{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7QGPLUT42FINTFUFP4FYV5HMRA","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":"7a0be161c0d00a107ebf15468c481bc95172f4a4c675bc6299ecff5152c84d76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-16T17:48:53Z","title_canon_sha256":"ea135116f1cb728c281065412cf9b8eca38635f57372030d7a0c862b7d63e644"},"schema_version":"1.0","source":{"id":"2407.12076","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.12076","created_at":"2026-07-05T11:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"2407.12076v2","created_at":"2026-07-05T11:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.12076","created_at":"2026-07-05T11:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"7QGPLUT42FIN","created_at":"2026-07-05T11:43:56Z"},{"alias_kind":"pith_short_16","alias_value":"7QGPLUT42FINTFUF","created_at":"2026-07-05T11:43:56Z"},{"alias_kind":"pith_short_8","alias_value":"7QGPLUT4","created_at":"2026-07-05T11:43:56Z"}],"graph_snapshots":[{"event_id":"sha256:3fda09652852d2c2bad72ebcd891e9f901e388a4d418c2d2d3a79518e10fea12","target":"graph","created_at":"2026-07-05T11:43:56Z","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/2407.12076/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Colored multiset Eulerian polynomials are a common generalization of MacMahon's multiset Eulerian polynomials and the colored Eulerian polynomials, both of which are known to satisfy well-studied distributional properties including real-rootedness, log-concavity and unimodality. The symmetric colored multiset Eulerian polynomials are characterized and used to prove sufficient conditions for a colored multiset Eulerian polynomial to be self-interlacing. The latter property implies the aforementioned distributional properties as well as others, including the alternatingly increasing property and","authors_text":"Bin Han, Danai Deligeorgaki, Liam Solus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-16T17:48:53Z","title":"Colored Multiset Eulerian Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12076","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":"sha256:6d539c0506d2d99823df81d258623deeeb3bce6dd4ac29407aa5ba4261d5c701","target":"record","created_at":"2026-07-05T11:43:56Z","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":"7a0be161c0d00a107ebf15468c481bc95172f4a4c675bc6299ecff5152c84d76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-16T17:48:53Z","title_canon_sha256":"ea135116f1cb728c281065412cf9b8eca38635f57372030d7a0c862b7d63e644"},"schema_version":"1.0","source":{"id":"2407.12076","kind":"arxiv","version":2}},"canonical_sha256":"fc0cf5d27cd150d996857f0b8af4ec88259bab00e2ab901e9c88065b7d4ca974","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc0cf5d27cd150d996857f0b8af4ec88259bab00e2ab901e9c88065b7d4ca974","first_computed_at":"2026-07-05T11:43:56.187962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:56.187962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LfU/vM6qYya6ClvBG832hYBnEKLKGhG9y87Z8f/mboWrj9j/t/WH5y+EQm5VGoKImRzJkh5IzobFzInEtOJtDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:56.188600Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.12076","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d539c0506d2d99823df81d258623deeeb3bce6dd4ac29407aa5ba4261d5c701","sha256:3fda09652852d2c2bad72ebcd891e9f901e388a4d418c2d2d3a79518e10fea12"],"state_sha256":"b1dbd6291e95cb5704d856e08ffe62bf7a996ca193d303fd128fff45349379a9"}