{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4PPW3LRHIOEEPEQNUPCS6TS573","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":"66c6a015da301765df18fc6b966bbf10cc7aaf9ce51ee2187494d403f431424f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-23T21:49:29Z","title_canon_sha256":"7902a8be76f2d34e510670ab589d59092edc3150c339a028abb8d2940dc3a469"},"schema_version":"1.0","source":{"id":"1502.06639","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06639","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06639v3","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06639","created_at":"2026-05-18T01:09:49Z"},{"alias_kind":"pith_short_12","alias_value":"4PPW3LRHIOEE","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4PPW3LRHIOEEPEQN","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4PPW3LRH","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:cd3cdc0999fea01cb99aa2692b4a77974d31e61a039c4e788980ad82932e4719","target":"graph","created_at":"2026-05-18T01:09:49Z","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":"An orthonormal basis consisting of unentangled (pure tensor) elements in a tensor product of Hilbert spaces is an Unentangled Orthogonal Basis (UOB). In general, for $n$ qubits, we prove that in its natural structure as a real variety, the space of UOB is a bouquet of products of Riemann spheres parametrized by a class of edge colorings of hypercubes. Its irreducible components of maximum dimension are products of $2^n-1$ two-spheres. Using a theorem of Walgate and Hardy, we observe that the UOB whose elements are distinguishable by local operations and classical communication (called locally ","authors_text":"Asif Shakeel, Jiri Lebl, Nolan Wallach","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-23T21:49:29Z","title":"Local Distinguishability of Generic Unentangled Orthonormal Bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06639","kind":"arxiv","version":3},"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":"sha256:45a1e4b25dbb738a77588f2139d4e42d01f5c97c45325bbb2d7f9e5846465213","target":"record","created_at":"2026-05-18T01:09:49Z","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":"66c6a015da301765df18fc6b966bbf10cc7aaf9ce51ee2187494d403f431424f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-23T21:49:29Z","title_canon_sha256":"7902a8be76f2d34e510670ab589d59092edc3150c339a028abb8d2940dc3a469"},"schema_version":"1.0","source":{"id":"1502.06639","kind":"arxiv","version":3}},"canonical_sha256":"e3df6dae27438847920da3c52f4e5dfefc84389cec6c92120f84cb9dcc0b61d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3df6dae27438847920da3c52f4e5dfefc84389cec6c92120f84cb9dcc0b61d3","first_computed_at":"2026-05-18T01:09:49.262129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:49.262129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"82OBSS6CihFCJTkKxPIwmeTHla6gi2EXH+xN/RQ1xMlkNUbi3BbzQ5N4lxjckpLjXE2D7CI+iQhV10n4qydODg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:49.262767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06639","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45a1e4b25dbb738a77588f2139d4e42d01f5c97c45325bbb2d7f9e5846465213","sha256:cd3cdc0999fea01cb99aa2692b4a77974d31e61a039c4e788980ad82932e4719"],"state_sha256":"15c37e7e3684ad56ce5548262bca42ca42ad8091eebd44cfe6d60398e68b85b8"}