{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:4M7IK76GAVVGKR3EL6366MVY6S","short_pith_number":"pith:4M7IK76G","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"},"canonical_sha256":"e33e857fc6056a6547645fb7ef32b8f4a4a42c81a3253af1d9048152677c2339","source":{"kind":"arxiv","id":"2311.05064","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.05064","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"2311.05064v2","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.05064","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"4M7IK76GAVVG","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_16","alias_value":"4M7IK76GAVVGKR3E","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_8","alias_value":"4M7IK76G","created_at":"2026-07-05T09:58:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:4M7IK76GAVVGKR3EL6366MVY6S","target":"record","payload":{"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"},"canonical_sha256":"e33e857fc6056a6547645fb7ef32b8f4a4a42c81a3253af1d9048152677c2339","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"},"source_kind":"arxiv","source_id":"2311.05064","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:58:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3cg3HIIORCIJd4FDOEPbNMnpYqmTLE+VKoyQI9c0BjpIRKMVlTduvvY9gWBOf5Pp8tf4aE1nMUrTlOMWCdT9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T03:22:12.661024Z"},"content_sha256":"6e9e10655e5d431edb4226058c392aa89150451794245f73998e27031e53dc44","schema_version":"1.0","event_id":"sha256:6e9e10655e5d431edb4226058c392aa89150451794245f73998e27031e53dc44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:4M7IK76GAVVGKR3EL6366MVY6S","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:58:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kr9KaxSAnvWM3XiugKjhDiqbCrKmOT72RzUiNe2GSfsL0miD3M0DuWRHUQDDljOuOyXt2BL9vdrpKMTtMXSZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T03:22:12.661528Z"},"content_sha256":"e9f0f8dc8242289f5ee4a5a568f87a02ab9334b0c80c1c584a2d6ae16f091fac","schema_version":"1.0","event_id":"sha256:e9f0f8dc8242289f5ee4a5a568f87a02ab9334b0c80c1c584a2d6ae16f091fac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/bundle.json","state_url":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4M7IK76GAVVGKR3EL6366MVY6S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-07T03:22:12Z","links":{"resolver":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S","bundle":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/bundle.json","state":"https://pith.science/pith/4M7IK76GAVVGKR3EL6366MVY6S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4M7IK76GAVVGKR3EL6366MVY6S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:4M7IK76GAVVGKR3EL6366MVY6S","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":"01564bb63dc7da9a6dc24177984ab69beec273fb1ddf939347df894fcd99f583","cross_cats_sorted":["physics.comp-ph","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-11-09T00:03:11Z","title_canon_sha256":"49c393cc9301d6dd5f08b48ad4f1e744c2a91c00132c6dd971ed90e3318d4877"},"schema_version":"1.0","source":{"id":"2311.05064","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.05064","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"2311.05064v2","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.05064","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"4M7IK76GAVVG","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_16","alias_value":"4M7IK76GAVVGKR3E","created_at":"2026-07-05T09:58:56Z"},{"alias_kind":"pith_short_8","alias_value":"4M7IK76G","created_at":"2026-07-05T09:58:56Z"}],"graph_snapshots":[{"event_id":"sha256:e9f0f8dc8242289f5ee4a5a568f87a02ab9334b0c80c1c584a2d6ae16f091fac","target":"graph","created_at":"2026-07-05T09:58:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.05064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Jianfeng Lu, Ziang Chen","cross_cats":["physics.comp-ph","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-11-09T00:03:11Z","title":"Exact and Efficient Representation of Totally Anti-Symmetric Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.05064","kind":"arxiv","version":2},"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":"sha256:6e9e10655e5d431edb4226058c392aa89150451794245f73998e27031e53dc44","target":"record","created_at":"2026-07-05T09:58:56Z","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":"01564bb63dc7da9a6dc24177984ab69beec273fb1ddf939347df894fcd99f583","cross_cats_sorted":["physics.comp-ph","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-11-09T00:03:11Z","title_canon_sha256":"49c393cc9301d6dd5f08b48ad4f1e744c2a91c00132c6dd971ed90e3318d4877"},"schema_version":"1.0","source":{"id":"2311.05064","kind":"arxiv","version":2}},"canonical_sha256":"e33e857fc6056a6547645fb7ef32b8f4a4a42c81a3253af1d9048152677c2339","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e33e857fc6056a6547645fb7ef32b8f4a4a42c81a3253af1d9048152677c2339","first_computed_at":"2026-07-05T09:58:56.897770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:58:56.897770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"siDteUA9erJpTT5x9Vu0+anNkD3mZwiES/ZG03aUqj7HXn1pfpmP+tX+pbiUMGenl2E+xgO64k419cDoYfRkBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:58:56.898198Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.05064","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e9e10655e5d431edb4226058c392aa89150451794245f73998e27031e53dc44","sha256:e9f0f8dc8242289f5ee4a5a568f87a02ab9334b0c80c1c584a2d6ae16f091fac"],"state_sha256":"3dcc2fc2dffcef7ed1b7ec4ef539f1bc1f7022345140265a3a61108c6f866c62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"St15C9B0zB90pXKYY7Fg0HhamNySVwWmeTwIPkazZ0EBhS28s5LaAGFkPiSLPx89Ok3VSOe/0uns4kEHxkLnAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T03:22:12.665339Z","bundle_sha256":"d535887318a4b9b9a122f3de97db84b882e689a6b7a01fc0b3bf1fc528f2b7f8"}}