{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5ZBV2YQOARXVZ277HFHDTKSK2X","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":"cdabcfb0fcde64ba72fc05420d6bd81c2d8b11a8b95daca3aca351870a60f849","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-04T10:13:48Z","title_canon_sha256":"6a0073db1c86a66082a8807a9f564ae1e645d624e7af9646724e578097212ef0"},"schema_version":"1.0","source":{"id":"1903.01157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01157","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01157v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01157","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"5ZBV2YQOARXV","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5ZBV2YQOARXVZ277","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5ZBV2YQO","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:593b4e64e0314651682caa72f02758cedc5e964bcf0e1415dd173dc6e2cbafe0","target":"graph","created_at":"2026-05-17T23:52:12Z","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":"We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\\c{s}ung\\\"oz. We also present some related polynomial and $q$-series identities.","authors_text":"Ali K. Uncu","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-04T10:13:48Z","title":"A Polynomial Identity Implying Schur's Partition Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01157","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":"sha256:0c77de2fc5b861457f895384f776119e486e6e99c85f5350b522f037b312d9df","target":"record","created_at":"2026-05-17T23:52:12Z","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":"cdabcfb0fcde64ba72fc05420d6bd81c2d8b11a8b95daca3aca351870a60f849","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-04T10:13:48Z","title_canon_sha256":"6a0073db1c86a66082a8807a9f564ae1e645d624e7af9646724e578097212ef0"},"schema_version":"1.0","source":{"id":"1903.01157","kind":"arxiv","version":1}},"canonical_sha256":"ee435d620e046f5cebff394e39aa4ad5dd6092a585c4f94af5d9b9553f844435","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee435d620e046f5cebff394e39aa4ad5dd6092a585c4f94af5d9b9553f844435","first_computed_at":"2026-05-17T23:52:12.117169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:12.117169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qnlVbs6N79Qm0Zm0+GqIcnhyxZLgb1SiiwbgLYwMRi2Fg98koSJZ8JY9w/Wx5hoM31Jm8Gn0kBmZUGIeGpceAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:12.117837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c77de2fc5b861457f895384f776119e486e6e99c85f5350b522f037b312d9df","sha256:593b4e64e0314651682caa72f02758cedc5e964bcf0e1415dd173dc6e2cbafe0"],"state_sha256":"c2eef198fae719d7075bd21e915b1c4e7e0b6203723d4630c849be358eb44296"}