{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AN7Z2IFDORFS35BPIUU62QJHLY","short_pith_number":"pith:AN7Z2IFD","canonical_record":{"source":{"id":"1111.0515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-02T14:38:11Z","cross_cats_sorted":["math-ph","math.CV","math.MP"],"title_canon_sha256":"346eda02b6a66c3bfcf2f4e1a9b7f8be55f2670f64c57007cb1a6140ca88f01d","abstract_canon_sha256":"ebe55a3bbf03b70603717ae7bf5fe0352191260434bc90aa0926cb62bfc29e0f"},"schema_version":"1.0"},"canonical_sha256":"037f9d20a3744b2df42f4529ed41275e0f607443aea3c9bab3e3f8d1f7f1b807","source":{"kind":"arxiv","id":"1111.0515","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0515","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0515v2","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0515","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"AN7Z2IFDORFS","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AN7Z2IFDORFS35BP","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AN7Z2IFD","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AN7Z2IFDORFS35BPIUU62QJHLY","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-02T14:38:11Z","cross_cats_sorted":["math-ph","math.CV","math.MP"],"title_canon_sha256":"346eda02b6a66c3bfcf2f4e1a9b7f8be55f2670f64c57007cb1a6140ca88f01d","abstract_canon_sha256":"ebe55a3bbf03b70603717ae7bf5fe0352191260434bc90aa0926cb62bfc29e0f"},"schema_version":"1.0"},"canonical_sha256":"037f9d20a3744b2df42f4529ed41275e0f607443aea3c9bab3e3f8d1f7f1b807","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:28.695521Z","signature_b64":"T037Wn4QSqxSAJ3D2VlIvQ8U821GtdzEYPnNvGkn+RncXxMqcIHGdxcckxcEeYXRJZclKitYC4bn9eG1Uwk5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"037f9d20a3744b2df42f4529ed41275e0f607443aea3c9bab3e3f8d1f7f1b807","last_reissued_at":"2026-05-18T03:32:28.694663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:28.694663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0515","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":"2026-05-18T03:32:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhW45tgiOeG/MMRX5m+9YSIcyWyYKUNpL1xnvtEtJ8Py+l+RTQdVJ/Z29YAyTfAC/tHReW0zkQ84BibOafXeCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:25:11.870842Z"},"content_sha256":"3f42300d7af35278644ddc5f83ebf884686b22f5a21522f71b9873d18fda246c","schema_version":"1.0","event_id":"sha256:3f42300d7af35278644ddc5f83ebf884686b22f5a21522f71b9873d18fda246c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AN7Z2IFDORFS35BPIUU62QJHLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.QA","authors_text":"Oleg Chalykh, Pavel Etingof","submitted_at":"2011-11-02T14:38:11Z","abstract_excerpt":"We establish orthogonality relations for the Baker-Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik-Macdonald-Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik-Macdonald-Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summation formula for BA functions. We also consider more general identities of Cherednik type, which we use to introduce and construct more general, twisted BA functions. This leads to a construction of new qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0515","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":"2026-05-18T03:32:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YRJpIzrqTkgpAZJMephGKJRd4RR2yTTyttb8m1wh3pPFYJxRUMjYu+7E4w9KF+3Zj+OF3AIb1Yf+VWbC3bhnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:25:11.871548Z"},"content_sha256":"fde6927353c39cc2fe645a8941c9b4b493751a76d139fe28c28aa41910b2c3b6","schema_version":"1.0","event_id":"sha256:fde6927353c39cc2fe645a8941c9b4b493751a76d139fe28c28aa41910b2c3b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AN7Z2IFDORFS35BPIUU62QJHLY/bundle.json","state_url":"https://pith.science/pith/AN7Z2IFDORFS35BPIUU62QJHLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AN7Z2IFDORFS35BPIUU62QJHLY/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":"2026-06-10T03:25:11Z","links":{"resolver":"https://pith.science/pith/AN7Z2IFDORFS35BPIUU62QJHLY","bundle":"https://pith.science/pith/AN7Z2IFDORFS35BPIUU62QJHLY/bundle.json","state":"https://pith.science/pith/AN7Z2IFDORFS35BPIUU62QJHLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AN7Z2IFDORFS35BPIUU62QJHLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AN7Z2IFDORFS35BPIUU62QJHLY","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":"ebe55a3bbf03b70603717ae7bf5fe0352191260434bc90aa0926cb62bfc29e0f","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-02T14:38:11Z","title_canon_sha256":"346eda02b6a66c3bfcf2f4e1a9b7f8be55f2670f64c57007cb1a6140ca88f01d"},"schema_version":"1.0","source":{"id":"1111.0515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0515","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0515v2","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0515","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"AN7Z2IFDORFS","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AN7Z2IFDORFS35BP","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AN7Z2IFD","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:fde6927353c39cc2fe645a8941c9b4b493751a76d139fe28c28aa41910b2c3b6","target":"graph","created_at":"2026-05-18T03:32:28Z","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":"We establish orthogonality relations for the Baker-Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik-Macdonald-Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik-Macdonald-Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summation formula for BA functions. We also consider more general identities of Cherednik type, which we use to introduce and construct more general, twisted BA functions. This leads to a construction of new qu","authors_text":"Oleg Chalykh, Pavel Etingof","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-02T14:38:11Z","title":"Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0515","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":"sha256:3f42300d7af35278644ddc5f83ebf884686b22f5a21522f71b9873d18fda246c","target":"record","created_at":"2026-05-18T03:32:28Z","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":"ebe55a3bbf03b70603717ae7bf5fe0352191260434bc90aa0926cb62bfc29e0f","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-02T14:38:11Z","title_canon_sha256":"346eda02b6a66c3bfcf2f4e1a9b7f8be55f2670f64c57007cb1a6140ca88f01d"},"schema_version":"1.0","source":{"id":"1111.0515","kind":"arxiv","version":2}},"canonical_sha256":"037f9d20a3744b2df42f4529ed41275e0f607443aea3c9bab3e3f8d1f7f1b807","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"037f9d20a3744b2df42f4529ed41275e0f607443aea3c9bab3e3f8d1f7f1b807","first_computed_at":"2026-05-18T03:32:28.694663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:28.694663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T037Wn4QSqxSAJ3D2VlIvQ8U821GtdzEYPnNvGkn+RncXxMqcIHGdxcckxcEeYXRJZclKitYC4bn9eG1Uwk5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:28.695521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f42300d7af35278644ddc5f83ebf884686b22f5a21522f71b9873d18fda246c","sha256:fde6927353c39cc2fe645a8941c9b4b493751a76d139fe28c28aa41910b2c3b6"],"state_sha256":"1568e86de526c2387332752f4c0cc60e5334dc18fa6bb9ec98e3cc47d1af7877"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xj7pj7v+O0D2ci901CQqW+hV8NicuuWSbS+46xFMhdHetoRXhWs3jxQX2P5/570VkKXuWEEk/OczYFcvV1vCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T03:25:11.875654Z","bundle_sha256":"467c0890fe41a4478ccfca9ea65aca7f2ef0c47ac8df2c40b4eba44fa53fe2e0"}}