{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PD7R2XKY7N3TVEAROFXWVE5KWS","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":"61b5bba90633bc7ffeb1c19c385288ae303e369579db382acc37839e14bbdced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T13:38:02Z","title_canon_sha256":"b621b3189a38f78a82559a906407644dc9d2d7a7626a873c41425407c0f2cdfe"},"schema_version":"1.0","source":{"id":"2605.28474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28474","created_at":"2026-05-28T02:04:54Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28474v1","created_at":"2026-05-28T02:04:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28474","created_at":"2026-05-28T02:04:54Z"},{"alias_kind":"pith_short_12","alias_value":"PD7R2XKY7N3T","created_at":"2026-05-28T02:04:54Z"},{"alias_kind":"pith_short_16","alias_value":"PD7R2XKY7N3TVEAR","created_at":"2026-05-28T02:04:54Z"},{"alias_kind":"pith_short_8","alias_value":"PD7R2XKY","created_at":"2026-05-28T02:04:54Z"}],"graph_snapshots":[{"event_id":"sha256:7553dcaca0d6ecbb3d2f19fca015548757b81fed0c81c3af572b3ecd798b00bf","target":"graph","created_at":"2026-05-28T02:04:54Z","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/2605.28474/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and study dual Chow functions associated to kernels in incidence algebras of weakly ranked posets. Given a kernel, its dual Chow function is defined as the Chow function associated to the sign-twisted reverse kernel. For kernels satisfying a natural skew-symmetry condition, such as the Eulerian kernel of an Eulerian poset or the kernel given by R-polynomials on Bruhat intervals, this construction recovers the ordinary Chow function. In contrast, when this skew-symmetry fails, the dual Chow function gives a genuinely different invariant.\n  The main example considered in this paper ","authors_text":"Elena Hoster, Giovanni Caiolo, Luis Ferroni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T13:38:02Z","title":"Dual Chow polynomials of matroids and posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28474","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":"sha256:769541a78eff31f173389bd4cb13f932f9a634eea936986afcb4d0a8e7cf25ec","target":"record","created_at":"2026-05-28T02:04:54Z","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":"61b5bba90633bc7ffeb1c19c385288ae303e369579db382acc37839e14bbdced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T13:38:02Z","title_canon_sha256":"b621b3189a38f78a82559a906407644dc9d2d7a7626a873c41425407c0f2cdfe"},"schema_version":"1.0","source":{"id":"2605.28474","kind":"arxiv","version":1}},"canonical_sha256":"78ff1d5d58fb773a9011716f6a93aab4a52f22d3b83fe49a2177bb95580a9da2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78ff1d5d58fb773a9011716f6a93aab4a52f22d3b83fe49a2177bb95580a9da2","first_computed_at":"2026-05-28T02:04:54.024900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T02:04:54.024900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dk95Frc+xNJNYMz+7p70z1CI2+DE2BLTwc0MYMClyP+ZnIOpxcDLkh1C273qPCUL5v1VyXGZ1R9Tgj+op72ECw==","signature_status":"signed_v1","signed_at":"2026-05-28T02:04:54.025302Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.28474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:769541a78eff31f173389bd4cb13f932f9a634eea936986afcb4d0a8e7cf25ec","sha256:7553dcaca0d6ecbb3d2f19fca015548757b81fed0c81c3af572b3ecd798b00bf"],"state_sha256":"277ac539898bd5444797dcbea8b269a25507e09e79e10b58c095711adf5c7979"}