{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:KY7YA232DVOQCXMBYKJBVSMZHA","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":"383ed7b349dcca361c75e5880736f1e72204aae99f43e2f3d955a5328ddc8357","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-17T17:08:40Z","title_canon_sha256":"2020d86d2c18bac0c3c327b8b3f0ba7cef2bc9c5c8c14ed7c579c27fe01d607a"},"schema_version":"1.0","source":{"id":"2003.07817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.07817","created_at":"2026-07-05T00:48:30Z"},{"alias_kind":"arxiv_version","alias_value":"2003.07817v1","created_at":"2026-07-05T00:48:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.07817","created_at":"2026-07-05T00:48:30Z"},{"alias_kind":"pith_short_12","alias_value":"KY7YA232DVOQ","created_at":"2026-07-05T00:48:30Z"},{"alias_kind":"pith_short_16","alias_value":"KY7YA232DVOQCXMB","created_at":"2026-07-05T00:48:30Z"},{"alias_kind":"pith_short_8","alias_value":"KY7YA232","created_at":"2026-07-05T00:48:30Z"}],"graph_snapshots":[{"event_id":"sha256:ac58676e8ad055d4d51989ec2f195af741e2c8feeaf7348c64608b7d6a742ec1","target":"graph","created_at":"2026-07-05T00:48:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2003.07817/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a set $X$ of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with $X$ is called the relaxation complexity $\\mathrm{rc}(X)$. This parameter was introduced by Kaibel & Weltge (2015) and captures the complexity of linear descriptions of $X$ without using auxiliary variables.\n  Using tools from combinatorics, geometry of numbers, and quantifier elimination, we make progress on several open questions regarding $\\mathrm{rc}(X)$ and its variant $\\mathrm{rc}_{\\mathbb{Q}}(X)$, restricting the descriptions of $X$ to rational polyh","authors_text":"Gennadiy Averkov, Matthias Schymura","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-17T17:08:40Z","title":"Complexity of linear relaxations in integer programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.07817","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":"sha256:5cab4e046b81461c6168187287e422eddf372a407e317517b24561ca9b46c3e5","target":"record","created_at":"2026-07-05T00:48:30Z","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":"383ed7b349dcca361c75e5880736f1e72204aae99f43e2f3d955a5328ddc8357","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-17T17:08:40Z","title_canon_sha256":"2020d86d2c18bac0c3c327b8b3f0ba7cef2bc9c5c8c14ed7c579c27fe01d607a"},"schema_version":"1.0","source":{"id":"2003.07817","kind":"arxiv","version":1}},"canonical_sha256":"563f806b7a1d5d015d81c2921ac999381ee63d442ab1975b986c584476041653","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"563f806b7a1d5d015d81c2921ac999381ee63d442ab1975b986c584476041653","first_computed_at":"2026-07-05T00:48:30.521238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:48:30.521238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t7wqvkAv12/L0zF0kuFxdyDKrCU+j1p33Zs2w3SKUSHmGuwYBzOyKH4YZlJvFvFmqoA7/I465IL0OpvefzCoDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:48:30.521706Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.07817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cab4e046b81461c6168187287e422eddf372a407e317517b24561ca9b46c3e5","sha256:ac58676e8ad055d4d51989ec2f195af741e2c8feeaf7348c64608b7d6a742ec1"],"state_sha256":"f5a131c63d09c05ad80c4375606a166ad97d21463d4812d5cde577ffcdbc1085"}