{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:NPOTXXU3A3DIW4HB5X2H7JWI2T","short_pith_number":"pith:NPOTXXU3","canonical_record":{"source":{"id":"math/0307315","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2003-07-23T14:24:17Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"9b7d348a51849070619e1de8e311356ca4e395111903cbaf29c568af5267c5d9","abstract_canon_sha256":"14c5fc621bba3af7c3d209d260c09c607b83b813a70e8ddb6b96effd0e5fb596"},"schema_version":"1.0"},"canonical_sha256":"6bdd3bde9b06c68b70e1edf47fa6c8d4e17119d30f05f26627f7a6b6936ed6b1","source":{"kind":"arxiv","id":"math/0307315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307315","created_at":"2026-05-17T23:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307315v1","created_at":"2026-05-17T23:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307315","created_at":"2026-05-17T23:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"NPOTXXU3A3DI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"NPOTXXU3A3DIW4HB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"NPOTXXU3","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:NPOTXXU3A3DIW4HB5X2H7JWI2T","target":"record","payload":{"canonical_record":{"source":{"id":"math/0307315","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2003-07-23T14:24:17Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"9b7d348a51849070619e1de8e311356ca4e395111903cbaf29c568af5267c5d9","abstract_canon_sha256":"14c5fc621bba3af7c3d209d260c09c607b83b813a70e8ddb6b96effd0e5fb596"},"schema_version":"1.0"},"canonical_sha256":"6bdd3bde9b06c68b70e1edf47fa6c8d4e17119d30f05f26627f7a6b6936ed6b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:03.275334Z","signature_b64":"PlOlUt/PCREX8umNq9x2ofeWV2uA1ZftI4pyBNgSo7Sog3/7xHNV8vdS/RDALTl09KK35BQ63eNFgUYx+mh6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bdd3bde9b06c68b70e1edf47fa6c8d4e17119d30f05f26627f7a6b6936ed6b1","last_reissued_at":"2026-05-17T23:53:03.274634Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:03.274634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0307315","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gr/JfpiR5/ojslUyD19z8Rp0FiUVBqc5y+R8PknsOpeMYUhVePWkpkW7iTSntZGFhFdGZZfMOM/+pWMd49cxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:59:01.165356Z"},"content_sha256":"90ec61de33f37ef5407bd233a61ef61ebafe894a96a0e67ef17a6305f0d2a3e8","schema_version":"1.0","event_id":"sha256:90ec61de33f37ef5407bd233a61ef61ebafe894a96a0e67ef17a6305f0d2a3e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:NPOTXXU3A3DIW4HB5X2H7JWI2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An analytic formula for Macdonald polynomials","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Michael Schlosser, Michel Lassalle","submitted_at":"2003-07-23T14:24:17Z","abstract_excerpt":"We give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtained by inverting the Pieri formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307315","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z5NZrfhnVWI0sP2uQtli8t8uPxNjymjywFkguBCHd+ZZ+JSUsJV55fQQq1lQqduRQTBX9v66nKtpEQ4h4rW2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:59:01.165705Z"},"content_sha256":"4d143b57b778de6919e9c06a799c480aa3760660da7b18b723b4f8a1dd8c5bfd","schema_version":"1.0","event_id":"sha256:4d143b57b778de6919e9c06a799c480aa3760660da7b18b723b4f8a1dd8c5bfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPOTXXU3A3DIW4HB5X2H7JWI2T/bundle.json","state_url":"https://pith.science/pith/NPOTXXU3A3DIW4HB5X2H7JWI2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPOTXXU3A3DIW4HB5X2H7JWI2T/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":"2026-06-22T20:59:01Z","links":{"resolver":"https://pith.science/pith/NPOTXXU3A3DIW4HB5X2H7JWI2T","bundle":"https://pith.science/pith/NPOTXXU3A3DIW4HB5X2H7JWI2T/bundle.json","state":"https://pith.science/pith/NPOTXXU3A3DIW4HB5X2H7JWI2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPOTXXU3A3DIW4HB5X2H7JWI2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:NPOTXXU3A3DIW4HB5X2H7JWI2T","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":"14c5fc621bba3af7c3d209d260c09c607b83b813a70e8ddb6b96effd0e5fb596","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.CO","submitted_at":"2003-07-23T14:24:17Z","title_canon_sha256":"9b7d348a51849070619e1de8e311356ca4e395111903cbaf29c568af5267c5d9"},"schema_version":"1.0","source":{"id":"math/0307315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307315","created_at":"2026-05-17T23:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307315v1","created_at":"2026-05-17T23:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307315","created_at":"2026-05-17T23:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"NPOTXXU3A3DI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"NPOTXXU3A3DIW4HB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"NPOTXXU3","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:4d143b57b778de6919e9c06a799c480aa3760660da7b18b723b4f8a1dd8c5bfd","target":"graph","created_at":"2026-05-17T23:53:03Z","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 give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtained by inverting the Pieri formula.","authors_text":"Michael Schlosser, Michel Lassalle","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2003-07-23T14:24:17Z","title":"An analytic formula for Macdonald polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307315","kind":"arxiv","version":1},"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":"sha256:90ec61de33f37ef5407bd233a61ef61ebafe894a96a0e67ef17a6305f0d2a3e8","target":"record","created_at":"2026-05-17T23:53:03Z","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":"14c5fc621bba3af7c3d209d260c09c607b83b813a70e8ddb6b96effd0e5fb596","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.CO","submitted_at":"2003-07-23T14:24:17Z","title_canon_sha256":"9b7d348a51849070619e1de8e311356ca4e395111903cbaf29c568af5267c5d9"},"schema_version":"1.0","source":{"id":"math/0307315","kind":"arxiv","version":1}},"canonical_sha256":"6bdd3bde9b06c68b70e1edf47fa6c8d4e17119d30f05f26627f7a6b6936ed6b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bdd3bde9b06c68b70e1edf47fa6c8d4e17119d30f05f26627f7a6b6936ed6b1","first_computed_at":"2026-05-17T23:53:03.274634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:03.274634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PlOlUt/PCREX8umNq9x2ofeWV2uA1ZftI4pyBNgSo7Sog3/7xHNV8vdS/RDALTl09KK35BQ63eNFgUYx+mh6Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:03.275334Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0307315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90ec61de33f37ef5407bd233a61ef61ebafe894a96a0e67ef17a6305f0d2a3e8","sha256:4d143b57b778de6919e9c06a799c480aa3760660da7b18b723b4f8a1dd8c5bfd"],"state_sha256":"21e75eb31dbd3cbe0a024b3f38b2b20ffd20378a23caf1a9cff91b68d2d6cc32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBrcWVXShRcBS9lbvsmKXpd7YleF2KxTJULKfqJgnV3YBQOGQEUQ4584DSzALsumEAn5ljdFL49kzlnTnK9DCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:59:01.167681Z","bundle_sha256":"281376846d16712c38830fb45faa7cfecbae7b58f63c22a1e7e57b625a6360d5"}}