{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S6L4BVAG34QUFVJIJ722SLTH2V","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":"ed8a01e44e09cef188e54c8abb7be2720b5bd1d5db92b23d3b00457560bc422d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-05T01:56:35Z","title_canon_sha256":"3daf9b493cb26ece9706da506e850d301af70cc10f9cefcd3a1d02509d286beb"},"schema_version":"1.0","source":{"id":"1302.0917","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0917","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0917v1","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0917","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"S6L4BVAG34QU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S6L4BVAG34QUFVJI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S6L4BVAG","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:df266eb16dbe536b1431564d51b6642187ae26ad56eda84116d0c2fb60817245","target":"graph","created_at":"2026-05-18T03:34:26Z","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":"Given collections A and B of residue classes modulo m and n, respectively, we investigate conditions on A and B that ensure that, for at least some a in A and b in B, the linear system x = a mod m, x = b mod n has an integer solution, and we quantify the number of such admissible pairs (a,b). The special case where A and B consist of intervals of residue classes has application to the Lonely Runner Conjecture.","authors_text":"Jason Gibson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-05T01:56:35Z","title":"A density Chinese Remainder Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0917","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":"sha256:58f28cdc36cdd7cf7349b6f85608e7d4df624a93366ca4e8d4ed5f0f5ffad46c","target":"record","created_at":"2026-05-18T03:34:26Z","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":"ed8a01e44e09cef188e54c8abb7be2720b5bd1d5db92b23d3b00457560bc422d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-05T01:56:35Z","title_canon_sha256":"3daf9b493cb26ece9706da506e850d301af70cc10f9cefcd3a1d02509d286beb"},"schema_version":"1.0","source":{"id":"1302.0917","kind":"arxiv","version":1}},"canonical_sha256":"9797c0d406df2142d5284ff5a92e67d5525c93df0de0fefee8723dc13eb42d91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9797c0d406df2142d5284ff5a92e67d5525c93df0de0fefee8723dc13eb42d91","first_computed_at":"2026-05-18T03:34:26.811339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:26.811339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NGQeJBWdzGm+MkolShw5yeSNd1EHRQQrPeb0YC7r1Alhhw0zjcPg1rGvWhpYCqIffqegaDL3g1JsT/aZQEr+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:26.811895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0917","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58f28cdc36cdd7cf7349b6f85608e7d4df624a93366ca4e8d4ed5f0f5ffad46c","sha256:df266eb16dbe536b1431564d51b6642187ae26ad56eda84116d0c2fb60817245"],"state_sha256":"9410071004d3d8ad60b58732307cf64d7a0ccbd3b8eea1dd9e67c48b27dd3d83"}