{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UNUE3JPFZAZHCNFQZ3XBVKJPY5","short_pith_number":"pith:UNUE3JPF","schema_version":"1.0","canonical_sha256":"a3684da5e5c8327134b0ceee1aa92fc7619faee2e90116373001eb27c19c1e81","source":{"kind":"arxiv","id":"1309.7487","version":2},"attestation_state":"computed","paper":{"title":"Representations of $a_{\\infty}$ and $d_{\\infty}$ with central charge 1 on the single neutral fermion Fock space $\\mathit{F^{\\otimes \\frac{1}{2}}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","math.RT"],"primary_cat":"math-ph","authors_text":"Ben Cox, Elizabeth Jurisich, Iana I. Anguelova","submitted_at":"2013-09-28T18:24:15Z","abstract_excerpt":"We construct a new representation of the infinite rank Lie algebra $a_{\\infty}$ with central charge $c=1$ on the Fock space $\\mathit{F^{\\otimes \\frac{1}{2}}}$ of a single neutral fermion. We show that $\\mathit{F^{\\otimes \\frac{1}{2}}}$ is a direct sum of irreducible integrable highest weight modules for $a_{\\infty}$ with central charge $c=1$. We prove that as $a_{\\infty}$ modules $\\mathit{F^{\\otimes \\frac{1}{2}}}$ is isomorphic to the Fock space $\\mathit{F^{\\otimes 1}}$ of the charged free fermions. As a corollary we obtain the decompositions of certain irreducible highest weight modules for $"},"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":"1309.7487","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-28T18:24:15Z","cross_cats_sorted":["math.MP","math.QA","math.RT"],"title_canon_sha256":"d7a1230b2ae555de0947e95d0d5565b748326b6197dbe0017b926e7045971981","abstract_canon_sha256":"866304b58d2c96f29be3fc3c0d01f2fc6e4fbc13622f3d53ac52dc3eebaa39ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:47:25.013813Z","signature_b64":"a35le+uXZTuPf1DYCTU2r8DmIs5KY7F8Mh9Nhr/ib3NhsQOcxLYg4VMFMdM70obmrANotmfocD3MriIpxis2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3684da5e5c8327134b0ceee1aa92fc7619faee2e90116373001eb27c19c1e81","last_reissued_at":"2026-05-18T01:47:25.013220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:47:25.013220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations of $a_{\\infty}$ and $d_{\\infty}$ with central charge 1 on the single neutral fermion Fock space $\\mathit{F^{\\otimes \\frac{1}{2}}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","math.RT"],"primary_cat":"math-ph","authors_text":"Ben Cox, Elizabeth Jurisich, Iana I. Anguelova","submitted_at":"2013-09-28T18:24:15Z","abstract_excerpt":"We construct a new representation of the infinite rank Lie algebra $a_{\\infty}$ with central charge $c=1$ on the Fock space $\\mathit{F^{\\otimes \\frac{1}{2}}}$ of a single neutral fermion. We show that $\\mathit{F^{\\otimes \\frac{1}{2}}}$ is a direct sum of irreducible integrable highest weight modules for $a_{\\infty}$ with central charge $c=1$. We prove that as $a_{\\infty}$ modules $\\mathit{F^{\\otimes \\frac{1}{2}}}$ is isomorphic to the Fock space $\\mathit{F^{\\otimes 1}}$ of the charged free fermions. As a corollary we obtain the decompositions of certain irreducible highest weight modules for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7487","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":"1309.7487","created_at":"2026-05-18T01:47:25.013330+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7487v2","created_at":"2026-05-18T01:47:25.013330+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7487","created_at":"2026-05-18T01:47:25.013330+00:00"},{"alias_kind":"pith_short_12","alias_value":"UNUE3JPFZAZH","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UNUE3JPFZAZHCNFQ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UNUE3JPF","created_at":"2026-05-18T12:28:02.375192+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/UNUE3JPFZAZHCNFQZ3XBVKJPY5","json":"https://pith.science/pith/UNUE3JPFZAZHCNFQZ3XBVKJPY5.json","graph_json":"https://pith.science/api/pith-number/UNUE3JPFZAZHCNFQZ3XBVKJPY5/graph.json","events_json":"https://pith.science/api/pith-number/UNUE3JPFZAZHCNFQZ3XBVKJPY5/events.json","paper":"https://pith.science/paper/UNUE3JPF"},"agent_actions":{"view_html":"https://pith.science/pith/UNUE3JPFZAZHCNFQZ3XBVKJPY5","download_json":"https://pith.science/pith/UNUE3JPFZAZHCNFQZ3XBVKJPY5.json","view_paper":"https://pith.science/paper/UNUE3JPF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7487&json=true","fetch_graph":"https://pith.science/api/pith-number/UNUE3JPFZAZHCNFQZ3XBVKJPY5/graph.json","fetch_events":"https://pith.science/api/pith-number/UNUE3JPFZAZHCNFQZ3XBVKJPY5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UNUE3JPFZAZHCNFQZ3XBVKJPY5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UNUE3JPFZAZHCNFQZ3XBVKJPY5/action/storage_attestation","attest_author":"https://pith.science/pith/UNUE3JPFZAZHCNFQZ3XBVKJPY5/action/author_attestation","sign_citation":"https://pith.science/pith/UNUE3JPFZAZHCNFQZ3XBVKJPY5/action/citation_signature","submit_replication":"https://pith.science/pith/UNUE3JPFZAZHCNFQZ3XBVKJPY5/action/replication_record"}},"created_at":"2026-05-18T01:47:25.013330+00:00","updated_at":"2026-05-18T01:47:25.013330+00:00"}