{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:65LLTH2SQSMN6YY2LKGUFDBZ6G","short_pith_number":"pith:65LLTH2S","canonical_record":{"source":{"id":"2404.03904","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T05:57:24Z","cross_cats_sorted":[],"title_canon_sha256":"a7bea20d353e152d70cc125124adc1c2e2887c1336aee4cf423c4d5f3eeacf2a","abstract_canon_sha256":"ec8015f32847854fa5de21d8d1f90917701c163fdf30660cb58f04db24bc2c35"},"schema_version":"1.0"},"canonical_sha256":"f756b99f528498df631a5a8d428c39f1b6b53559a072b440f2be33aee058cca0","source":{"kind":"arxiv","id":"2404.03904","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.03904","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"arxiv_version","alias_value":"2404.03904v2","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.03904","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"pith_short_12","alias_value":"65LLTH2SQSMN","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"pith_short_16","alias_value":"65LLTH2SQSMN6YY2","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"pith_short_8","alias_value":"65LLTH2S","created_at":"2026-05-20T00:01:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:65LLTH2SQSMN6YY2LKGUFDBZ6G","target":"record","payload":{"canonical_record":{"source":{"id":"2404.03904","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T05:57:24Z","cross_cats_sorted":[],"title_canon_sha256":"a7bea20d353e152d70cc125124adc1c2e2887c1336aee4cf423c4d5f3eeacf2a","abstract_canon_sha256":"ec8015f32847854fa5de21d8d1f90917701c163fdf30660cb58f04db24bc2c35"},"schema_version":"1.0"},"canonical_sha256":"f756b99f528498df631a5a8d428c39f1b6b53559a072b440f2be33aee058cca0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:32.090092Z","signature_b64":"OJDDBezgXxJqA7nm8GmO96tmmG8Zu7btiHBhIyFuJ+3R2ktp2A/Kv3/2G2SpIB7irqeHnwkGN3EMapFjz5S2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f756b99f528498df631a5a8d428c39f1b6b53559a072b440f2be33aee058cca0","last_reissued_at":"2026-05-20T00:01:32.089265Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:32.089265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.03904","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":"2026-05-20T00:01:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlUs+eL0nw0Ys+m9BO2n+PSRi6Kf7t722eX62av+vZIMLoGYK7xgIudUv0dNFqjxGJnSXyMwy38DWYJYhzn7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T02:54:15.244723Z"},"content_sha256":"fca986c1bc546044fd0d3f08e146d70107d05aac7db281eab853d8dbfe187faf","schema_version":"1.0","event_id":"sha256:fca986c1bc546044fd0d3f08e146d70107d05aac7db281eab853d8dbfe187faf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:65LLTH2SQSMN6YY2LKGUFDBZ6G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Macdonald characters from a new formula for Macdonald polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Houcine Ben Dali, Michele D'Adderio","submitted_at":"2024-04-05T05:57:24Z","abstract_excerpt":"We introduce a new operator $\\Gamma$ on symmetric functions, which enables us to obtain a creation formula for Macdonald polynomials. This formula provides a connection between the theory of Macdonald operators initiated by Bergeron, Garsia, Haiman and Tesler, and shifted Macdonald polynomials introduced by Knop, Lassalle, Okounkov and Sahi.\n  We use this formula to introduce a two-parameter generalization of Jack characters, which we call Macdonald characters. Finally, we provide a change of variables in order to formulate several positivity conjectures related to these generalized characters"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03904","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.03904/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":"2026-05-20T00:01:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DwI9SudybElxAkmJtek0tp0q7VNV4MtnhWgQP6ZU+SZLeYx7OmwC4JWrgYiN6mAnpXG4pmwNR6TCdgAdrJQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T02:54:15.245112Z"},"content_sha256":"3cd26a8caa6371f370cc85ceb3cf7465a60b0550560f02676b87687298318573","schema_version":"1.0","event_id":"sha256:3cd26a8caa6371f370cc85ceb3cf7465a60b0550560f02676b87687298318573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/65LLTH2SQSMN6YY2LKGUFDBZ6G/bundle.json","state_url":"https://pith.science/pith/65LLTH2SQSMN6YY2LKGUFDBZ6G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/65LLTH2SQSMN6YY2LKGUFDBZ6G/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":"2026-05-22T02:54:15Z","links":{"resolver":"https://pith.science/pith/65LLTH2SQSMN6YY2LKGUFDBZ6G","bundle":"https://pith.science/pith/65LLTH2SQSMN6YY2LKGUFDBZ6G/bundle.json","state":"https://pith.science/pith/65LLTH2SQSMN6YY2LKGUFDBZ6G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/65LLTH2SQSMN6YY2LKGUFDBZ6G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:65LLTH2SQSMN6YY2LKGUFDBZ6G","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":"ec8015f32847854fa5de21d8d1f90917701c163fdf30660cb58f04db24bc2c35","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T05:57:24Z","title_canon_sha256":"a7bea20d353e152d70cc125124adc1c2e2887c1336aee4cf423c4d5f3eeacf2a"},"schema_version":"1.0","source":{"id":"2404.03904","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.03904","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"arxiv_version","alias_value":"2404.03904v2","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.03904","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"pith_short_12","alias_value":"65LLTH2SQSMN","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"pith_short_16","alias_value":"65LLTH2SQSMN6YY2","created_at":"2026-05-20T00:01:32Z"},{"alias_kind":"pith_short_8","alias_value":"65LLTH2S","created_at":"2026-05-20T00:01:32Z"}],"graph_snapshots":[{"event_id":"sha256:3cd26a8caa6371f370cc85ceb3cf7465a60b0550560f02676b87687298318573","target":"graph","created_at":"2026-05-20T00:01:32Z","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/2404.03904/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new operator $\\Gamma$ on symmetric functions, which enables us to obtain a creation formula for Macdonald polynomials. This formula provides a connection between the theory of Macdonald operators initiated by Bergeron, Garsia, Haiman and Tesler, and shifted Macdonald polynomials introduced by Knop, Lassalle, Okounkov and Sahi.\n  We use this formula to introduce a two-parameter generalization of Jack characters, which we call Macdonald characters. Finally, we provide a change of variables in order to formulate several positivity conjectures related to these generalized characters","authors_text":"Houcine Ben Dali, Michele D'Adderio","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T05:57:24Z","title":"Macdonald characters from a new formula for Macdonald polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03904","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:fca986c1bc546044fd0d3f08e146d70107d05aac7db281eab853d8dbfe187faf","target":"record","created_at":"2026-05-20T00:01:32Z","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":"ec8015f32847854fa5de21d8d1f90917701c163fdf30660cb58f04db24bc2c35","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-04-05T05:57:24Z","title_canon_sha256":"a7bea20d353e152d70cc125124adc1c2e2887c1336aee4cf423c4d5f3eeacf2a"},"schema_version":"1.0","source":{"id":"2404.03904","kind":"arxiv","version":2}},"canonical_sha256":"f756b99f528498df631a5a8d428c39f1b6b53559a072b440f2be33aee058cca0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f756b99f528498df631a5a8d428c39f1b6b53559a072b440f2be33aee058cca0","first_computed_at":"2026-05-20T00:01:32.089265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:32.089265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OJDDBezgXxJqA7nm8GmO96tmmG8Zu7btiHBhIyFuJ+3R2ktp2A/Kv3/2G2SpIB7irqeHnwkGN3EMapFjz5S2Bw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:32.090092Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.03904","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fca986c1bc546044fd0d3f08e146d70107d05aac7db281eab853d8dbfe187faf","sha256:3cd26a8caa6371f370cc85ceb3cf7465a60b0550560f02676b87687298318573"],"state_sha256":"6bfc6098c27b302637a5c8ba1807bd4974d2aba5c4af1e1494e852ca5fd59869"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SnXlO3HIXh5hTkYk6HL4IOKX+saTSzl0ydfE+4i7XwR5nwK57fZzrz/kc8WYJDZtgDgBsxLdXOx2E+IdwpsjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T02:54:15.247723Z","bundle_sha256":"49b960350f541b762a9014e276c180192b5f416869662bea6cec1cbaa88cbc2f"}}