{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZTIPZLRB3KA5GDPJPGWF5VSMVT","short_pith_number":"pith:ZTIPZLRB","canonical_record":{"source":{"id":"1306.3146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-06-13T15:44:49Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"864d5a02b72c2cbb916908a0211e57dfce56f2c9f4dada6be142a6fda221816e","abstract_canon_sha256":"c01bd95d6336532c5abeb2c16171514ec3f91087c8c70078d15f54fdc80e8d9c"},"schema_version":"1.0"},"canonical_sha256":"ccd0fcae21da81d30de979ac5ed64cacf938be30804fa835a85f84c57b5f346f","source":{"kind":"arxiv","id":"1306.3146","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3146","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3146v1","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3146","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZTIPZLRB3KA5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZTIPZLRB3KA5GDPJ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZTIPZLRB","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZTIPZLRB3KA5GDPJPGWF5VSMVT","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-06-13T15:44:49Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"864d5a02b72c2cbb916908a0211e57dfce56f2c9f4dada6be142a6fda221816e","abstract_canon_sha256":"c01bd95d6336532c5abeb2c16171514ec3f91087c8c70078d15f54fdc80e8d9c"},"schema_version":"1.0"},"canonical_sha256":"ccd0fcae21da81d30de979ac5ed64cacf938be30804fa835a85f84c57b5f346f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:59.473178Z","signature_b64":"q0b09oW5XsIK5Q7B+OrxDj+LOBzhRScFgT35kxual0FhVwBBb3DbNwnbFctOUr48eee4Coai/uH5P+4oLaRMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccd0fcae21da81d30de979ac5ed64cacf938be30804fa835a85f84c57b5f346f","last_reissued_at":"2026-05-18T03:20:59.472626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:59.472626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3146","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":"2026-05-18T03:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q8HtmZa7pjll+dfz6/HZ0j1xhC4HdQbNsUZhxzSZQWtOl53oNTCYZWk9OF4+xZevzGwrCRoBGJgrktM33WBGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:50:05.767578Z"},"content_sha256":"778cab120d9a5051654113b561ece5edc354cf623eb45e15a530f0b6dff09afd","schema_version":"1.0","event_id":"sha256:778cab120d9a5051654113b561ece5edc354cf623eb45e15a530f0b6dff09afd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZTIPZLRB3KA5GDPJPGWF5VSMVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremal part of the PBW-filtration and E-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Evgeny Feigin, Ivan Cherednik","submitted_at":"2013-06-13T15:44:49Z","abstract_excerpt":"Given a reduced irreducible root system, the corresponding nil-DAHA is used to calculate the extremal coefficients of nonsymmetric Macdonald polynomials, also called E-polynomails, in the limit t=infinity and for antidominant weights, which is an important ingredient of the new theory of nonsymmetric q-Whittaker function. These coefficients are pure q-powers and their degrees are expected to coincide in the untwisted setting with the extremal degrees of the so-called PBW-filtration in the corresponding finite-dimensional irreducible representations of the simple Lie algebra for any root system"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3146","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":"2026-05-18T03:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0m5tRL8pQQJ1TB6hZKt3fOApkWULcaV5UPoXU+k5BUyCHqlWzwuKZ1jCM/PCYOTnxuVdvJFzAM+Uu4sYSbScAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:50:05.768185Z"},"content_sha256":"8f36cc70b25ca5f69a985daa2157346971a136a180e5e59c68425ae196d2d990","schema_version":"1.0","event_id":"sha256:8f36cc70b25ca5f69a985daa2157346971a136a180e5e59c68425ae196d2d990"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTIPZLRB3KA5GDPJPGWF5VSMVT/bundle.json","state_url":"https://pith.science/pith/ZTIPZLRB3KA5GDPJPGWF5VSMVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTIPZLRB3KA5GDPJPGWF5VSMVT/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":"2026-05-27T07:50:05Z","links":{"resolver":"https://pith.science/pith/ZTIPZLRB3KA5GDPJPGWF5VSMVT","bundle":"https://pith.science/pith/ZTIPZLRB3KA5GDPJPGWF5VSMVT/bundle.json","state":"https://pith.science/pith/ZTIPZLRB3KA5GDPJPGWF5VSMVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTIPZLRB3KA5GDPJPGWF5VSMVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZTIPZLRB3KA5GDPJPGWF5VSMVT","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":"c01bd95d6336532c5abeb2c16171514ec3f91087c8c70078d15f54fdc80e8d9c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-06-13T15:44:49Z","title_canon_sha256":"864d5a02b72c2cbb916908a0211e57dfce56f2c9f4dada6be142a6fda221816e"},"schema_version":"1.0","source":{"id":"1306.3146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3146","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3146v1","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3146","created_at":"2026-05-18T03:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZTIPZLRB3KA5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZTIPZLRB3KA5GDPJ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZTIPZLRB","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:8f36cc70b25ca5f69a985daa2157346971a136a180e5e59c68425ae196d2d990","target":"graph","created_at":"2026-05-18T03:20:59Z","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":"Given a reduced irreducible root system, the corresponding nil-DAHA is used to calculate the extremal coefficients of nonsymmetric Macdonald polynomials, also called E-polynomails, in the limit t=infinity and for antidominant weights, which is an important ingredient of the new theory of nonsymmetric q-Whittaker function. These coefficients are pure q-powers and their degrees are expected to coincide in the untwisted setting with the extremal degrees of the so-called PBW-filtration in the corresponding finite-dimensional irreducible representations of the simple Lie algebra for any root system","authors_text":"Evgeny Feigin, Ivan Cherednik","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-06-13T15:44:49Z","title":"Extremal part of the PBW-filtration and E-polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3146","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":"sha256:778cab120d9a5051654113b561ece5edc354cf623eb45e15a530f0b6dff09afd","target":"record","created_at":"2026-05-18T03:20:59Z","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":"c01bd95d6336532c5abeb2c16171514ec3f91087c8c70078d15f54fdc80e8d9c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-06-13T15:44:49Z","title_canon_sha256":"864d5a02b72c2cbb916908a0211e57dfce56f2c9f4dada6be142a6fda221816e"},"schema_version":"1.0","source":{"id":"1306.3146","kind":"arxiv","version":1}},"canonical_sha256":"ccd0fcae21da81d30de979ac5ed64cacf938be30804fa835a85f84c57b5f346f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccd0fcae21da81d30de979ac5ed64cacf938be30804fa835a85f84c57b5f346f","first_computed_at":"2026-05-18T03:20:59.472626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:59.472626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q0b09oW5XsIK5Q7B+OrxDj+LOBzhRScFgT35kxual0FhVwBBb3DbNwnbFctOUr48eee4Coai/uH5P+4oLaRMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:59.473178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:778cab120d9a5051654113b561ece5edc354cf623eb45e15a530f0b6dff09afd","sha256:8f36cc70b25ca5f69a985daa2157346971a136a180e5e59c68425ae196d2d990"],"state_sha256":"eed3091b93069c75ae3ac4223bf456968eb7e814d5b2762c9610f05e09c9d71a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wniEu5QWVZH+LwECC6OlCRMmHaJColWze2vukXXfp8a5QKWrpoN6093r23CjB+QaAN8FLWvbbYPZfHyqUQP+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:50:05.771536Z","bundle_sha256":"9be41074290fbad5d170b7548657e061661004ef35e44342c496c2c35389ca5d"}}