{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BBPTNWFWSZ2KYO7MFDDHAH2MSO","short_pith_number":"pith:BBPTNWFW","schema_version":"1.0","canonical_sha256":"085f36d8b69674ac3bec28c6701f4c939c45f6d5c9d26a20e986c2eddf9933ce","source":{"kind":"arxiv","id":"1411.7697","version":1},"attestation_state":"computed","paper":{"title":"Exploring $\\mathcal{W}_{\\infty}$ in the quadratic basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Tomas Prochazka","submitted_at":"2014-11-27T20:57:26Z","abstract_excerpt":"We study the operator product expansions in the chiral algebra $\\mathcal{W}_{\\infty}$, first using the associativity conditions in the basis of primary generating fields and second using a different basis coming from the free field representation in which the OPE takes a simpler quadratic form. The results in the quadratic basis can be compactly written using certain bilocal combinations of the generating fields and we conjecture a closed-form formula for the complete OPE in this basis. Next we show that the commutation relations as well as correlation functions can be easily computed using pr"},"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":"1411.7697","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-27T20:57:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"541ccaee1eb626188774f8f3caa277cd404c948fa17e31bce2da734c797c29b9","abstract_canon_sha256":"8a04001cf61a74ffceb531d4fa68ab7a1844bd24180ec52df914ea60b0763d28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:04.488508Z","signature_b64":"xT6b8+DO5qbFwAfsiVb9BBA2IV7gB+YmZRTUTYbBQ3wZ13jR8XwWFrGhzamaZWWxw9inMtioCx1GjVm6nFYnDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"085f36d8b69674ac3bec28c6701f4c939c45f6d5c9d26a20e986c2eddf9933ce","last_reissued_at":"2026-05-18T01:29:04.487805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:04.487805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exploring $\\mathcal{W}_{\\infty}$ in the quadratic basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Tomas Prochazka","submitted_at":"2014-11-27T20:57:26Z","abstract_excerpt":"We study the operator product expansions in the chiral algebra $\\mathcal{W}_{\\infty}$, first using the associativity conditions in the basis of primary generating fields and second using a different basis coming from the free field representation in which the OPE takes a simpler quadratic form. The results in the quadratic basis can be compactly written using certain bilocal combinations of the generating fields and we conjecture a closed-form formula for the complete OPE in this basis. Next we show that the commutation relations as well as correlation functions can be easily computed using pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7697","kind":"arxiv","version":1},"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":"1411.7697","created_at":"2026-05-18T01:29:04.487927+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.7697v1","created_at":"2026-05-18T01:29:04.487927+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7697","created_at":"2026-05-18T01:29:04.487927+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBPTNWFWSZ2K","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBPTNWFWSZ2KYO7M","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBPTNWFW","created_at":"2026-05-18T12:28:22.404517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.20643","citing_title":"Non-Commutative Gauge Theory at the Beach","ref_index":65,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO","json":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO.json","graph_json":"https://pith.science/api/pith-number/BBPTNWFWSZ2KYO7MFDDHAH2MSO/graph.json","events_json":"https://pith.science/api/pith-number/BBPTNWFWSZ2KYO7MFDDHAH2MSO/events.json","paper":"https://pith.science/paper/BBPTNWFW"},"agent_actions":{"view_html":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO","download_json":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO.json","view_paper":"https://pith.science/paper/BBPTNWFW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.7697&json=true","fetch_graph":"https://pith.science/api/pith-number/BBPTNWFWSZ2KYO7MFDDHAH2MSO/graph.json","fetch_events":"https://pith.science/api/pith-number/BBPTNWFWSZ2KYO7MFDDHAH2MSO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO/action/storage_attestation","attest_author":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO/action/author_attestation","sign_citation":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO/action/citation_signature","submit_replication":"https://pith.science/pith/BBPTNWFWSZ2KYO7MFDDHAH2MSO/action/replication_record"}},"created_at":"2026-05-18T01:29:04.487927+00:00","updated_at":"2026-05-18T01:29:04.487927+00:00"}