{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D6DWZPO4IY2TLNOKFQHUE6NOQF","short_pith_number":"pith:D6DWZPO4","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"},"canonical_sha256":"1f876cbddc463535b5ca2c0f4279ae816c5acac45d194a2a295faebbbedc314c","source":{"kind":"arxiv","id":"1006.5612","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5612","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5612v2","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5612","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"pith_short_12","alias_value":"D6DWZPO4IY2T","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D6DWZPO4IY2TLNOK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D6DWZPO4","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D6DWZPO4IY2TLNOKFQHUE6NOQF","target":"record","payload":{"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"},"canonical_sha256":"1f876cbddc463535b5ca2c0f4279ae816c5acac45d194a2a295faebbbedc314c","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"},"source_kind":"arxiv","source_id":"1006.5612","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:27:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"otf4z2zKKS0FZZPC2eK+O8a7ucA7fpcOYKtyJvF5unmMJbt9BI/zYYRaemnRIdklCbCgLxVAy4QISpsNNnMOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:18:09.673507Z"},"content_sha256":"96fcef7a9b730ee3346e297a0ff2f74bb1b73d83a512c7a42d6f65c596537ad1","schema_version":"1.0","event_id":"sha256:96fcef7a9b730ee3346e297a0ff2f74bb1b73d83a512c7a42d6f65c596537ad1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D6DWZPO4IY2TLNOKFQHUE6NOQF","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:27:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wp3Eh3VDRqT/lpVR6GOaNx9WAb7s4XiyiNdofhEfkUf/oOtUTvyjazzM6vnbo2V2eRADaTyVML9Z29r4B0rBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:18:09.674166Z"},"content_sha256":"2432b87625001611d88b8ef480c9d5cfc95e8d23ff65fe8bad52a238f3b1561c","schema_version":"1.0","event_id":"sha256:2432b87625001611d88b8ef480c9d5cfc95e8d23ff65fe8bad52a238f3b1561c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/bundle.json","state_url":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T14:18:09Z","links":{"resolver":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF","bundle":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/bundle.json","state":"https://pith.science/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6DWZPO4IY2TLNOKFQHUE6NOQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D6DWZPO4IY2TLNOKFQHUE6NOQF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7fc4f172509657032bc55a360098aa56a646dfcf0dedfa5eb08c91a4f1f9a918","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-06-29T13:38:15Z","title_canon_sha256":"bf098855623097af4e690811caa54b0e5b0398ccfea401d6146b8835eb689fae"},"schema_version":"1.0","source":{"id":"1006.5612","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5612","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5612v2","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5612","created_at":"2026-05-18T04:27:28Z"},{"alias_kind":"pith_short_12","alias_value":"D6DWZPO4IY2T","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D6DWZPO4IY2TLNOK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D6DWZPO4","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:2432b87625001611d88b8ef480c9d5cfc95e8d23ff65fe8bad52a238f3b1561c","target":"graph","created_at":"2026-05-18T04:27:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Eva Linke","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-06-29T13:38:15Z","title":"Rational Ehrhart quasi-polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5612","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:96fcef7a9b730ee3346e297a0ff2f74bb1b73d83a512c7a42d6f65c596537ad1","target":"record","created_at":"2026-05-18T04:27:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7fc4f172509657032bc55a360098aa56a646dfcf0dedfa5eb08c91a4f1f9a918","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-06-29T13:38:15Z","title_canon_sha256":"bf098855623097af4e690811caa54b0e5b0398ccfea401d6146b8835eb689fae"},"schema_version":"1.0","source":{"id":"1006.5612","kind":"arxiv","version":2}},"canonical_sha256":"1f876cbddc463535b5ca2c0f4279ae816c5acac45d194a2a295faebbbedc314c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f876cbddc463535b5ca2c0f4279ae816c5acac45d194a2a295faebbbedc314c","first_computed_at":"2026-05-18T04:27:28.085942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:28.085942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W55rLWCxbvG8lFok/NB/DT46+5RHEHzrnvR/qJP84CvvrqloLS6kOVZLcEgOZItWMDJuQkd+vG/RB4lhNv7TBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:28.086375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5612","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96fcef7a9b730ee3346e297a0ff2f74bb1b73d83a512c7a42d6f65c596537ad1","sha256:2432b87625001611d88b8ef480c9d5cfc95e8d23ff65fe8bad52a238f3b1561c"],"state_sha256":"3b0ddf0ca04180ba71b0b5be1dc797ac5aa5881c36f852958e11868e97ad1706"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8kqXTzKp6YfcA9XWg6+ZcmZ9KF3wg7sIjeDZFNBrBwEdcUebIKhjZrpOGU8ipTTXjZQ/9/9GZfBmXTRki8iaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T14:18:09.677644Z","bundle_sha256":"22c1b5c2fdd511e33bac2659eb02fc9899eb40b2b91ebb342f9a109f2a6341ba"}}