{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:IPZENYRDK4CV5NPGBGQUV42LJ2","short_pith_number":"pith:IPZENYRD","canonical_record":{"source":{"id":"0804.4716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-30T13:15:00Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e906931b87a9e9505e0da75a9fa9ff1f2036a414733ae9e9c7c11ca6b47cb660","abstract_canon_sha256":"c5064e9e02e703da4e71485a2ef4d32cf898dc1d984a4436dcad655fe737f022"},"schema_version":"1.0"},"canonical_sha256":"43f246e22357055eb5e609a14af34b4e8b7eff4560f39a61c9d3f6747e02ab0e","source":{"kind":"arxiv","id":"0804.4716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.4716","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"arxiv_version","alias_value":"0804.4716v1","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.4716","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"pith_short_12","alias_value":"IPZENYRDK4CV","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"pith_short_16","alias_value":"IPZENYRDK4CV5NPG","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"pith_short_8","alias_value":"IPZENYRD","created_at":"2026-07-04T15:11:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:IPZENYRDK4CV5NPGBGQUV42LJ2","target":"record","payload":{"canonical_record":{"source":{"id":"0804.4716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-30T13:15:00Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e906931b87a9e9505e0da75a9fa9ff1f2036a414733ae9e9c7c11ca6b47cb660","abstract_canon_sha256":"c5064e9e02e703da4e71485a2ef4d32cf898dc1d984a4436dcad655fe737f022"},"schema_version":"1.0"},"canonical_sha256":"43f246e22357055eb5e609a14af34b4e8b7eff4560f39a61c9d3f6747e02ab0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:11:15.269507Z","signature_b64":"ErLyCRtGWCT01nZTWAIuM7L2bMMEnj4R6kGsvdNXr7ue27hecUaQ0zhmagmZLTWwmIHFN1anyhRh8klWG+G4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43f246e22357055eb5e609a14af34b4e8b7eff4560f39a61c9d3f6747e02ab0e","last_reissued_at":"2026-07-04T15:11:15.269119Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:11:15.269119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0804.4716","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":"2026-07-04T15:11:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bAMZsFLzrZeX9z6cd3P4dpadgWzqDem1h+fMSGl2WmCK5e9e1MFn1FjnwammDo7zlXxii50rqyKJ1esydMfPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T18:31:18.703016Z"},"content_sha256":"535a7e07477f645695a44e9eb1072e20d9ff4777b6a1c2a6e44233138e405f92","schema_version":"1.0","event_id":"sha256:535a7e07477f645695a44e9eb1072e20d9ff4777b6a1c2a6e44233138e405f92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:IPZENYRDK4CV5NPGBGQUV42LJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Combinatorial Formulas for Macdonald Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Cristian Lenart","submitted_at":"2008-04-30T13:15:00Z","abstract_excerpt":"A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent-Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by explaining how the Ram-Yip formula compresses to a new formula, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.4716","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0804.4716/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:11:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aP142wEEOp7lFGC1A8D0gjAxh8CQtLn5fj5SA3udhkAZ6+ryou8XprAmPeTAJYcQfp7a5CLexMBnEEr4kIt0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T18:31:18.703516Z"},"content_sha256":"f7ca8c540094d5bfabfa8f2e79ab0d5f6308043aacb87faddad47601c063f522","schema_version":"1.0","event_id":"sha256:f7ca8c540094d5bfabfa8f2e79ab0d5f6308043aacb87faddad47601c063f522"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IPZENYRDK4CV5NPGBGQUV42LJ2/bundle.json","state_url":"https://pith.science/pith/IPZENYRDK4CV5NPGBGQUV42LJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IPZENYRDK4CV5NPGBGQUV42LJ2/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":"2026-08-21T18:31:18Z","links":{"resolver":"https://pith.science/pith/IPZENYRDK4CV5NPGBGQUV42LJ2","bundle":"https://pith.science/pith/IPZENYRDK4CV5NPGBGQUV42LJ2/bundle.json","state":"https://pith.science/pith/IPZENYRDK4CV5NPGBGQUV42LJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IPZENYRDK4CV5NPGBGQUV42LJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:IPZENYRDK4CV5NPGBGQUV42LJ2","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":"c5064e9e02e703da4e71485a2ef4d32cf898dc1d984a4436dcad655fe737f022","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-30T13:15:00Z","title_canon_sha256":"e906931b87a9e9505e0da75a9fa9ff1f2036a414733ae9e9c7c11ca6b47cb660"},"schema_version":"1.0","source":{"id":"0804.4716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.4716","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"arxiv_version","alias_value":"0804.4716v1","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.4716","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"pith_short_12","alias_value":"IPZENYRDK4CV","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"pith_short_16","alias_value":"IPZENYRDK4CV5NPG","created_at":"2026-07-04T15:11:15Z"},{"alias_kind":"pith_short_8","alias_value":"IPZENYRD","created_at":"2026-07-04T15:11:15Z"}],"graph_snapshots":[{"event_id":"sha256:f7ca8c540094d5bfabfa8f2e79ab0d5f6308043aacb87faddad47601c063f522","target":"graph","created_at":"2026-07-04T15:11:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0804.4716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent-Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by explaining how the Ram-Yip formula compresses to a new formula, whi","authors_text":"Cristian Lenart","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-30T13:15:00Z","title":"On Combinatorial Formulas for Macdonald Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.4716","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":"sha256:535a7e07477f645695a44e9eb1072e20d9ff4777b6a1c2a6e44233138e405f92","target":"record","created_at":"2026-07-04T15:11:15Z","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":"c5064e9e02e703da4e71485a2ef4d32cf898dc1d984a4436dcad655fe737f022","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-30T13:15:00Z","title_canon_sha256":"e906931b87a9e9505e0da75a9fa9ff1f2036a414733ae9e9c7c11ca6b47cb660"},"schema_version":"1.0","source":{"id":"0804.4716","kind":"arxiv","version":1}},"canonical_sha256":"43f246e22357055eb5e609a14af34b4e8b7eff4560f39a61c9d3f6747e02ab0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43f246e22357055eb5e609a14af34b4e8b7eff4560f39a61c9d3f6747e02ab0e","first_computed_at":"2026-07-04T15:11:15.269119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:11:15.269119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ErLyCRtGWCT01nZTWAIuM7L2bMMEnj4R6kGsvdNXr7ue27hecUaQ0zhmagmZLTWwmIHFN1anyhRh8klWG+G4AA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:11:15.269507Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.4716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:535a7e07477f645695a44e9eb1072e20d9ff4777b6a1c2a6e44233138e405f92","sha256:f7ca8c540094d5bfabfa8f2e79ab0d5f6308043aacb87faddad47601c063f522"],"state_sha256":"d34e0384200fe9bd5c629c56669b249219469453f5b0e72c6fa7b6af7052604d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BkYFezoX+Ps9X4tbkFm+m4eBC1XVVYtgZfj/sdhEJLaUsIlL5BXDRkgoYHXneGlLgG55IWcHNRvE2jsBRkvADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T18:31:18.707502Z","bundle_sha256":"3d8fb56199aae830c0fc37dcdfda62f18f6eadcd588be3b1f1e118631c24ada0"}}