{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HMGHZVACFYFPSP2X4QYPBVYA22","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":"6048b203a06ef9dfee3b1bcdace288bfb86f90ebe3f8a018756b5949dac2024f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-27T12:23:04Z","title_canon_sha256":"defe5138a421b1265ba6bcbbef61fc40a25591722b9193d6f146cac63e901f22"},"schema_version":"1.0","source":{"id":"1309.7220","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7220","created_at":"2026-05-18T02:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7220v3","created_at":"2026-05-18T02:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7220","created_at":"2026-05-18T02:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"HMGHZVACFYFP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HMGHZVACFYFPSP2X","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HMGHZVAC","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:bd40e3d0c471384cad51295565fd2c1aa9ce1ee80532566c95c707db15d2e7c1","target":"graph","created_at":"2026-05-18T02:37:58Z","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 define a linear homogeneous equation to be strongly r-regular if, when a finite number of inequalities is added to the equation, the system of the equation and inequalities is still r-regular. In this paper, we show that, if a linear homogeneous equation is r-regular, then it is strongly r-regular. In 2009, Alexeev and Tsimerman introduced a family of equations, each of which is (n-1)-regular but not n-regular, verifying a conjecture of Rado from 1933. These equations are actually strongly (n-1)-regular as an immediate corollary of our results.","authors_text":"Kavish Gandhi, L\\'aszl\\'o Mikl\\'os Lov\\'asz (Massachusetts Institute of Technology), Noah Golowich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-27T12:23:04Z","title":"Degree of Regularity of Linear Homogeneous Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7220","kind":"arxiv","version":3},"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:f8fd29fa7a0f0e22f92fc2da0b533ffd98e752e66f46623a391f2357ee9561ff","target":"record","created_at":"2026-05-18T02:37:58Z","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":"6048b203a06ef9dfee3b1bcdace288bfb86f90ebe3f8a018756b5949dac2024f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-27T12:23:04Z","title_canon_sha256":"defe5138a421b1265ba6bcbbef61fc40a25591722b9193d6f146cac63e901f22"},"schema_version":"1.0","source":{"id":"1309.7220","kind":"arxiv","version":3}},"canonical_sha256":"3b0c7cd4022e0af93f57e430f0d700d693683e04eff003444df5bc9a4e81958f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b0c7cd4022e0af93f57e430f0d700d693683e04eff003444df5bc9a4e81958f","first_computed_at":"2026-05-18T02:37:58.901404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:58.901404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fcIT6uQqppE64kyNDft8euU/VDFKQE7DXyYFd3wnPNNUDcty3+OskHzjMx1jnKkwYqUeVvYQ2TRG3Ips/o0KAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:58.901792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7220","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8fd29fa7a0f0e22f92fc2da0b533ffd98e752e66f46623a391f2357ee9561ff","sha256:bd40e3d0c471384cad51295565fd2c1aa9ce1ee80532566c95c707db15d2e7c1"],"state_sha256":"8922cbe245e6ea5b203d46d7b6f288d127db56a9da485579ba154549aa432260"}