{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:4M7IK76GAVVGKR3EL6366MVY6S","short_pith_number":"pith:4M7IK76G","schema_version":"1.0","canonical_sha256":"e33e857fc6056a6547645fb7ef32b8f4a4a42c81a3253af1d9048152677c2339","source":{"kind":"arxiv","id":"2311.05064","version":2},"attestation_state":"computed","paper":{"title":"Exact and Efficient Representation of Totally Anti-Symmetric Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph","quant-ph"],"primary_cat":"math.CA","authors_text":"Jianfeng Lu, Ziang Chen","submitted_at":"2023-11-09T00:03:11Z","abstract_excerpt":"This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd function with a fixed set of anti-symmetric basis functions. We prove that this ansatz can exactly represent every anti-symmetric and continuous function and the number of basis functions has efficient scaling with respect to dimension (number of particles). The singular locus of the anti-symmetric basis functions is precisely identified."},"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":"2311.05064","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-11-09T00:03:11Z","cross_cats_sorted":["physics.comp-ph","quant-ph"],"title_canon_sha256":"49c393cc9301d6dd5f08b48ad4f1e744c2a91c00132c6dd971ed90e3318d4877","abstract_canon_sha256":"01564bb63dc7da9a6dc24177984ab69beec273fb1ddf939347df894fcd99f583"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:58:56.898198Z","signature_b64":"siDteUA9erJpTT5x9Vu0+anNkD3mZwiES/ZG03aUqj7HXn1pfpmP+tX+pbiUMGenl2E+xgO64k419cDoYfRkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e33e857fc6056a6547645fb7ef32b8f4a4a42c81a3253af1d9048152677c2339","last_reissued_at":"2026-07-05T09:58:56.897770Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:58:56.897770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact and Efficient Representation of Totally Anti-Symmetric Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph","quant-ph"],"primary_cat":"math.CA","authors_text":"Jianfeng Lu, Ziang Chen","submitted_at":"2023-11-09T00:03:11Z","abstract_excerpt":"This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd function with a fixed set of anti-symmetric basis functions. We prove that this ansatz can exactly represent every anti-symmetric and continuous function and the number of basis functions has efficient scaling with respect to dimension (number of particles). The singular locus of the anti-symmetric basis functions is precisely identified."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.05064","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.05064/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2311.05064","created_at":"2026-07-05T09:58:56.897831+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.05064v2","created_at":"2026-07-05T09:58:56.897831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.05064","created_at":"2026-07-05T09:58:56.897831+00:00"},{"alias_kind":"pith_short_12","alias_value":"4M7IK76GAVVG","created_at":"2026-07-05T09:58:56.897831+00:00"},{"alias_kind":"pith_short_16","alias_value":"4M7IK76GAVVGKR3E","created_at":"2026-07-05T09:58:56.897831+00:00"},{"alias_kind":"pith_short_8","alias_value":"4M7IK76G","created_at":"2026-07-05T09:58:56.897831+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2501.05958","citing_title":"Lower Bound on the Representation Complexity of Antisymmetric Tensor Product Functions","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2601.02508","citing_title":"Fermi Sets: Universal and interpretable neural architectures for fermions","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S","json":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S.json","graph_json":"https://pith.science/api/pith-number/4M7IK76GAVVGKR3EL6366MVY6S/graph.json","events_json":"https://pith.science/api/pith-number/4M7IK76GAVVGKR3EL6366MVY6S/events.json","paper":"https://pith.science/paper/4M7IK76G"},"agent_actions":{"view_html":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S","download_json":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S.json","view_paper":"https://pith.science/paper/4M7IK76G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.05064&json=true","fetch_graph":"https://pith.science/api/pith-number/4M7IK76GAVVGKR3EL6366MVY6S/graph.json","fetch_events":"https://pith.science/api/pith-number/4M7IK76GAVVGKR3EL6366MVY6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/action/storage_attestation","attest_author":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/action/author_attestation","sign_citation":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/action/citation_signature","submit_replication":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/action/replication_record"}},"created_at":"2026-07-05T09:58:56.897831+00:00","updated_at":"2026-07-05T09:58:56.897831+00:00"}