{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:B5D5QH2LVEXUQKYTNTFYPO24YF","short_pith_number":"pith:B5D5QH2L","canonical_record":{"source":{"id":"2212.04033","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-08T02:10:17Z","cross_cats_sorted":[],"title_canon_sha256":"c744f7993e51d4e24accf02fc2fef1133cebfe70e43196b89f9ac6c19f693acd","abstract_canon_sha256":"0ef836964f93e820c3d150f7ff6da99f6aebdb7301ae3f1bfa3faf316d73db21"},"schema_version":"1.0"},"canonical_sha256":"0f47d81f4ba92f482b136ccb87bb5cc14816f96fa95f33d2f1332879194c3a88","source":{"kind":"arxiv","id":"2212.04033","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.04033","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"2212.04033v1","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.04033","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"B5D5QH2LVEXU","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"pith_short_16","alias_value":"B5D5QH2LVEXUQKYT","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"pith_short_8","alias_value":"B5D5QH2L","created_at":"2026-07-05T05:23:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:B5D5QH2LVEXUQKYTNTFYPO24YF","target":"record","payload":{"canonical_record":{"source":{"id":"2212.04033","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-08T02:10:17Z","cross_cats_sorted":[],"title_canon_sha256":"c744f7993e51d4e24accf02fc2fef1133cebfe70e43196b89f9ac6c19f693acd","abstract_canon_sha256":"0ef836964f93e820c3d150f7ff6da99f6aebdb7301ae3f1bfa3faf316d73db21"},"schema_version":"1.0"},"canonical_sha256":"0f47d81f4ba92f482b136ccb87bb5cc14816f96fa95f33d2f1332879194c3a88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:23:35.569251Z","signature_b64":"eKWfJtiD70+9BOxrvklBMLodF1pxkzbru6qHgxasuv5h3C/DmgPE3Qm6JP4Z6TNp2NWA3MF+ubqCcIbN1FSmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f47d81f4ba92f482b136ccb87bb5cc14816f96fa95f33d2f1332879194c3a88","last_reissued_at":"2026-07-05T05:23:35.568895Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:23:35.568895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.04033","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":"2026-07-05T05:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rX42h6+B+6AEq9L6ZMCjlk7yOtIfXpctruUixIrnHeYJuX/MfYsjWU9pD3mIlyQcTmeHewXRrx1txu/rnPrlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T03:04:01.751649Z"},"content_sha256":"01eda0569cc6ef83f8e45ed19c60c3b7c3db78029efc6b3f01c4502d5add6642","schema_version":"1.0","event_id":"sha256:01eda0569cc6ef83f8e45ed19c60c3b7c3db78029efc6b3f01c4502d5add6642"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:B5D5QH2LVEXUQKYTNTFYPO24YF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Set-valued tableaux for Macdonald polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arun Ram, Zajj Daugherty","submitted_at":"2022-12-08T02:10:17Z","abstract_excerpt":"Set-valued tableaux formulas play an important role in Schubert calculus. Using the box greedy reduced word for the construction of the Macdonald polynomials, we convert the alcove walk formula for Macdonald polynomials to a set-valued tableaux formula for Macdonald polynomials. Our hope is that providing set-valued tableaux formulas for Macdonald polynomials will help to strengthen the analogies and possible connections between the calculus of Macdonald polynomials and Schubert calculus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.04033","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/2212.04033/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":"2026-07-05T05:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Phnq2pF/0GZhiON4y2/zJ/+FvU+09T5gPzZ2zLP7C2Ypkaw5F+wWeTUgKCjZrEsyd66WSyo+Pv9QGHWn1dn/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T03:04:01.752151Z"},"content_sha256":"3d9ea2b8240d80e93ac8f279c8337af7c9676f726956e27be97b200880ed8bdf","schema_version":"1.0","event_id":"sha256:3d9ea2b8240d80e93ac8f279c8337af7c9676f726956e27be97b200880ed8bdf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B5D5QH2LVEXUQKYTNTFYPO24YF/bundle.json","state_url":"https://pith.science/pith/B5D5QH2LVEXUQKYTNTFYPO24YF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B5D5QH2LVEXUQKYTNTFYPO24YF/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":"2026-08-16T03:04:01Z","links":{"resolver":"https://pith.science/pith/B5D5QH2LVEXUQKYTNTFYPO24YF","bundle":"https://pith.science/pith/B5D5QH2LVEXUQKYTNTFYPO24YF/bundle.json","state":"https://pith.science/pith/B5D5QH2LVEXUQKYTNTFYPO24YF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B5D5QH2LVEXUQKYTNTFYPO24YF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:B5D5QH2LVEXUQKYTNTFYPO24YF","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":"0ef836964f93e820c3d150f7ff6da99f6aebdb7301ae3f1bfa3faf316d73db21","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-08T02:10:17Z","title_canon_sha256":"c744f7993e51d4e24accf02fc2fef1133cebfe70e43196b89f9ac6c19f693acd"},"schema_version":"1.0","source":{"id":"2212.04033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.04033","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"2212.04033v1","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.04033","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"B5D5QH2LVEXU","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"pith_short_16","alias_value":"B5D5QH2LVEXUQKYT","created_at":"2026-07-05T05:23:35Z"},{"alias_kind":"pith_short_8","alias_value":"B5D5QH2L","created_at":"2026-07-05T05:23:35Z"}],"graph_snapshots":[{"event_id":"sha256:3d9ea2b8240d80e93ac8f279c8337af7c9676f726956e27be97b200880ed8bdf","target":"graph","created_at":"2026-07-05T05:23:35Z","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/2212.04033/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Set-valued tableaux formulas play an important role in Schubert calculus. Using the box greedy reduced word for the construction of the Macdonald polynomials, we convert the alcove walk formula for Macdonald polynomials to a set-valued tableaux formula for Macdonald polynomials. Our hope is that providing set-valued tableaux formulas for Macdonald polynomials will help to strengthen the analogies and possible connections between the calculus of Macdonald polynomials and Schubert calculus.","authors_text":"Arun Ram, Zajj Daugherty","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-08T02:10:17Z","title":"Set-valued tableaux for Macdonald polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.04033","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":"sha256:01eda0569cc6ef83f8e45ed19c60c3b7c3db78029efc6b3f01c4502d5add6642","target":"record","created_at":"2026-07-05T05:23:35Z","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":"0ef836964f93e820c3d150f7ff6da99f6aebdb7301ae3f1bfa3faf316d73db21","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-08T02:10:17Z","title_canon_sha256":"c744f7993e51d4e24accf02fc2fef1133cebfe70e43196b89f9ac6c19f693acd"},"schema_version":"1.0","source":{"id":"2212.04033","kind":"arxiv","version":1}},"canonical_sha256":"0f47d81f4ba92f482b136ccb87bb5cc14816f96fa95f33d2f1332879194c3a88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f47d81f4ba92f482b136ccb87bb5cc14816f96fa95f33d2f1332879194c3a88","first_computed_at":"2026-07-05T05:23:35.568895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:23:35.568895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eKWfJtiD70+9BOxrvklBMLodF1pxkzbru6qHgxasuv5h3C/DmgPE3Qm6JP4Z6TNp2NWA3MF+ubqCcIbN1FSmDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:23:35.569251Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.04033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01eda0569cc6ef83f8e45ed19c60c3b7c3db78029efc6b3f01c4502d5add6642","sha256:3d9ea2b8240d80e93ac8f279c8337af7c9676f726956e27be97b200880ed8bdf"],"state_sha256":"e50826a5a561051264b2d58cc41284c05f2eb4694ad8533b0f7fd024da536e3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/wtTm6Nay0R9a3S7P7/1nwVwuoNZrJptycjwws9wQQLUYRi/9pRyET76vrDFffpoEPFTgR8M1VjICXpQkt0YAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T03:04:01.757899Z","bundle_sha256":"0aaef4b9728d8888fd2f040f7770c74919ab2c1f5f94e5b0ed85ae2b66daf4d5"}}