{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ES4NN7LK76E3CTA3YIYMDTOTHH","short_pith_number":"pith:ES4NN7LK","schema_version":"1.0","canonical_sha256":"24b8d6fd6aff89b14c1bc230c1cdd339d1f620c5e0eebcbe8f26c6eeeab10b34","source":{"kind":"arxiv","id":"2503.04247","version":2},"attestation_state":"computed","paper":{"title":"On posets and polytopes attached to arbors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Chapoton (IRMA)","submitted_at":"2025-03-06T09:30:38Z","abstract_excerpt":"Starting from the data of an arbor, which is a rooted tree with vertices decorated by disjoint sets, we introduce a lattice polytope and a partial order on its lattice points. We give recursive algorithms for various classical invariants of these polytopes and posets, using the tree structure. For linear arbors, we propose a conjecture exchanging the Ehrhart polynomial of the polytope with the Zeta polynomial of the poset for the reverse arbor. The general motivation comes from the action of a transmutation operator acting on M -triangles, which should link the posets considered here with some"},"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":"2503.04247","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-03-06T09:30:38Z","cross_cats_sorted":[],"title_canon_sha256":"d2e8195dd5bae6a6e0d2ae69c789119f46c37cb4a61685d96ebaa64d3162e7af","abstract_canon_sha256":"cd33ff24b3ab9560efbedc0bf559a89f1035e44e7ac31e264753314edd81bfb2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:58:25.746056Z","signature_b64":"mP1uKFa/46GT/VEwFb3yTIs0yujO6YWJKq13CnQ/Tta0sO8caM5VmDL7und88nG6E/cRGNnqvhuNx39PYz7uDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24b8d6fd6aff89b14c1bc230c1cdd339d1f620c5e0eebcbe8f26c6eeeab10b34","last_reissued_at":"2026-07-05T11:58:25.745588Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:58:25.745588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On posets and polytopes attached to arbors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Chapoton (IRMA)","submitted_at":"2025-03-06T09:30:38Z","abstract_excerpt":"Starting from the data of an arbor, which is a rooted tree with vertices decorated by disjoint sets, we introduce a lattice polytope and a partial order on its lattice points. We give recursive algorithms for various classical invariants of these polytopes and posets, using the tree structure. For linear arbors, we propose a conjecture exchanging the Ehrhart polynomial of the polytope with the Zeta polynomial of the poset for the reverse arbor. The general motivation comes from the action of a transmutation operator acting on M -triangles, which should link the posets considered here with some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04247","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/2503.04247/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":"2503.04247","created_at":"2026-07-05T11:58:25.745647+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.04247v2","created_at":"2026-07-05T11:58:25.745647+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04247","created_at":"2026-07-05T11:58:25.745647+00:00"},{"alias_kind":"pith_short_12","alias_value":"ES4NN7LK76E3","created_at":"2026-07-05T11:58:25.745647+00:00"},{"alias_kind":"pith_short_16","alias_value":"ES4NN7LK76E3CTA3","created_at":"2026-07-05T11:58:25.745647+00:00"},{"alias_kind":"pith_short_8","alias_value":"ES4NN7LK","created_at":"2026-07-05T11:58:25.745647+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/ES4NN7LK76E3CTA3YIYMDTOTHH","json":"https://pith.science/pith/ES4NN7LK76E3CTA3YIYMDTOTHH.json","graph_json":"https://pith.science/api/pith-number/ES4NN7LK76E3CTA3YIYMDTOTHH/graph.json","events_json":"https://pith.science/api/pith-number/ES4NN7LK76E3CTA3YIYMDTOTHH/events.json","paper":"https://pith.science/paper/ES4NN7LK"},"agent_actions":{"view_html":"https://pith.science/pith/ES4NN7LK76E3CTA3YIYMDTOTHH","download_json":"https://pith.science/pith/ES4NN7LK76E3CTA3YIYMDTOTHH.json","view_paper":"https://pith.science/paper/ES4NN7LK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.04247&json=true","fetch_graph":"https://pith.science/api/pith-number/ES4NN7LK76E3CTA3YIYMDTOTHH/graph.json","fetch_events":"https://pith.science/api/pith-number/ES4NN7LK76E3CTA3YIYMDTOTHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ES4NN7LK76E3CTA3YIYMDTOTHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ES4NN7LK76E3CTA3YIYMDTOTHH/action/storage_attestation","attest_author":"https://pith.science/pith/ES4NN7LK76E3CTA3YIYMDTOTHH/action/author_attestation","sign_citation":"https://pith.science/pith/ES4NN7LK76E3CTA3YIYMDTOTHH/action/citation_signature","submit_replication":"https://pith.science/pith/ES4NN7LK76E3CTA3YIYMDTOTHH/action/replication_record"}},"created_at":"2026-07-05T11:58:25.745647+00:00","updated_at":"2026-07-05T11:58:25.745647+00:00"}