{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZH4NQUDWBXDKX3ROU6HTGK7BFK","short_pith_number":"pith:ZH4NQUDW","canonical_record":{"source":{"id":"1611.06259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T21:49:13Z","cross_cats_sorted":[],"title_canon_sha256":"91aafe6db474d334189caf55ae9b930fd8b41d21668731bd67b0f7dd3af138bc","abstract_canon_sha256":"b6f09366290bf70f26a4b2ddace41fa50905c3e5865221c461aa6847dcb1918f"},"schema_version":"1.0"},"canonical_sha256":"c9f8d850760dc6abee2ea78f332be12ab3821549de48cca83f5c8e859817faf4","source":{"kind":"arxiv","id":"1611.06259","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06259","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06259v1","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06259","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZH4NQUDWBXDK","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZH4NQUDWBXDKX3RO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZH4NQUDW","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZH4NQUDWBXDKX3ROU6HTGK7BFK","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T21:49:13Z","cross_cats_sorted":[],"title_canon_sha256":"91aafe6db474d334189caf55ae9b930fd8b41d21668731bd67b0f7dd3af138bc","abstract_canon_sha256":"b6f09366290bf70f26a4b2ddace41fa50905c3e5865221c461aa6847dcb1918f"},"schema_version":"1.0"},"canonical_sha256":"c9f8d850760dc6abee2ea78f332be12ab3821549de48cca83f5c8e859817faf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:39.224923Z","signature_b64":"8+RzwwnYsqvVuHU2TBhRIvsodj/MRfEXL+izL2YPtJ3dPRBpzA4eYQpDLSDknDFBHJVqVln6fFCAfpwdEGBbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9f8d850760dc6abee2ea78f332be12ab3821549de48cca83f5c8e859817faf4","last_reissued_at":"2026-05-18T00:57:39.224367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:39.224367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06259","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":"2026-05-18T00:57:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vVWGkyu7qhWiplW8d7Wuoiq6vkalKGVhjzO20XtR8p4c0wqFdAw4zS1FhDIC/XjeONBEC1KhM2b+wiAZaPlIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:42:07.305416Z"},"content_sha256":"4055b93d0757ff103a77805618cf8224e1e1e988fee436832c6893fd40824a59","schema_version":"1.0","event_id":"sha256:4055b93d0757ff103a77805618cf8224e1e1e988fee436832c6893fd40824a59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZH4NQUDWBXDKX3ROU6HTGK7BFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flag Descents and Eulerian Polynomials for Wreath Product Quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cyrus Hettle, Dustin Hedmark, McCabe Olsen","submitted_at":"2016-11-18T21:49:13Z","abstract_excerpt":"We investigate the $\\alpha$-colored Eulerian polynomials and a notion of descents introduced in a recent paper of Hedmark and show that such polynomials can be computed as a polynomial encoding descents computed over a quotient of the wreath product $\\mathbb{Z}_\\alpha\\wr\\mathfrak{S}_n$. Moreover, we consider the flag descent statistic computed over this same quotient and find that the flag Eulerian polynomial remains palindromic. We prove that the flag descent polynomial is palindromic over this same quotient by giving a combinatorial proof that the flag descent statistic is symmetrically dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06259","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":"2026-05-18T00:57:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3LT7KwzjTNPTbRgB9Fid4BhvAlKu7t25tDiQ8mOqGxGFB+XYYNekxPdLLFhV1h1FpMBjEAniNA8SGy7xqhVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:42:07.305776Z"},"content_sha256":"0349da724b94d97032c023ea070511162dfdba988ad01303f7f25c59dfae56ee","schema_version":"1.0","event_id":"sha256:0349da724b94d97032c023ea070511162dfdba988ad01303f7f25c59dfae56ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZH4NQUDWBXDKX3ROU6HTGK7BFK/bundle.json","state_url":"https://pith.science/pith/ZH4NQUDWBXDKX3ROU6HTGK7BFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZH4NQUDWBXDKX3ROU6HTGK7BFK/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":"2026-06-25T11:42:07Z","links":{"resolver":"https://pith.science/pith/ZH4NQUDWBXDKX3ROU6HTGK7BFK","bundle":"https://pith.science/pith/ZH4NQUDWBXDKX3ROU6HTGK7BFK/bundle.json","state":"https://pith.science/pith/ZH4NQUDWBXDKX3ROU6HTGK7BFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZH4NQUDWBXDKX3ROU6HTGK7BFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZH4NQUDWBXDKX3ROU6HTGK7BFK","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":"b6f09366290bf70f26a4b2ddace41fa50905c3e5865221c461aa6847dcb1918f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T21:49:13Z","title_canon_sha256":"91aafe6db474d334189caf55ae9b930fd8b41d21668731bd67b0f7dd3af138bc"},"schema_version":"1.0","source":{"id":"1611.06259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06259","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06259v1","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06259","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZH4NQUDWBXDK","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZH4NQUDWBXDKX3RO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZH4NQUDW","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:0349da724b94d97032c023ea070511162dfdba988ad01303f7f25c59dfae56ee","target":"graph","created_at":"2026-05-18T00:57:39Z","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":"We investigate the $\\alpha$-colored Eulerian polynomials and a notion of descents introduced in a recent paper of Hedmark and show that such polynomials can be computed as a polynomial encoding descents computed over a quotient of the wreath product $\\mathbb{Z}_\\alpha\\wr\\mathfrak{S}_n$. Moreover, we consider the flag descent statistic computed over this same quotient and find that the flag Eulerian polynomial remains palindromic. We prove that the flag descent polynomial is palindromic over this same quotient by giving a combinatorial proof that the flag descent statistic is symmetrically dist","authors_text":"Cyrus Hettle, Dustin Hedmark, McCabe Olsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T21:49:13Z","title":"Flag Descents and Eulerian Polynomials for Wreath Product Quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06259","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":"sha256:4055b93d0757ff103a77805618cf8224e1e1e988fee436832c6893fd40824a59","target":"record","created_at":"2026-05-18T00:57:39Z","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":"b6f09366290bf70f26a4b2ddace41fa50905c3e5865221c461aa6847dcb1918f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T21:49:13Z","title_canon_sha256":"91aafe6db474d334189caf55ae9b930fd8b41d21668731bd67b0f7dd3af138bc"},"schema_version":"1.0","source":{"id":"1611.06259","kind":"arxiv","version":1}},"canonical_sha256":"c9f8d850760dc6abee2ea78f332be12ab3821549de48cca83f5c8e859817faf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9f8d850760dc6abee2ea78f332be12ab3821549de48cca83f5c8e859817faf4","first_computed_at":"2026-05-18T00:57:39.224367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:39.224367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+RzwwnYsqvVuHU2TBhRIvsodj/MRfEXL+izL2YPtJ3dPRBpzA4eYQpDLSDknDFBHJVqVln6fFCAfpwdEGBbAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:39.224923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4055b93d0757ff103a77805618cf8224e1e1e988fee436832c6893fd40824a59","sha256:0349da724b94d97032c023ea070511162dfdba988ad01303f7f25c59dfae56ee"],"state_sha256":"a39632259fd2025a3a5bca7ecd8e4b13a28e314192c66ae24cc3729cde5b6059"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B+jo8GDim2zoa1wwn8ya6rAlnZet5rW6rgHD/CDF4RMncrvaYbjafiY9D+r3DrElrXxMvlwSTifUA77Jx/mTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:42:07.307651Z","bundle_sha256":"b87ced898a72ee9d6ce628b7dbdf6ec8a00f44bae0ae0d756da26232851a15f6"}}