{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:57WDQS4B4RPL337PRZAM7F4Z3Q","short_pith_number":"pith:57WDQS4B","canonical_record":{"source":{"id":"1712.02176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-12-06T13:15:32Z","cross_cats_sorted":["cs.DS","math.OC"],"title_canon_sha256":"1dfa003980b3f2585d9b74fbf0160d3cd7b5dcae9b94adc3a17e9121de95d486","abstract_canon_sha256":"8976c25b4b8dc1bd0f9c0613953602a0d0498e226a311bf7130b0a6c76229d62"},"schema_version":"1.0"},"canonical_sha256":"efec384b81e45ebdefef8e40cf9799dc02bcab0fe9c3927c7225eb2f0017e289","source":{"kind":"arxiv","id":"1712.02176","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02176","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02176v1","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02176","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"57WDQS4B4RPL","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"57WDQS4B4RPL337P","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"57WDQS4B","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:57WDQS4B4RPL337PRZAM7F4Z3Q","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-12-06T13:15:32Z","cross_cats_sorted":["cs.DS","math.OC"],"title_canon_sha256":"1dfa003980b3f2585d9b74fbf0160d3cd7b5dcae9b94adc3a17e9121de95d486","abstract_canon_sha256":"8976c25b4b8dc1bd0f9c0613953602a0d0498e226a311bf7130b0a6c76229d62"},"schema_version":"1.0"},"canonical_sha256":"efec384b81e45ebdefef8e40cf9799dc02bcab0fe9c3927c7225eb2f0017e289","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:38.939111Z","signature_b64":"6R2XvHenJWhx63ckcAb/CGAjSnhiDUtnl+ZVg5pi543ln6bZuY0vXUG+Fa6n49JdF2b4JWUlxrnhYWMGHDVuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efec384b81e45ebdefef8e40cf9799dc02bcab0fe9c3927c7225eb2f0017e289","last_reissued_at":"2026-05-18T00:28:38.938487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:38.938487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02176","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":"2026-05-18T00:28:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVkcEel5jQPxPLuMhDJtWDEWPjkUhD87hwbMxEshvY2ELwAWA1nRQtdX9IB7GTMAwGksLSUIho6vbJX+RuhKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:31:31.399615Z"},"content_sha256":"0ba33e6ee26fd0556cf96fb29cfc5929fa0f776d0dc404108496902ae371223b","schema_version":"1.0","event_id":"sha256:0ba33e6ee26fd0556cf96fb29cfc5929fa0f776d0dc404108496902ae371223b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:57WDQS4B4RPL337PRZAM7F4Z3Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lifting Linear Extension Complexity Bounds to the Mixed-Integer Setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"cs.DM","authors_text":"Alfonso Cevallos, Rico Zenklusen, Stefan Weltge","submitted_at":"2017-12-06T13:15:32Z","abstract_excerpt":"Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer programs. In particular, prior to this work, it was open whether some classical problems, like the minimum odd-cut problem, can be expressed by a compact mixed-integer program with few (even constantly many) integer variables. This is in stark contrast to linear formulations, where recent breakthroughs in the field of extended formulations have shown that man"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02176","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":""},"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":"2026-05-18T00:28:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y6QEnbeBin0Vhrr0syxCBSc/aCXTlOVM3TpvGGQD0jA/FvQcxNkqvCeaABNsiLQjkmkcWcZM+q5tctfb9WL4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:31:31.400025Z"},"content_sha256":"c98bbf0139f67aee912a72ca64fc98f35ce6dfadf0694f4a847ff780816f1845","schema_version":"1.0","event_id":"sha256:c98bbf0139f67aee912a72ca64fc98f35ce6dfadf0694f4a847ff780816f1845"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57WDQS4B4RPL337PRZAM7F4Z3Q/bundle.json","state_url":"https://pith.science/pith/57WDQS4B4RPL337PRZAM7F4Z3Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57WDQS4B4RPL337PRZAM7F4Z3Q/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":"2026-05-26T12:31:31Z","links":{"resolver":"https://pith.science/pith/57WDQS4B4RPL337PRZAM7F4Z3Q","bundle":"https://pith.science/pith/57WDQS4B4RPL337PRZAM7F4Z3Q/bundle.json","state":"https://pith.science/pith/57WDQS4B4RPL337PRZAM7F4Z3Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57WDQS4B4RPL337PRZAM7F4Z3Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:57WDQS4B4RPL337PRZAM7F4Z3Q","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":"8976c25b4b8dc1bd0f9c0613953602a0d0498e226a311bf7130b0a6c76229d62","cross_cats_sorted":["cs.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-12-06T13:15:32Z","title_canon_sha256":"1dfa003980b3f2585d9b74fbf0160d3cd7b5dcae9b94adc3a17e9121de95d486"},"schema_version":"1.0","source":{"id":"1712.02176","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02176","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02176v1","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02176","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"57WDQS4B4RPL","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"57WDQS4B4RPL337P","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"57WDQS4B","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:c98bbf0139f67aee912a72ca64fc98f35ce6dfadf0694f4a847ff780816f1845","target":"graph","created_at":"2026-05-18T00:28:38Z","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":"Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer programs. In particular, prior to this work, it was open whether some classical problems, like the minimum odd-cut problem, can be expressed by a compact mixed-integer program with few (even constantly many) integer variables. This is in stark contrast to linear formulations, where recent breakthroughs in the field of extended formulations have shown that man","authors_text":"Alfonso Cevallos, Rico Zenklusen, Stefan Weltge","cross_cats":["cs.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-12-06T13:15:32Z","title":"Lifting Linear Extension Complexity Bounds to the Mixed-Integer Setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02176","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":"sha256:0ba33e6ee26fd0556cf96fb29cfc5929fa0f776d0dc404108496902ae371223b","target":"record","created_at":"2026-05-18T00:28:38Z","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":"8976c25b4b8dc1bd0f9c0613953602a0d0498e226a311bf7130b0a6c76229d62","cross_cats_sorted":["cs.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-12-06T13:15:32Z","title_canon_sha256":"1dfa003980b3f2585d9b74fbf0160d3cd7b5dcae9b94adc3a17e9121de95d486"},"schema_version":"1.0","source":{"id":"1712.02176","kind":"arxiv","version":1}},"canonical_sha256":"efec384b81e45ebdefef8e40cf9799dc02bcab0fe9c3927c7225eb2f0017e289","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efec384b81e45ebdefef8e40cf9799dc02bcab0fe9c3927c7225eb2f0017e289","first_computed_at":"2026-05-18T00:28:38.938487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:38.938487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6R2XvHenJWhx63ckcAb/CGAjSnhiDUtnl+ZVg5pi543ln6bZuY0vXUG+Fa6n49JdF2b4JWUlxrnhYWMGHDVuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:38.939111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02176","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ba33e6ee26fd0556cf96fb29cfc5929fa0f776d0dc404108496902ae371223b","sha256:c98bbf0139f67aee912a72ca64fc98f35ce6dfadf0694f4a847ff780816f1845"],"state_sha256":"1b209c409ae4396c45eea6b833acd084e354a57e2fc33c17380dc2e3eb736d27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3An4QVr7sr4VANc07PUoKbzmnXvj56UjEFdpMgC+5kP9XrkyPMbdbPBRW4zE1n1vmXLQjbgpnJ6Y3u6d8e+WCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:31:31.402423Z","bundle_sha256":"6a6a088152b71c58ee9d2b37a6000ca64d7a98e7b72a1c3b6f7f76627a3bd268"}}