{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7QGPLUT42FINTFUFP4FYV5HMRA","short_pith_number":"pith:7QGPLUT4","schema_version":"1.0","canonical_sha256":"fc0cf5d27cd150d996857f0b8af4ec88259bab00e2ab901e9c88065b7d4ca974","source":{"kind":"arxiv","id":"2407.12076","version":2},"attestation_state":"computed","paper":{"title":"Colored Multiset Eulerian Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Han, Danai Deligeorgaki, Liam Solus","submitted_at":"2024-07-16T17:48:53Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2407.12076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-16T17:48:53Z","cross_cats_sorted":[],"title_canon_sha256":"ea135116f1cb728c281065412cf9b8eca38635f57372030d7a0c862b7d63e644","abstract_canon_sha256":"7a0be161c0d00a107ebf15468c481bc95172f4a4c675bc6299ecff5152c84d76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:56.188600Z","signature_b64":"LfU/vM6qYya6ClvBG832hYBnEKLKGhG9y87Z8f/mboWrj9j/t/WH5y+EQm5VGoKImRzJkh5IzobFzInEtOJtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc0cf5d27cd150d996857f0b8af4ec88259bab00e2ab901e9c88065b7d4ca974","last_reissued_at":"2026-07-05T11:43:56.187962Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:56.187962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Colored Multiset Eulerian Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Han, Danai Deligeorgaki, Liam Solus","submitted_at":"2024-07-16T17:48:53Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12076","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/2407.12076/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2407.12076","created_at":"2026-07-05T11:43:56.188045+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.12076v2","created_at":"2026-07-05T11:43:56.188045+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.12076","created_at":"2026-07-05T11:43:56.188045+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QGPLUT42FIN","created_at":"2026-07-05T11:43:56.188045+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QGPLUT42FINTFUF","created_at":"2026-07-05T11:43:56.188045+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QGPLUT4","created_at":"2026-07-05T11:43:56.188045+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA","json":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA.json","graph_json":"https://pith.science/api/pith-number/7QGPLUT42FINTFUFP4FYV5HMRA/graph.json","events_json":"https://pith.science/api/pith-number/7QGPLUT42FINTFUFP4FYV5HMRA/events.json","paper":"https://pith.science/paper/7QGPLUT4"},"agent_actions":{"view_html":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA","download_json":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA.json","view_paper":"https://pith.science/paper/7QGPLUT4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.12076&json=true","fetch_graph":"https://pith.science/api/pith-number/7QGPLUT42FINTFUFP4FYV5HMRA/graph.json","fetch_events":"https://pith.science/api/pith-number/7QGPLUT42FINTFUFP4FYV5HMRA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA/action/storage_attestation","attest_author":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA/action/author_attestation","sign_citation":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA/action/citation_signature","submit_replication":"https://pith.science/pith/7QGPLUT42FINTFUFP4FYV5HMRA/action/replication_record"}},"created_at":"2026-07-05T11:43:56.188045+00:00","updated_at":"2026-07-05T11:43:56.188045+00:00"}