{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A5FHTJDWCEW2YQZ24MOUO7F2RT","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":"5258a17be96748a887c9cedc0bd63b9cf7f250eb6eb508b15cd74c97b49471a7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-05-11T00:09:11Z","title_canon_sha256":"3338a74b3d9dcfee9cc1824d331f8da900dc792607defe4550fdd9871c8bab13"},"schema_version":"1.0","source":{"id":"1405.2480","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2480","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2480v3","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2480","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"A5FHTJDWCEW2","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A5FHTJDWCEW2YQZ2","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A5FHTJDW","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:a8730c33617c173517c5276d953f818f79396ee6bf57f4f3a5cff819cd257578","target":"graph","created_at":"2026-05-18T01:33:57Z","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":"The famous Doignon-Bell-Scarf Theorem is a Helly-type result about the existence of integer solutions on systems of linear inequalities. The purpose of this paper is to present the following quantitative generalization: Given an integer $k$, we prove that there exists a constant $c(n,k)$, depending only on the dimension $n$ and $k$, such that if a polyhedron ${x: Ax \\leq b}$ contains exactly k integer solutions, then there exists a subset of the rows, of cardinality no more than $c(n,k)$, defining a polyhedron that contains exactly the same $k$ integer points. In this case $c(n,0) = 2^n$ is th","authors_text":"Iskander Aliev, Jesus A. De Loera, Quentin Louveaux, Robert Bassett","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-05-11T00:09:11Z","title":"A Quantitative Doignon-Bell-Scarf Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2480","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":"sha256:26a342bdce3904a14bbf87345d55b39edb2040fc09345b7a8db8cc7ea164e435","target":"record","created_at":"2026-05-18T01:33:57Z","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":"5258a17be96748a887c9cedc0bd63b9cf7f250eb6eb508b15cd74c97b49471a7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-05-11T00:09:11Z","title_canon_sha256":"3338a74b3d9dcfee9cc1824d331f8da900dc792607defe4550fdd9871c8bab13"},"schema_version":"1.0","source":{"id":"1405.2480","kind":"arxiv","version":3}},"canonical_sha256":"074a79a476112dac433ae31d477cba8cd050255f3d6a59b51c206aac49b1a694","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"074a79a476112dac433ae31d477cba8cd050255f3d6a59b51c206aac49b1a694","first_computed_at":"2026-05-18T01:33:57.069663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:57.069663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QqHk6LFGPBShOrhczT/gaqoEBDkOOro6QK1Tp5f31Ouklwp4piL9tIVbC2TNltmPoxHsH+GkyXSE3ONo4guqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:57.070035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2480","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26a342bdce3904a14bbf87345d55b39edb2040fc09345b7a8db8cc7ea164e435","sha256:a8730c33617c173517c5276d953f818f79396ee6bf57f4f3a5cff819cd257578"],"state_sha256":"ffc738882af0d3236f5dc6d324bfdbdd6a8ce1ea7fb021c5bfaa6b2aa19068be"}