{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:K6JTLIHSRBJZL7PGJIMGCCRFB3","short_pith_number":"pith:K6JTLIHS","schema_version":"1.0","canonical_sha256":"579335a0f2885395fde64a18610a250eff2026633cd02bf4ae336a3983947adf","source":{"kind":"arxiv","id":"1306.3072","version":2},"attestation_state":"computed","paper":{"title":"The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Johan van de Leur","submitted_at":"2013-06-13T10:47:36Z","abstract_excerpt":"The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W-algebra. This was used by Liu, Yang and Zhang to prove its uniqueness. We construct this principal hierarchy of type D in a different way, viz. as a reduction of some DKP hierarchy. This gives a Lax type and a Grassmannian formulation of this hierarchy. We show in particular that the string equation induces a large part of the W constraints of Bakalov and Milanov. These constraints are not only"},"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":"1306.3072","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2013-06-13T10:47:36Z","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"title_canon_sha256":"1992809b3fe1af6d375831b57af6af7cda134b070ac8637a47723bc6181975c1","abstract_canon_sha256":"75532473522e22d9b432ec12793eb9084db59b030bac6899145a687bdd616be2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:17.574307Z","signature_b64":"exi9OI9Orq82N+I85487BXj1bCMunzkbNU1Ps/6S287bvG6h93/nd/oJmWPE/8zLsNDSjbAU3pXNDULr7gpIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"579335a0f2885395fde64a18610a250eff2026633cd02bf4ae336a3983947adf","last_reissued_at":"2026-05-18T03:02:17.573385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:17.573385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Johan van de Leur","submitted_at":"2013-06-13T10:47:36Z","abstract_excerpt":"The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W-algebra. This was used by Liu, Yang and Zhang to prove its uniqueness. We construct this principal hierarchy of type D in a different way, viz. as a reduction of some DKP hierarchy. This gives a Lax type and a Grassmannian formulation of this hierarchy. We show in particular that the string equation induces a large part of the W constraints of Bakalov and Milanov. These constraints are not only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3072","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":"1306.3072","created_at":"2026-05-18T03:02:17.573509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3072v2","created_at":"2026-05-18T03:02:17.573509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3072","created_at":"2026-05-18T03:02:17.573509+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6JTLIHSRBJZ","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6JTLIHSRBJZL7PG","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6JTLIHS","created_at":"2026-05-18T12:27:49.015174+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/K6JTLIHSRBJZL7PGJIMGCCRFB3","json":"https://pith.science/pith/K6JTLIHSRBJZL7PGJIMGCCRFB3.json","graph_json":"https://pith.science/api/pith-number/K6JTLIHSRBJZL7PGJIMGCCRFB3/graph.json","events_json":"https://pith.science/api/pith-number/K6JTLIHSRBJZL7PGJIMGCCRFB3/events.json","paper":"https://pith.science/paper/K6JTLIHS"},"agent_actions":{"view_html":"https://pith.science/pith/K6JTLIHSRBJZL7PGJIMGCCRFB3","download_json":"https://pith.science/pith/K6JTLIHSRBJZL7PGJIMGCCRFB3.json","view_paper":"https://pith.science/paper/K6JTLIHS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3072&json=true","fetch_graph":"https://pith.science/api/pith-number/K6JTLIHSRBJZL7PGJIMGCCRFB3/graph.json","fetch_events":"https://pith.science/api/pith-number/K6JTLIHSRBJZL7PGJIMGCCRFB3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6JTLIHSRBJZL7PGJIMGCCRFB3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6JTLIHSRBJZL7PGJIMGCCRFB3/action/storage_attestation","attest_author":"https://pith.science/pith/K6JTLIHSRBJZL7PGJIMGCCRFB3/action/author_attestation","sign_citation":"https://pith.science/pith/K6JTLIHSRBJZL7PGJIMGCCRFB3/action/citation_signature","submit_replication":"https://pith.science/pith/K6JTLIHSRBJZL7PGJIMGCCRFB3/action/replication_record"}},"created_at":"2026-05-18T03:02:17.573509+00:00","updated_at":"2026-05-18T03:02:17.573509+00:00"}