_computed_at":"2026-05-17T23:55:24.651867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:24.651867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Ma4R0MWH/m+ls9m2WUSEPk22IE5lWmGnaRyZAYA1W1d7FkSOyw1F/ItEcAL8FyjFFFEzc4+7vJSIcg/HZNiDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:24.652337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.09480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:524065244f13bc5fe462f424e4482ce21e853f21bf6b429836a998d62640ab43","sha256:cecd245a437aa717bb414548e563b4425d5bde1caeed838c85dc1f0e8a3a23a2"],"state_sha256":"a1411762e90fee56fb30ce1a6489ddf007a213c1b639a6d3b74ca5960520a5dc"}