{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6C6KYTEPNAYF7JEOQJ4DOCCEXD","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":"dbd9d1a793a3777b0fba73ff3eaa3faa0e9dd0e916902eb9a264aff6b0eb4d73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-10-20T15:52:06Z","title_canon_sha256":"94cc1b7502db75b6cd3f82f25a006d8b8371bd2c87ec9492fd8761dc9c273ab2"},"schema_version":"1.0","source":{"id":"2510.17679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.17679","created_at":"2026-08-11T02:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"2510.17679v2","created_at":"2026-08-11T02:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.17679","created_at":"2026-08-11T02:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"6C6KYTEPNAYF","created_at":"2026-08-11T02:23:44Z"},{"alias_kind":"pith_short_16","alias_value":"6C6KYTEPNAYF7JEO","created_at":"2026-08-11T02:23:44Z"},{"alias_kind":"pith_short_8","alias_value":"6C6KYTEP","created_at":"2026-08-11T02:23:44Z"}],"graph_snapshots":[{"event_id":"sha256:657ed11c691c05211c6c9b83e19e94f99314390b34b32c0282bd24101718e055","target":"graph","created_at":"2026-08-11T02:23:44Z","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/2510.17679/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $P$ be a finite partially ordered set. In a recent series of works, Proudfoot introduced the notion of $Z$-polynomials associated with $P$-kernels, providing a unified framework for various intersection cohomology Poincar\\'e polynomials arising in diverse areas of mathematics. One of the problems posed by Proudfoot was to interpret the $Z$-polynomial in a fundamental setting---namely, when $P$ is the lattice of faces of a convex polytope (or, more generally, an Eulerian poset). We resolve this problem by proving that the $Z$-polynomial of any Eulerian poset coincides with the toric $h$-pol","authors_text":"Luis Ferroni, Roberto Riccardi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-10-20T15:52:06Z","title":"Eulerian posets and $Z$-polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.17679","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":"sha256:48754fce7628e725f60d18d12f4c2f23c42481f807ce5a336243b506477fac11","target":"record","created_at":"2026-08-11T02:23:44Z","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":"dbd9d1a793a3777b0fba73ff3eaa3faa0e9dd0e916902eb9a264aff6b0eb4d73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-10-20T15:52:06Z","title_canon_sha256":"94cc1b7502db75b6cd3f82f25a006d8b8371bd2c87ec9492fd8761dc9c273ab2"},"schema_version":"1.0","source":{"id":"2510.17679","kind":"arxiv","version":2}},"canonical_sha256":"f0bcac4c8f68305fa48e8278370844b8e83850fb58da87b86069856b16eef904","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0bcac4c8f68305fa48e8278370844b8e83850fb58da87b86069856b16eef904","first_computed_at":"2026-08-11T02:23:44.160230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T02:23:44.160230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cRGOUh3tEBYM4CYTsyRzTMB8WwifAvdfSQc09Y2BKwn2RozTB286MmAp4wfaO+VHGDDqGgeKobsCOvAcajiJAg==","signature_status":"signed_v1","signed_at":"2026-08-11T02:23:44.162383Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.17679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48754fce7628e725f60d18d12f4c2f23c42481f807ce5a336243b506477fac11","sha256:657ed11c691c05211c6c9b83e19e94f99314390b34b32c0282bd24101718e055"],"state_sha256":"55f1a920c7e5bf2cd2b42adabbabbf6d1d8545d34e5a03552c6b2b26ad8ce23e"}