{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BPXNEAQFDTLNXYPDZKUFYYDYGF","short_pith_number":"pith:BPXNEAQF","schema_version":"1.0","canonical_sha256":"0beed202051cd6dbe1e3caa85c6078316a6f6f962355491279fdb774df34b8cb","source":{"kind":"arxiv","id":"1301.3421","version":2},"attestation_state":"computed","paper":{"title":"Universal Subspaces for Local Unitary Groups of Fermionic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Bei Zeng, Dragomir Z. Djokovic, Jianxin Chen, Lin Chen","submitted_at":"2013-01-15T17:17:10Z","abstract_excerpt":"Let $\\mathcal{V}=\\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\\ket{v_1},...,\\ket{v_M}$ of $V$. Then the Slater determinants $e_{i_1,...,i_N}:= \\ket{v_{i_1}\\we v_{i_2}\\we...\\we v_{i_N}}$ with $i_1<...<i_N$ form an o.n. basis of $\\cV$. Let $\\cS\\subseteq\\cV$ be the subspace spanned by all $e_{i_1,...,i_N}$ such that the set $\\{i_1,...,i_N\\}$ contains no pair $\\{2k-1,2k\\}$, $k$ an integer. We say that the $\\ket{\\psi}\\in\\cS$ are "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.3421","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-01-15T17:17:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8f737caf1fa69780c39478139f8a337929c2da29131255b32edd5cf8603f6681","abstract_canon_sha256":"a697690ed261ffc7bab134391907469980b6198b19a4df0f0a912ed918894805"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:45.741481Z","signature_b64":"jLHNKre4Oj2Z2rs1LsdfY0q//o+GeDQThMI8UiIqeLgkHcyyF/jyFU20Dxt+/epVNBp/KW1zC0ptl5RANIt6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0beed202051cd6dbe1e3caa85c6078316a6f6f962355491279fdb774df34b8cb","last_reissued_at":"2026-05-18T02:29:45.741108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:45.741108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal Subspaces for Local Unitary Groups of Fermionic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Bei Zeng, Dragomir Z. Djokovic, Jianxin Chen, Lin Chen","submitted_at":"2013-01-15T17:17:10Z","abstract_excerpt":"Let $\\mathcal{V}=\\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\\ket{v_1},...,\\ket{v_M}$ of $V$. Then the Slater determinants $e_{i_1,...,i_N}:= \\ket{v_{i_1}\\we v_{i_2}\\we...\\we v_{i_N}}$ with $i_1<...<i_N$ form an o.n. basis of $\\cV$. Let $\\cS\\subseteq\\cV$ be the subspace spanned by all $e_{i_1,...,i_N}$ such that the set $\\{i_1,...,i_N\\}$ contains no pair $\\{2k-1,2k\\}$, $k$ an integer. We say that the $\\ket{\\psi}\\in\\cS$ are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3421","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.3421","created_at":"2026-05-18T02:29:45.741163+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.3421v2","created_at":"2026-05-18T02:29:45.741163+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3421","created_at":"2026-05-18T02:29:45.741163+00:00"},{"alias_kind":"pith_short_12","alias_value":"BPXNEAQFDTLN","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BPXNEAQFDTLNXYPD","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BPXNEAQF","created_at":"2026-05-18T12:27:40.988391+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF","json":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF.json","graph_json":"https://pith.science/api/pith-number/BPXNEAQFDTLNXYPDZKUFYYDYGF/graph.json","events_json":"https://pith.science/api/pith-number/BPXNEAQFDTLNXYPDZKUFYYDYGF/events.json","paper":"https://pith.science/paper/BPXNEAQF"},"agent_actions":{"view_html":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF","download_json":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF.json","view_paper":"https://pith.science/paper/BPXNEAQF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.3421&json=true","fetch_graph":"https://pith.science/api/pith-number/BPXNEAQFDTLNXYPDZKUFYYDYGF/graph.json","fetch_events":"https://pith.science/api/pith-number/BPXNEAQFDTLNXYPDZKUFYYDYGF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF/action/storage_attestation","attest_author":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF/action/author_attestation","sign_citation":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF/action/citation_signature","submit_replication":"https://pith.science/pith/BPXNEAQFDTLNXYPDZKUFYYDYGF/action/replication_record"}},"created_at":"2026-05-18T02:29:45.741163+00:00","updated_at":"2026-05-18T02:29:45.741163+00:00"}