{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UU2GHAWKIGFXL6BO6FA74E45ZT","short_pith_number":"pith:UU2GHAWK","schema_version":"1.0","canonical_sha256":"a5346382ca418b75f82ef141fe139dccfd896473e86b5cd7f9155fde8d3ba555","source":{"kind":"arxiv","id":"1901.01417","version":2},"attestation_state":"computed","paper":{"title":"Antichain Simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Benjamin Braun, Brian Davis","submitted_at":"2019-01-05T14:02:13Z","abstract_excerpt":"To each lattice simplex $\\Delta$ we associate a poset encoding the additive structure of lattice points in the fundamental parallelepiped for $\\Delta$. When this poset is an antichain, we say $\\Delta$ is antichain. To each partition $\\lambda$ of $n$, we associate a lattice simplex $\\Delta_\\lambda$ having one unimodular facet, and we investigate their associated posets. We give a number-theoretic characterization of the relations in these posets, as well as a simplified characterization in the case where each part of $\\lambda$ is relatively prime to $n-1$. We use these characterizations to expe"},"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":"1901.01417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-05T14:02:13Z","cross_cats_sorted":["math.AC","math.NT"],"title_canon_sha256":"515051fb4c6431343f94d9a654c4a6f9d258e57b5ee6d5758955c28a733ad4a4","abstract_canon_sha256":"34869319e4c49688e867b60cdec8954a55dfcb8a371bc05b6f9614b839529e19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:35.011978Z","signature_b64":"XSrfP+sPWkidh5QL6vCW5PZtx7Qa77pwM9OjA1be9/2OaG7nPhBUh88w+R6TTg8StxX9fkOJ06Hntd6BGn5oCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5346382ca418b75f82ef141fe139dccfd896473e86b5cd7f9155fde8d3ba555","last_reissued_at":"2026-05-17T23:56:35.011482Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:35.011482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Antichain Simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Benjamin Braun, Brian Davis","submitted_at":"2019-01-05T14:02:13Z","abstract_excerpt":"To each lattice simplex $\\Delta$ we associate a poset encoding the additive structure of lattice points in the fundamental parallelepiped for $\\Delta$. When this poset is an antichain, we say $\\Delta$ is antichain. To each partition $\\lambda$ of $n$, we associate a lattice simplex $\\Delta_\\lambda$ having one unimodular facet, and we investigate their associated posets. We give a number-theoretic characterization of the relations in these posets, as well as a simplified characterization in the case where each part of $\\lambda$ is relatively prime to $n-1$. We use these characterizations to expe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01417","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":""},"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":"1901.01417","created_at":"2026-05-17T23:56:35.011550+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01417v2","created_at":"2026-05-17T23:56:35.011550+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01417","created_at":"2026-05-17T23:56:35.011550+00:00"},{"alias_kind":"pith_short_12","alias_value":"UU2GHAWKIGFX","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UU2GHAWKIGFXL6BO","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UU2GHAWK","created_at":"2026-05-18T12:33:30.264802+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/UU2GHAWKIGFXL6BO6FA74E45ZT","json":"https://pith.science/pith/UU2GHAWKIGFXL6BO6FA74E45ZT.json","graph_json":"https://pith.science/api/pith-number/UU2GHAWKIGFXL6BO6FA74E45ZT/graph.json","events_json":"https://pith.science/api/pith-number/UU2GHAWKIGFXL6BO6FA74E45ZT/events.json","paper":"https://pith.science/paper/UU2GHAWK"},"agent_actions":{"view_html":"https://pith.science/pith/UU2GHAWKIGFXL6BO6FA74E45ZT","download_json":"https://pith.science/pith/UU2GHAWKIGFXL6BO6FA74E45ZT.json","view_paper":"https://pith.science/paper/UU2GHAWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01417&json=true","fetch_graph":"https://pith.science/api/pith-number/UU2GHAWKIGFXL6BO6FA74E45ZT/graph.json","fetch_events":"https://pith.science/api/pith-number/UU2GHAWKIGFXL6BO6FA74E45ZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UU2GHAWKIGFXL6BO6FA74E45ZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UU2GHAWKIGFXL6BO6FA74E45ZT/action/storage_attestation","attest_author":"https://pith.science/pith/UU2GHAWKIGFXL6BO6FA74E45ZT/action/author_attestation","sign_citation":"https://pith.science/pith/UU2GHAWKIGFXL6BO6FA74E45ZT/action/citation_signature","submit_replication":"https://pith.science/pith/UU2GHAWKIGFXL6BO6FA74E45ZT/action/replication_record"}},"created_at":"2026-05-17T23:56:35.011550+00:00","updated_at":"2026-05-17T23:56:35.011550+00:00"}