{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:53LNXFEAUMONJ4GMPJVUZW3SY4","short_pith_number":"pith:53LNXFEA","schema_version":"1.0","canonical_sha256":"eed6db9480a31cd4f0cc7a6b4cdb72c737d317f832fd3653405218f09bf0210f","source":{"kind":"arxiv","id":"0710.2665","version":2},"attestation_state":"computed","paper":{"title":"Lower bounds on the coefficients of Ehrhart polynomials","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Makoto Tagami, Martin Henk","submitted_at":"2007-10-14T14:14:41Z","abstract_excerpt":"We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. Concerning the coefficients of the Ehrhart series of a lattice polytope we show that Hibi's lower bound is not true for lattice polytopes without interior lattice points. The counterexample is based on a formula of the Ehrhart series of the join of two lattice polytope. We also present a formula for calculating the Ehrhart series of integral dilates of a polytope."},"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":"0710.2665","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.MG","submitted_at":"2007-10-14T14:14:41Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b9c521016fcf885a251da22ebcde595343311aa5f1b2cca37e78177b9c076a0c","abstract_canon_sha256":"5341a0b08e612c19eabc6c98e963c7ea34e69bfa7cd0d642623399632d790c21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:09:46.459562Z","signature_b64":"20baiPRDiuiYGZNl/d+B01ysObQXwDxduBB+z1g//ghBkuvlim4M09Ffe+sshT+xmBxdZ2F4PU1sV42nKHtFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eed6db9480a31cd4f0cc7a6b4cdb72c737d317f832fd3653405218f09bf0210f","last_reissued_at":"2026-07-04T15:09:46.459162Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:09:46.459162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower bounds on the coefficients of Ehrhart polynomials","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Makoto Tagami, Martin Henk","submitted_at":"2007-10-14T14:14:41Z","abstract_excerpt":"We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. Concerning the coefficients of the Ehrhart series of a lattice polytope we show that Hibi's lower bound is not true for lattice polytopes without interior lattice points. The counterexample is based on a formula of the Ehrhart series of the join of two lattice polytope. We also present a formula for calculating the Ehrhart series of integral dilates of a polytope."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2665","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/0710.2665/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":"0710.2665","created_at":"2026-07-04T15:09:46.459222+00:00"},{"alias_kind":"arxiv_version","alias_value":"0710.2665v2","created_at":"2026-07-04T15:09:46.459222+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.2665","created_at":"2026-07-04T15:09:46.459222+00:00"},{"alias_kind":"pith_short_12","alias_value":"53LNXFEAUMON","created_at":"2026-07-04T15:09:46.459222+00:00"},{"alias_kind":"pith_short_16","alias_value":"53LNXFEAUMONJ4GM","created_at":"2026-07-04T15:09:46.459222+00:00"},{"alias_kind":"pith_short_8","alias_value":"53LNXFEA","created_at":"2026-07-04T15:09:46.459222+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/53LNXFEAUMONJ4GMPJVUZW3SY4","json":"https://pith.science/pith/53LNXFEAUMONJ4GMPJVUZW3SY4.json","graph_json":"https://pith.science/api/pith-number/53LNXFEAUMONJ4GMPJVUZW3SY4/graph.json","events_json":"https://pith.science/api/pith-number/53LNXFEAUMONJ4GMPJVUZW3SY4/events.json","paper":"https://pith.science/paper/53LNXFEA"},"agent_actions":{"view_html":"https://pith.science/pith/53LNXFEAUMONJ4GMPJVUZW3SY4","download_json":"https://pith.science/pith/53LNXFEAUMONJ4GMPJVUZW3SY4.json","view_paper":"https://pith.science/paper/53LNXFEA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0710.2665&json=true","fetch_graph":"https://pith.science/api/pith-number/53LNXFEAUMONJ4GMPJVUZW3SY4/graph.json","fetch_events":"https://pith.science/api/pith-number/53LNXFEAUMONJ4GMPJVUZW3SY4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53LNXFEAUMONJ4GMPJVUZW3SY4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53LNXFEAUMONJ4GMPJVUZW3SY4/action/storage_attestation","attest_author":"https://pith.science/pith/53LNXFEAUMONJ4GMPJVUZW3SY4/action/author_attestation","sign_citation":"https://pith.science/pith/53LNXFEAUMONJ4GMPJVUZW3SY4/action/citation_signature","submit_replication":"https://pith.science/pith/53LNXFEAUMONJ4GMPJVUZW3SY4/action/replication_record"}},"created_at":"2026-07-04T15:09:46.459222+00:00","updated_at":"2026-07-04T15:09:46.459222+00:00"}