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For N=4 and scaling dimension \\lambda=0, the D-module representations of the A(1,1) superalgebra are obtained. For $\\lambda\\neq 0$, the D-module representations of the D(2,1;\\alpha) superalgebras are obtained, with $\\alpha$ determined in terms of the scaling dimension $\\lambda$ according to: $\\alpha=-2\\lambda$ for k=4"},"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":"1112.0995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-05T16:58:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d3710823ca04d12562c7a2fd4bc1e5c128990f267a7d9b66c83817ff05de5cd8","abstract_canon_sha256":"8ad77ad3647109f02ccb29467b6185429ba44fbbe77aa115385cd9d1fc3eea0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:44.959674Z","signature_b64":"zcbzTtJ3veZkC/SwHZNQGw4iYFBubFENpBCTAdRkvx0WWIoPbnFDoIEoZdpQCGM5X9JB0evxZ4Yj27tWltKjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8688d34fc017a4859eebe3784fb3974c5d5d9e8c76d3fa5835bb6c11c4729325","last_reissued_at":"2026-05-18T03:56:44.959116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:44.959116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Francesco Toppan, Zhanna Kuznetsova","submitted_at":"2011-12-05T16:58:08Z","abstract_excerpt":"The linear (homogeneous and inhomogeneous) (k, N, N-k) supermultiplets of the N-extended one-dimensional Supersymmetry Algebra induce D-module representations for the N=2,4,8 superconformal algebras.\n  For N=2, the D-module representations of the A(1,0) superalgebra are obtained. For N=4 and scaling dimension \\lambda=0, the D-module representations of the A(1,1) superalgebra are obtained. For $\\lambda\\neq 0$, the D-module representations of the D(2,1;\\alpha) superalgebras are obtained, with $\\alpha$ determined in terms of the scaling dimension $\\lambda$ according to: $\\alpha=-2\\lambda$ for k=4"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0995","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":"1112.0995","created_at":"2026-05-18T03:56:44.959195+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0995v1","created_at":"2026-05-18T03:56:44.959195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0995","created_at":"2026-05-18T03:56:44.959195+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q2ENGT6AC6SI","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q2ENGT6AC6SILHXL","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q2ENGT6A","created_at":"2026-05-18T12:26:39.201973+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/Q2ENGT6AC6SILHXL4N4E7M4XJR","json":"https://pith.science/pith/Q2ENGT6AC6SILHXL4N4E7M4XJR.json","graph_json":"https://pith.science/api/pith-number/Q2ENGT6AC6SILHXL4N4E7M4XJR/graph.json","events_json":"https://pith.science/api/pith-number/Q2ENGT6AC6SILHXL4N4E7M4XJR/events.json","paper":"https://pith.science/paper/Q2ENGT6A"},"agent_actions":{"view_html":"https://pith.science/pith/Q2ENGT6AC6SILHXL4N4E7M4XJR","download_json":"https://pith.science/pith/Q2ENGT6AC6SILHXL4N4E7M4XJR.json","view_paper":"https://pith.science/paper/Q2ENGT6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0995&json=true","fetch_graph":"https://pith.science/api/pith-number/Q2ENGT6AC6SILHXL4N4E7M4XJR/graph.json","fetch_events":"https://pith.science/api/pith-number/Q2ENGT6AC6SILHXL4N4E7M4XJR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q2ENGT6AC6SILHXL4N4E7M4XJR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q2ENGT6AC6SILHXL4N4E7M4XJR/action/storage_attestation","attest_author":"https://pith.science/pith/Q2ENGT6AC6SILHXL4N4E7M4XJR/action/author_attestation","sign_citation":"https://pith.science/pith/Q2ENGT6AC6SILHXL4N4E7M4XJR/action/citation_signature","submit_replication":"https://pith.science/pith/Q2ENGT6AC6SILHXL4N4E7M4XJR/action/replication_record"}},"created_at":"2026-05-18T03:56:44.959195+00:00","updated_at":"2026-05-18T03:56:44.959195+00:00"}