{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PD7R2XKY7N3TVEAROFXWVE5KWS","short_pith_number":"pith:PD7R2XKY","schema_version":"1.0","canonical_sha256":"78ff1d5d58fb773a9011716f6a93aab4a52f22d3b83fe49a2177bb95580a9da2","source":{"kind":"arxiv","id":"2605.28474","version":1},"attestation_state":"computed","paper":{"title":"Dual Chow polynomials of matroids and posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elena Hoster, Giovanni Caiolo, Luis Ferroni","submitted_at":"2026-05-27T13:38:02Z","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 "},"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":"2605.28474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T13:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"b621b3189a38f78a82559a906407644dc9d2d7a7626a873c41425407c0f2cdfe","abstract_canon_sha256":"61b5bba90633bc7ffeb1c19c385288ae303e369579db382acc37839e14bbdced"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:54.025302Z","signature_b64":"Dk95Frc+xNJNYMz+7p70z1CI2+DE2BLTwc0MYMClyP+ZnIOpxcDLkh1C273qPCUL5v1VyXGZ1R9Tgj+op72ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78ff1d5d58fb773a9011716f6a93aab4a52f22d3b83fe49a2177bb95580a9da2","last_reissued_at":"2026-05-28T02:04:54.024900Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:54.024900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dual Chow polynomials of matroids and posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elena Hoster, Giovanni Caiolo, Luis Ferroni","submitted_at":"2026-05-27T13:38:02Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28474","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.28474/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":"2605.28474","created_at":"2026-05-28T02:04:54.024957+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.28474v1","created_at":"2026-05-28T02:04:54.024957+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28474","created_at":"2026-05-28T02:04:54.024957+00:00"},{"alias_kind":"pith_short_12","alias_value":"PD7R2XKY7N3T","created_at":"2026-05-28T02:04:54.024957+00:00"},{"alias_kind":"pith_short_16","alias_value":"PD7R2XKY7N3TVEAR","created_at":"2026-05-28T02:04:54.024957+00:00"},{"alias_kind":"pith_short_8","alias_value":"PD7R2XKY","created_at":"2026-05-28T02:04:54.024957+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/PD7R2XKY7N3TVEAROFXWVE5KWS","json":"https://pith.science/pith/PD7R2XKY7N3TVEAROFXWVE5KWS.json","graph_json":"https://pith.science/api/pith-number/PD7R2XKY7N3TVEAROFXWVE5KWS/graph.json","events_json":"https://pith.science/api/pith-number/PD7R2XKY7N3TVEAROFXWVE5KWS/events.json","paper":"https://pith.science/paper/PD7R2XKY"},"agent_actions":{"view_html":"https://pith.science/pith/PD7R2XKY7N3TVEAROFXWVE5KWS","download_json":"https://pith.science/pith/PD7R2XKY7N3TVEAROFXWVE5KWS.json","view_paper":"https://pith.science/paper/PD7R2XKY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.28474&json=true","fetch_graph":"https://pith.science/api/pith-number/PD7R2XKY7N3TVEAROFXWVE5KWS/graph.json","fetch_events":"https://pith.science/api/pith-number/PD7R2XKY7N3TVEAROFXWVE5KWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PD7R2XKY7N3TVEAROFXWVE5KWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PD7R2XKY7N3TVEAROFXWVE5KWS/action/storage_attestation","attest_author":"https://pith.science/pith/PD7R2XKY7N3TVEAROFXWVE5KWS/action/author_attestation","sign_citation":"https://pith.science/pith/PD7R2XKY7N3TVEAROFXWVE5KWS/action/citation_signature","submit_replication":"https://pith.science/pith/PD7R2XKY7N3TVEAROFXWVE5KWS/action/replication_record"}},"created_at":"2026-05-28T02:04:54.024957+00:00","updated_at":"2026-05-28T02:04:54.024957+00:00"}