{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VX5KGALREDUBPCIUXWSCDUNSTK","short_pith_number":"pith:VX5KGALR","canonical_record":{"source":{"id":"2506.09015","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T17:42:42Z","cross_cats_sorted":[],"title_canon_sha256":"73fbdbd1863b6978351085315c1a7f39d8b7efb58d8ae7c10a0d2386f7deff35","abstract_canon_sha256":"5d18f506b930a1cf11b46fe0bac6b1f99a05341ec102d204551fa208610b92d0"},"schema_version":"1.0"},"canonical_sha256":"adfaa3017120e8178914bda421d1b29ab98f938e95bad1cd4925216ff13497be","source":{"kind":"arxiv","id":"2506.09015","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09015","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09015v2","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09015","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"VX5KGALREDUB","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"pith_short_16","alias_value":"VX5KGALREDUBPCIU","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"pith_short_8","alias_value":"VX5KGALR","created_at":"2026-07-05T11:44:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VX5KGALREDUBPCIUXWSCDUNSTK","target":"record","payload":{"canonical_record":{"source":{"id":"2506.09015","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T17:42:42Z","cross_cats_sorted":[],"title_canon_sha256":"73fbdbd1863b6978351085315c1a7f39d8b7efb58d8ae7c10a0d2386f7deff35","abstract_canon_sha256":"5d18f506b930a1cf11b46fe0bac6b1f99a05341ec102d204551fa208610b92d0"},"schema_version":"1.0"},"canonical_sha256":"adfaa3017120e8178914bda421d1b29ab98f938e95bad1cd4925216ff13497be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:07.177496Z","signature_b64":"/EjhtVHHpQnZyJ41xFAlb0y8Qu/HDsmB3KhQiFsZhF8M4sThwtIHwqROo0HTEYoL0CbTum9NNUDjF+xiz8YvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adfaa3017120e8178914bda421d1b29ab98f938e95bad1cd4925216ff13497be","last_reissued_at":"2026-07-05T11:44:07.176998Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:07.176998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.09015","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":"2026-07-05T11:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W3vvorJZpDLf20IfDEVEnmLLwLyYXKmYEt4i1LNBA18OlmtQZ//8C//DLwVUTu2CVuxFoOpbbT6lGnYvcxrMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:34:36.007215Z"},"content_sha256":"fc4f1dc3c3607c3cdf07a0f0cb5973e4f330196c193cced404993d39c975b6c8","schema_version":"1.0","event_id":"sha256:fc4f1dc3c3607c3cdf07a0f0cb5973e4f330196c193cced404993d39c975b6c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VX5KGALREDUBPCIUXWSCDUNSTK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flagged LLT polynomials, nonsymmetric plethysm, and nonsymmetric Macdonald polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anna Pun, George H. Seelinger, Jennifer Morse, Jonah Blasiak, Mark Haiman","submitted_at":"2025-06-10T17:42:42Z","abstract_excerpt":"The plethystic transformation $f[X] \\mapsto f[X/(1-t)]$ and LLT polynomials are central to the theory of symmetric Macdonald polynomials. In this work, we introduce and study nonsymmetric flagged LLT polynomials. We show that these admit both an algebraic and a combinatorial description, that they Weyl symmetrize to the usual symmetric LLT polynomials, and we conjecture that they expand positively in terms of Demazure atoms. Additionally, we construct a nonsymmetric plethysm operator $\\Pi_{t,x}$ on $\\mathfrak{K}[x_1,\\ldots,x_n]$, which serves as an analogue of $f[X] \\mapsto f[X/(1-t)]$. We pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09015","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/2506.09015/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":"2026-07-05T11:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u5JUx6+3fUXA/+EQ0Gp9ohOnJn/IyD6op5WRKSDUf8tuK2VdZmol8ADeVIP8fFVgkVybxOrlXRivZCVm7qu+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:34:36.007719Z"},"content_sha256":"df2035b5557b66beae30364e7587ef84496777e1eb7ee1f6f9bc48e8044c737d","schema_version":"1.0","event_id":"sha256:df2035b5557b66beae30364e7587ef84496777e1eb7ee1f6f9bc48e8044c737d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VX5KGALREDUBPCIUXWSCDUNSTK/bundle.json","state_url":"https://pith.science/pith/VX5KGALREDUBPCIUXWSCDUNSTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VX5KGALREDUBPCIUXWSCDUNSTK/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":"2026-08-08T07:34:36Z","links":{"resolver":"https://pith.science/pith/VX5KGALREDUBPCIUXWSCDUNSTK","bundle":"https://pith.science/pith/VX5KGALREDUBPCIUXWSCDUNSTK/bundle.json","state":"https://pith.science/pith/VX5KGALREDUBPCIUXWSCDUNSTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VX5KGALREDUBPCIUXWSCDUNSTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VX5KGALREDUBPCIUXWSCDUNSTK","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":"5d18f506b930a1cf11b46fe0bac6b1f99a05341ec102d204551fa208610b92d0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T17:42:42Z","title_canon_sha256":"73fbdbd1863b6978351085315c1a7f39d8b7efb58d8ae7c10a0d2386f7deff35"},"schema_version":"1.0","source":{"id":"2506.09015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09015","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09015v2","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09015","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"VX5KGALREDUB","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"pith_short_16","alias_value":"VX5KGALREDUBPCIU","created_at":"2026-07-05T11:44:07Z"},{"alias_kind":"pith_short_8","alias_value":"VX5KGALR","created_at":"2026-07-05T11:44:07Z"}],"graph_snapshots":[{"event_id":"sha256:df2035b5557b66beae30364e7587ef84496777e1eb7ee1f6f9bc48e8044c737d","target":"graph","created_at":"2026-07-05T11:44:07Z","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/2506.09015/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The plethystic transformation $f[X] \\mapsto f[X/(1-t)]$ and LLT polynomials are central to the theory of symmetric Macdonald polynomials. In this work, we introduce and study nonsymmetric flagged LLT polynomials. We show that these admit both an algebraic and a combinatorial description, that they Weyl symmetrize to the usual symmetric LLT polynomials, and we conjecture that they expand positively in terms of Demazure atoms. Additionally, we construct a nonsymmetric plethysm operator $\\Pi_{t,x}$ on $\\mathfrak{K}[x_1,\\ldots,x_n]$, which serves as an analogue of $f[X] \\mapsto f[X/(1-t)]$. We pro","authors_text":"Anna Pun, George H. Seelinger, Jennifer Morse, Jonah Blasiak, Mark Haiman","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T17:42:42Z","title":"Flagged LLT polynomials, nonsymmetric plethysm, and nonsymmetric Macdonald polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09015","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:fc4f1dc3c3607c3cdf07a0f0cb5973e4f330196c193cced404993d39c975b6c8","target":"record","created_at":"2026-07-05T11:44:07Z","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":"5d18f506b930a1cf11b46fe0bac6b1f99a05341ec102d204551fa208610b92d0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T17:42:42Z","title_canon_sha256":"73fbdbd1863b6978351085315c1a7f39d8b7efb58d8ae7c10a0d2386f7deff35"},"schema_version":"1.0","source":{"id":"2506.09015","kind":"arxiv","version":2}},"canonical_sha256":"adfaa3017120e8178914bda421d1b29ab98f938e95bad1cd4925216ff13497be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adfaa3017120e8178914bda421d1b29ab98f938e95bad1cd4925216ff13497be","first_computed_at":"2026-07-05T11:44:07.176998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:44:07.176998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/EjhtVHHpQnZyJ41xFAlb0y8Qu/HDsmB3KhQiFsZhF8M4sThwtIHwqROo0HTEYoL0CbTum9NNUDjF+xiz8YvDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:44:07.177496Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.09015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc4f1dc3c3607c3cdf07a0f0cb5973e4f330196c193cced404993d39c975b6c8","sha256:df2035b5557b66beae30364e7587ef84496777e1eb7ee1f6f9bc48e8044c737d"],"state_sha256":"894c24646d39d90d82c91e59bc1e2f3f4c6dc6318d0a2ca72baca03f2b17d048"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4NIm+//yZx3Zb/1f3ZlQ0W1bHq8CYXbsQ4B078UW+D9UKHT7MfO9iGa12DX1njOHDOA1OJ5xfsQvPplu1RyAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T07:34:36.011750Z","bundle_sha256":"71b776ebeda0c1e4e24b4180d02be4b5b0c95056a152d30f5b43da30ec31107e"}}