{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NSOJCAGDGRSECUTMCQPAGYKIQT","short_pith_number":"pith:NSOJCAGD","canonical_record":{"source":{"id":"1202.3922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-17T14:48:28Z","cross_cats_sorted":["hep-th","math.CO","math.MP"],"title_canon_sha256":"06d25593cace7c97bf6782d14fff132a725e47efe3dada675700f3888f2fa240","abstract_canon_sha256":"46e5bdae17b6580647bc4d485f632beadcc60d43013b324d30441815736c073f"},"schema_version":"1.0"},"canonical_sha256":"6c9c9100c3346441526c141e03614884df227c4901dd17354c67423b768da0ba","source":{"kind":"arxiv","id":"1202.3922","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3922","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3922v2","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3922","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"NSOJCAGDGRSE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NSOJCAGDGRSECUTM","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NSOJCAGD","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NSOJCAGDGRSECUTMCQPAGYKIQT","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-17T14:48:28Z","cross_cats_sorted":["hep-th","math.CO","math.MP"],"title_canon_sha256":"06d25593cace7c97bf6782d14fff132a725e47efe3dada675700f3888f2fa240","abstract_canon_sha256":"46e5bdae17b6580647bc4d485f632beadcc60d43013b324d30441815736c073f"},"schema_version":"1.0"},"canonical_sha256":"6c9c9100c3346441526c141e03614884df227c4901dd17354c67423b768da0ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:24.438704Z","signature_b64":"i6T0DkkWFgMO8d7zOlvaMqdGajbEQlpbPcJy+DLaIVEQm+yei4zAo0E+eOtKDUkuWOV0vhNP+66QOmZW+eQgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c9c9100c3346441526c141e03614884df227c4901dd17354c67423b768da0ba","last_reissued_at":"2026-05-18T03:19:24.438010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:24.438010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3922","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRFcioewRmIPxoUeopwp8Y6w3dGMk1G0V9bCV1piO7IB5nGIqaclfdyMYzu8Aokyy3LfF22bGYhdJr2zMoo7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:56:07.964478Z"},"content_sha256":"3f3186d0d8ce1931839d29703654743476b3300daae03b7eaba91d9adc8ca15a","schema_version":"1.0","event_id":"sha256:3f3186d0d8ce1931839d29703654743476b3300daae03b7eaba91d9adc8ca15a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NSOJCAGDGRSECUTMCQPAGYKIQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Macdonald polynomials in superspace as eigenfunctions of commuting operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"L. Lapointe, O. Blondeau-Fournier, P. Desrosiers, P. Mathieu","submitted_at":"2012-02-17T14:48:28Z","abstract_excerpt":"A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonality and triangularity relations. Although many superpolynomials were constructed as solutions of highly over-determined system, the existence issue was left open. This is resolved here: we demonstrate that the underlying construction has a (unique) solution. The proof uses, as a starting point, the definition of the Macdonald superpolynomials in terms of the Macdonald non-symmetric polynomials via a non-standard (anti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3922","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0/XFqCCVs+KdPN/kwVPF298AG92+SgqfzgY9RZMTtl1fK5CndK8vA7coNXMN4fKvg+vKdGa9vliywgW5yCaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:56:07.965106Z"},"content_sha256":"b15ef687b3e1b73325c6426530b70e314cd1f0b968ddf69f96dcb59b33bc6dca","schema_version":"1.0","event_id":"sha256:b15ef687b3e1b73325c6426530b70e314cd1f0b968ddf69f96dcb59b33bc6dca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSOJCAGDGRSECUTMCQPAGYKIQT/bundle.json","state_url":"https://pith.science/pith/NSOJCAGDGRSECUTMCQPAGYKIQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSOJCAGDGRSECUTMCQPAGYKIQT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-21T12:56:07Z","links":{"resolver":"https://pith.science/pith/NSOJCAGDGRSECUTMCQPAGYKIQT","bundle":"https://pith.science/pith/NSOJCAGDGRSECUTMCQPAGYKIQT/bundle.json","state":"https://pith.science/pith/NSOJCAGDGRSECUTMCQPAGYKIQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSOJCAGDGRSECUTMCQPAGYKIQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NSOJCAGDGRSECUTMCQPAGYKIQT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"46e5bdae17b6580647bc4d485f632beadcc60d43013b324d30441815736c073f","cross_cats_sorted":["hep-th","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-17T14:48:28Z","title_canon_sha256":"06d25593cace7c97bf6782d14fff132a725e47efe3dada675700f3888f2fa240"},"schema_version":"1.0","source":{"id":"1202.3922","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3922","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3922v2","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3922","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"NSOJCAGDGRSE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NSOJCAGDGRSECUTM","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NSOJCAGD","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:b15ef687b3e1b73325c6426530b70e314cd1f0b968ddf69f96dcb59b33bc6dca","target":"graph","created_at":"2026-05-18T03:19:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonality and triangularity relations. Although many superpolynomials were constructed as solutions of highly over-determined system, the existence issue was left open. This is resolved here: we demonstrate that the underlying construction has a (unique) solution. The proof uses, as a starting point, the definition of the Macdonald superpolynomials in terms of the Macdonald non-symmetric polynomials via a non-standard (anti","authors_text":"L. Lapointe, O. Blondeau-Fournier, P. Desrosiers, P. Mathieu","cross_cats":["hep-th","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-17T14:48:28Z","title":"Macdonald polynomials in superspace as eigenfunctions of commuting operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3922","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3f3186d0d8ce1931839d29703654743476b3300daae03b7eaba91d9adc8ca15a","target":"record","created_at":"2026-05-18T03:19:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"46e5bdae17b6580647bc4d485f632beadcc60d43013b324d30441815736c073f","cross_cats_sorted":["hep-th","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-17T14:48:28Z","title_canon_sha256":"06d25593cace7c97bf6782d14fff132a725e47efe3dada675700f3888f2fa240"},"schema_version":"1.0","source":{"id":"1202.3922","kind":"arxiv","version":2}},"canonical_sha256":"6c9c9100c3346441526c141e03614884df227c4901dd17354c67423b768da0ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c9c9100c3346441526c141e03614884df227c4901dd17354c67423b768da0ba","first_computed_at":"2026-05-18T03:19:24.438010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:24.438010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6T0DkkWFgMO8d7zOlvaMqdGajbEQlpbPcJy+DLaIVEQm+yei4zAo0E+eOtKDUkuWOV0vhNP+66QOmZW+eQgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:24.438704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3922","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f3186d0d8ce1931839d29703654743476b3300daae03b7eaba91d9adc8ca15a","sha256:b15ef687b3e1b73325c6426530b70e314cd1f0b968ddf69f96dcb59b33bc6dca"],"state_sha256":"a07be013b6c04f577f2b76d15f11a14cbc4e924fa9017039701662c2148f6067"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0Tq/E01igfMkpqpsWSHeZ0QyOnGXk82jzDJ++X35wN1S6wTsc6kNiM7Jw7j0whuQTonNNMNJozIFAmb536vDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T12:56:07.968137Z","bundle_sha256":"cbf45944b79cb2ecf25b47247fa318b5fd3a9b4c88abde3bf56ed2dba4c4f59e"}}