{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:D6DWZPO4IY2TLNOKFQHUE6NOQF","short_pith_number":"pith:D6DWZPO4","schema_version":"1.0","canonical_sha256":"1f876cbddc463535b5ca2c0f4279ae816c5acac45d194a2a295faebbbedc314c","source":{"kind":"arxiv","id":"1006.5612","version":2},"attestation_state":"computed","paper":{"title":"Rational Ehrhart quasi-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Eva Linke","submitted_at":"2010-06-29T13:38:15Z","abstract_excerpt":"Ehrhart's famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors and it turns out that the number of integral points can still be written as a rational quasi-polynomial. Furthermore the coefficients of this rational quasi-polynomial are piecewise polynomial functions and related to each other by derivation."},"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":"1006.5612","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-06-29T13:38:15Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"bf098855623097af4e690811caa54b0e5b0398ccfea401d6146b8835eb689fae","abstract_canon_sha256":"7fc4f172509657032bc55a360098aa56a646dfcf0dedfa5eb08c91a4f1f9a918"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:28.086375Z","signature_b64":"W55rLWCxbvG8lFok/NB/DT46+5RHEHzrnvR/qJP84CvvrqloLS6kOVZLcEgOZItWMDJuQkd+vG/RB4lhNv7TBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f876cbddc463535b5ca2c0f4279ae816c5acac45d194a2a295faebbbedc314c","last_reissued_at":"2026-05-18T04:27:28.085942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:28.085942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational Ehrhart quasi-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Eva Linke","submitted_at":"2010-06-29T13:38:15Z","abstract_excerpt":"Ehrhart's famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors and it turns out that the number of integral points can still be written as a rational quasi-polynomial. Furthermore the coefficients of this rational quasi-polynomial are piecewise polynomial functions and related to each other by derivation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5612","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":"1006.5612","created_at":"2026-05-18T04:27:28.086000+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.5612v2","created_at":"2026-05-18T04:27:28.086000+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5612","created_at":"2026-05-18T04:27:28.086000+00:00"},{"alias_kind":"pith_short_12","alias_value":"D6DWZPO4IY2T","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"D6DWZPO4IY2TLNOK","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"D6DWZPO4","created_at":"2026-05-18T12:26:06.534383+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/D6DWZPO4IY2TLNOKFQHUE6NOQF","json":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF.json","graph_json":"https://pith.science/api/pith-number/D6DWZPO4IY2TLNOKFQHUE6NOQF/graph.json","events_json":"https://pith.science/api/pith-number/D6DWZPO4IY2TLNOKFQHUE6NOQF/events.json","paper":"https://pith.science/paper/D6DWZPO4"},"agent_actions":{"view_html":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF","download_json":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF.json","view_paper":"https://pith.science/paper/D6DWZPO4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.5612&json=true","fetch_graph":"https://pith.science/api/pith-number/D6DWZPO4IY2TLNOKFQHUE6NOQF/graph.json","fetch_events":"https://pith.science/api/pith-number/D6DWZPO4IY2TLNOKFQHUE6NOQF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/action/storage_attestation","attest_author":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/action/author_attestation","sign_citation":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/action/citation_signature","submit_replication":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/action/replication_record"}},"created_at":"2026-05-18T04:27:28.086000+00:00","updated_at":"2026-05-18T04:27:28.086000+00:00"}