{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6CQN4G6NUK4S6CE2TCKEWUDY3W","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":"b1ba3ad88e2140315effc5831ce93017bf44429fc2419ca96aa2f17beaa06ecf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-11T22:12:24Z","title_canon_sha256":"d64744b5dd55c94f7783efa1f95dfd155aa5c55d67eca35c27fa6021ac7239fa"},"schema_version":"1.0","source":{"id":"1509.03680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03680","created_at":"2026-05-18T01:33:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03680v1","created_at":"2026-05-18T01:33:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03680","created_at":"2026-05-18T01:33:14Z"},{"alias_kind":"pith_short_12","alias_value":"6CQN4G6NUK4S","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6CQN4G6NUK4S6CE2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6CQN4G6N","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:9bfb9299006929c848a973866d97cf4ce72800fa2f9f3b53e81731cc01dec6a3","target":"graph","created_at":"2026-05-18T01:33:14Z","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":"In 1976, P. R. Scott characterized the Ehrhart polynomials of convex integral polygons. We study the same question for Ehrhart polynomials and quasi-polynomials of *non*-integral convex polygons. Turning to the case in which the Ehrhart quasi-polynomial has nontrivial quasi-period, we determine the possible minimal periods of the coefficient functions of the Ehrhart quasi-polynomial of a rational polygon.","authors_text":"Matthew Moriarity, Tyrrell B. McAllister","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-11T22:12:24Z","title":"Ehrhart quasi-period collapse in rational polygons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03680","kind":"arxiv","version":1},"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":"sha256:9e948c681733269967bdf34347387f8f2a2ba1be499910eebcf5b12afec39567","target":"record","created_at":"2026-05-18T01:33:14Z","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":"b1ba3ad88e2140315effc5831ce93017bf44429fc2419ca96aa2f17beaa06ecf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-11T22:12:24Z","title_canon_sha256":"d64744b5dd55c94f7783efa1f95dfd155aa5c55d67eca35c27fa6021ac7239fa"},"schema_version":"1.0","source":{"id":"1509.03680","kind":"arxiv","version":1}},"canonical_sha256":"f0a0de1bcda2b92f089a98944b5078dd916f3abaf3902a1e5c4b3f345dabe9fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0a0de1bcda2b92f089a98944b5078dd916f3abaf3902a1e5c4b3f345dabe9fc","first_computed_at":"2026-05-18T01:33:14.843646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:14.843646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9R/oqpiguOxgh57h78L2iaFYnJvwp+UCrn8IfQ8dPDlR52kyZeZGMzO+Ws6Mc31fXoimcZ7Ffj5RfsfEtNxVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:14.844289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e948c681733269967bdf34347387f8f2a2ba1be499910eebcf5b12afec39567","sha256:9bfb9299006929c848a973866d97cf4ce72800fa2f9f3b53e81731cc01dec6a3"],"state_sha256":"2fa16c8df49347e7690c8ad45e2e45b0032cd9fea239924bfa4bc67aa2cce8c9"}