{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:KY7YA232DVOQCXMBYKJBVSMZHA","short_pith_number":"pith:KY7YA232","canonical_record":{"source":{"id":"2003.07817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-17T17:08:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"2020d86d2c18bac0c3c327b8b3f0ba7cef2bc9c5c8c14ed7c579c27fe01d607a","abstract_canon_sha256":"383ed7b349dcca361c75e5880736f1e72204aae99f43e2f3d955a5328ddc8357"},"schema_version":"1.0"},"canonical_sha256":"563f806b7a1d5d015d81c2921ac999381ee63d442ab1975b986c584476041653","source":{"kind":"arxiv","id":"2003.07817","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:KY7YA232DVOQCXMBYKJBVSMZHA","target":"record","payload":{"canonical_record":{"source":{"id":"2003.07817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-17T17:08:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"2020d86d2c18bac0c3c327b8b3f0ba7cef2bc9c5c8c14ed7c579c27fe01d607a","abstract_canon_sha256":"383ed7b349dcca361c75e5880736f1e72204aae99f43e2f3d955a5328ddc8357"},"schema_version":"1.0"},"canonical_sha256":"563f806b7a1d5d015d81c2921ac999381ee63d442ab1975b986c584476041653","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:30.521706Z","signature_b64":"t7wqvkAv12/L0zF0kuFxdyDKrCU+j1p33Zs2w3SKUSHmGuwYBzOyKH4YZlJvFvFmqoA7/I465IL0OpvefzCoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"563f806b7a1d5d015d81c2921ac999381ee63d442ab1975b986c584476041653","last_reissued_at":"2026-07-05T00:48:30.521238Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:30.521238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2003.07817","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:48:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ltpIsFbypoFJfPNbLstDVPrO4KOvjiDyn2wC6Cd0iMXwqMsidAsAnuZ4rwniOKXIZF+kv0ipkVfMtVKt+ezWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T22:42:17.106423Z"},"content_sha256":"5cab4e046b81461c6168187287e422eddf372a407e317517b24561ca9b46c3e5","schema_version":"1.0","event_id":"sha256:5cab4e046b81461c6168187287e422eddf372a407e317517b24561ca9b46c3e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:KY7YA232DVOQCXMBYKJBVSMZHA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity of linear relaxations in integer programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Gennadiy Averkov, Matthias Schymura","submitted_at":"2020-03-17T17:08:40Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.07817","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.07817/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:48:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fhEVEx5SmWo5suiuJPHrmkMsudN40HjrwF4TOQhm8MhX8rSH04HAW9C2cgq/TRRtMHcMt9HmWS7qRsVfrviHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T22:42:17.106942Z"},"content_sha256":"ac58676e8ad055d4d51989ec2f195af741e2c8feeaf7348c64608b7d6a742ec1","schema_version":"1.0","event_id":"sha256:ac58676e8ad055d4d51989ec2f195af741e2c8feeaf7348c64608b7d6a742ec1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KY7YA232DVOQCXMBYKJBVSMZHA/bundle.json","state_url":"https://pith.science/pith/KY7YA232DVOQCXMBYKJBVSMZHA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KY7YA232DVOQCXMBYKJBVSMZHA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-22T22:42:17Z","links":{"resolver":"https://pith.science/pith/KY7YA232DVOQCXMBYKJBVSMZHA","bundle":"https://pith.science/pith/KY7YA232DVOQCXMBYKJBVSMZHA/bundle.json","state":"https://pith.science/pith/KY7YA232DVOQCXMBYKJBVSMZHA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KY7YA232DVOQCXMBYKJBVSMZHA/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n5HrN6woVzVuH7KfyI22Nd4vNoB3XDgNbVZhfQ6M8n1eO982U23I86jQ08FYDHkDsiP3m6q69J+kLwcKmLMAAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T22:42:17.110811Z","bundle_sha256":"db6ad9a29ce04f4393d7f551e0b9f75ca52a04051a765e51f5b47cfb7bd0e110"}}