{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:X34ISISXYBPQHEROOWMXNCRSU2","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":"4eb9aea1843dc52c82236a72d90fb1eb52ceee57d6d775cd418fd70b16ea6bb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-18T06:13:13Z","title_canon_sha256":"06bd40e8465eb3d778c7d7ffbec04e1179b18e9cf585e4d260f2ab3e4b6e49c8"},"schema_version":"1.0","source":{"id":"1907.07886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07886","created_at":"2026-05-17T23:40:15Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07886v1","created_at":"2026-05-17T23:40:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07886","created_at":"2026-05-17T23:40:15Z"},{"alias_kind":"pith_short_12","alias_value":"X34ISISXYBPQ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"X34ISISXYBPQHERO","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"X34ISISX","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:f5c29e18a5fc70d9e033c745ac3294530d3fc085efff0b2e79a3b621f3b82886","target":"graph","created_at":"2026-05-17T23:40:15Z","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 examine how sparse feasible solutions of integer programs are, on average. Average case here means that we fix the constraint matrix and vary the right-hand side vectors. For a problem in standard form with m equations, there exist LP feasible solutions with at most m many nonzero entries. We show that under relatively mild assumptions, integer programs in standard form have feasible solutions with O(m) many nonzero entries, on average. Our proof uses ideas from the theory of groups, lattices, and Ehrhart polynomials. From our main theorem we obtain the best known upper bounds on the intege","authors_text":"Joseph Paat, Robert Weismantel, Timm Oertel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-18T06:13:13Z","title":"Sparsity of integer solutions in the average case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07886","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":"sha256:103bf821a89b10a09bceb8440616b832f1317da911b317077463fb62a492f028","target":"record","created_at":"2026-05-17T23:40:15Z","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":"4eb9aea1843dc52c82236a72d90fb1eb52ceee57d6d775cd418fd70b16ea6bb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-18T06:13:13Z","title_canon_sha256":"06bd40e8465eb3d778c7d7ffbec04e1179b18e9cf585e4d260f2ab3e4b6e49c8"},"schema_version":"1.0","source":{"id":"1907.07886","kind":"arxiv","version":1}},"canonical_sha256":"bef8892257c05f03922e7599768a32a6adb0a26974fdb509234c11daaee17081","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bef8892257c05f03922e7599768a32a6adb0a26974fdb509234c11daaee17081","first_computed_at":"2026-05-17T23:40:15.818942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:15.818942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n7jRBmtByz9bBXEqceqrtiqosucQANw27pxoTXztyhPNi6J4+xzjTRCi8YhMEyShcTLnpYMBPtjYWRuEXJq3Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:15.819718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:103bf821a89b10a09bceb8440616b832f1317da911b317077463fb62a492f028","sha256:f5c29e18a5fc70d9e033c745ac3294530d3fc085efff0b2e79a3b621f3b82886"],"state_sha256":"09095a0bbcf3b8eadd1719c195560fd5edf9a93dac1fff7df73904261357c954"}