{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:ZGVEBXX3EAMX6T3QFJ7LCLCGAU","short_pith_number":"pith:ZGVEBXX3","schema_version":"1.0","canonical_sha256":"c9aa40defb20197f4f702a7eb12c4605082f6be2de204bf972557e1718257dda","source":{"kind":"arxiv","id":"hep-th/9312088","version":1},"attestation_state":"computed","paper":{"title":"Poisson-Lie group of pseudodifferential symbols","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"Boris Khesin, Ilya Zakharevich","submitted_at":"1993-12-10T21:02:17Z","abstract_excerpt":"We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of pseudodifferential symbols of an arbitrary real (or complex) order. We show that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP Poisson structures are naturally realized as restrictions of this Poisson structure to submanifolds of this ``universal'' Poisson--Lie group.\n  Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebra"},"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":"hep-th/9312088","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-12-10T21:02:17Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"51945892f922302ac4344e92859dc50c1360a60dccab7af253a4f189d44c8be5","abstract_canon_sha256":"e73c2739bf1f8d501bdb441f632f8ada2a788263b34049d61577546f0735cb0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:56:22.083085Z","signature_b64":"k/6BpSCxvnBODzHgDGWuxvE3giMIXQEPAT0CFjgZrzUhT1xCz9OBWGmu9su38szvfPdw9UKn6YU2gACrqDFiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9aa40defb20197f4f702a7eb12c4605082f6be2de204bf972557e1718257dda","last_reissued_at":"2026-07-04T15:56:22.082703Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:56:22.082703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson-Lie group of pseudodifferential symbols","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"Boris Khesin, Ilya Zakharevich","submitted_at":"1993-12-10T21:02:17Z","abstract_excerpt":"We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of pseudodifferential symbols of an arbitrary real (or complex) order. We show that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP Poisson structures are naturally realized as restrictions of this Poisson structure to submanifolds of this ``universal'' Poisson--Lie group.\n  Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9312088","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9312088/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":"hep-th/9312088","created_at":"2026-07-04T15:56:22.082760+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9312088v1","created_at":"2026-07-04T15:56:22.082760+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9312088","created_at":"2026-07-04T15:56:22.082760+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZGVEBXX3EAMX","created_at":"2026-07-04T15:56:22.082760+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZGVEBXX3EAMX6T3Q","created_at":"2026-07-04T15:56:22.082760+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZGVEBXX3","created_at":"2026-07-04T15:56:22.082760+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.15678","citing_title":"A universal W-algebra for N=4 super Yang-Mills","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU","json":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU.json","graph_json":"https://pith.science/api/pith-number/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/graph.json","events_json":"https://pith.science/api/pith-number/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/events.json","paper":"https://pith.science/paper/ZGVEBXX3"},"agent_actions":{"view_html":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU","download_json":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU.json","view_paper":"https://pith.science/paper/ZGVEBXX3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9312088&json=true","fetch_graph":"https://pith.science/api/pith-number/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/graph.json","fetch_events":"https://pith.science/api/pith-number/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/action/storage_attestation","attest_author":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/action/author_attestation","sign_citation":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/action/citation_signature","submit_replication":"https://pith.science/pith/ZGVEBXX3EAMX6T3QFJ7LCLCGAU/action/replication_record"}},"created_at":"2026-07-04T15:56:22.082760+00:00","updated_at":"2026-07-04T15:56:22.082760+00:00"}