{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C3X3BGJDQCZUU76ZDQWE6G4CC2","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":"55aa48e7a9b4e4337bca28a915a6e91e5dd6d8d38c9d80f310a7295f7b8c0477","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-16T15:15:49Z","title_canon_sha256":"8de9203fbaeda9d174021cb4dcd7e3855e7e7c9ca524ac284df2f97e8eb88db9"},"schema_version":"1.0","source":{"id":"1503.04680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04680","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04680v1","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04680","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"pith_short_12","alias_value":"C3X3BGJDQCZU","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C3X3BGJDQCZUU76Z","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C3X3BGJD","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:aad2f5318574b7745a59827d76edd690c6d5f20a893b485aea09b72a39df8fc1","target":"graph","created_at":"2026-05-18T02:23:24Z","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 a seminal paper, De Loera et. al introduce the algorithm NulLA (Nullstellensatz Linear Algebra) and use it to measure the difficulty of determining if a graph is not 3-colorable. The crux of this relies on a correspondence between 3-colorings of a graph and solutions to a certain system of polynomial equations over a field $\\mathbb{k}$. In this article, we give a new direct combinatorial characterization of graphs that can be determined to be non-3-colorable in the first iteration of this algorithm when $\\mathbb{k}=GF(2)$. This greatly simplifies the work of De Loera et. al, as we express t","authors_text":"Benjamin Lowenstein, Bo Li, Mohamed Omar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-16T15:15:49Z","title":"Low Degree Nullstellensatz Certificates for 3-Colorability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04680","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:a989056bfc13ee97eafb584838e76b76241433f6baff88e0f5110e254b779cff","target":"record","created_at":"2026-05-18T02:23:24Z","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":"55aa48e7a9b4e4337bca28a915a6e91e5dd6d8d38c9d80f310a7295f7b8c0477","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-16T15:15:49Z","title_canon_sha256":"8de9203fbaeda9d174021cb4dcd7e3855e7e7c9ca524ac284df2f97e8eb88db9"},"schema_version":"1.0","source":{"id":"1503.04680","kind":"arxiv","version":1}},"canonical_sha256":"16efb0992380b34a7fd91c2c4f1b8216944494bbddf1ef3490d9b2ea543085fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16efb0992380b34a7fd91c2c4f1b8216944494bbddf1ef3490d9b2ea543085fd","first_computed_at":"2026-05-18T02:23:24.295088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:24.295088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0ubWVxw0SVPpj6deP/n2E1hnNldaDn/CEkk9e6q+MrXqd8LjaOqXuC8h6QinnHQlT5ZZiXhnAepGflXpea4sBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:24.295855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a989056bfc13ee97eafb584838e76b76241433f6baff88e0f5110e254b779cff","sha256:aad2f5318574b7745a59827d76edd690c6d5f20a893b485aea09b72a39df8fc1"],"state_sha256":"6ad808cfc2b2abb5ea81561f0f91d6d99da297805b011bee336da9d15e76711e"}