{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JXW5M7WAQZJFKUM563EZGR2TB7","short_pith_number":"pith:JXW5M7WA","canonical_record":{"source":{"id":"1709.10132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T19:09:57Z","cross_cats_sorted":[],"title_canon_sha256":"eacb4caf49a33ebf18a48d8520c53a8c80120f01d7ffc998f08e030303f0e4bf","abstract_canon_sha256":"6348dc24af930626ba67e6cb85a57fe8ac2d75c666c00730aad868fa5b4333bf"},"schema_version":"1.0"},"canonical_sha256":"4dedd67ec0865255519df6c99347530ff5b73d08cfed609cb6cd164799e05213","source":{"kind":"arxiv","id":"1709.10132","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10132","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10132v2","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10132","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"JXW5M7WAQZJF","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JXW5M7WAQZJFKUM5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JXW5M7WA","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JXW5M7WAQZJFKUM563EZGR2TB7","target":"record","payload":{"canonical_record":{"source":{"id":"1709.10132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T19:09:57Z","cross_cats_sorted":[],"title_canon_sha256":"eacb4caf49a33ebf18a48d8520c53a8c80120f01d7ffc998f08e030303f0e4bf","abstract_canon_sha256":"6348dc24af930626ba67e6cb85a57fe8ac2d75c666c00730aad868fa5b4333bf"},"schema_version":"1.0"},"canonical_sha256":"4dedd67ec0865255519df6c99347530ff5b73d08cfed609cb6cd164799e05213","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:01.120955Z","signature_b64":"Z0RU0J4ExdjoHb1Km8uoOiqD59qr19Jf3T9BKWipQ1Wh3qqE02nIDGtbm3qD0rAEkCjIDmL4RYAEN3SG4G51Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dedd67ec0865255519df6c99347530ff5b73d08cfed609cb6cd164799e05213","last_reissued_at":"2026-05-18T00:29:01.120482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:01.120482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.10132","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FrVja9yTH0x15VxqwC6SeKIWis/XmPcPJjay83EGhxx5av/+8I6IsM1BK0WXWEHIWi9z4Xm5+NQoLdQuceg6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:17:48.977187Z"},"content_sha256":"271e81fb798bcf1309f5563090fd13836582f94394cd459caf49827aafdec559","schema_version":"1.0","event_id":"sha256:271e81fb798bcf1309f5563090fd13836582f94394cd459caf49827aafdec559"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JXW5M7WAQZJFKUM563EZGR2TB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A mixed-integer branching approach for very small formulations of disjunctive constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Joey Huchette, Juan Pablo Vielma","submitted_at":"2017-09-28T19:09:57Z","abstract_excerpt":"An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by lower bounds on the number of integer variables that are required by traditional MIP formulations, we present a more general mixed-integer branching formulation framework. Our approach maintains favorable algorithmic properties of traditional MIP formulations: in particular, amenability to branch-and-bound and branch-and-cut algorithms. Our main technical result gives an explicit linear inequality description for both t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10132","kind":"arxiv","version":2},"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":"2026-05-18T00:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9iFp2/RyFHDbg44sWikJ+GBdJNYg2CELw5Th/F4lZ4Fu6fACxcTbcJ5iM2SS59by368GwH8GL+OL7SYaQetDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:17:48.977619Z"},"content_sha256":"dc59b5a33e3a793a128238d7f37b9b4e869b60293c88423fea1a5df5ffc94b86","schema_version":"1.0","event_id":"sha256:dc59b5a33e3a793a128238d7f37b9b4e869b60293c88423fea1a5df5ffc94b86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JXW5M7WAQZJFKUM563EZGR2TB7/bundle.json","state_url":"https://pith.science/pith/JXW5M7WAQZJFKUM563EZGR2TB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JXW5M7WAQZJFKUM563EZGR2TB7/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":"2026-05-27T02:17:48Z","links":{"resolver":"https://pith.science/pith/JXW5M7WAQZJFKUM563EZGR2TB7","bundle":"https://pith.science/pith/JXW5M7WAQZJFKUM563EZGR2TB7/bundle.json","state":"https://pith.science/pith/JXW5M7WAQZJFKUM563EZGR2TB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JXW5M7WAQZJFKUM563EZGR2TB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JXW5M7WAQZJFKUM563EZGR2TB7","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":"6348dc24af930626ba67e6cb85a57fe8ac2d75c666c00730aad868fa5b4333bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T19:09:57Z","title_canon_sha256":"eacb4caf49a33ebf18a48d8520c53a8c80120f01d7ffc998f08e030303f0e4bf"},"schema_version":"1.0","source":{"id":"1709.10132","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10132","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10132v2","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10132","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"JXW5M7WAQZJF","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JXW5M7WAQZJFKUM5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JXW5M7WA","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:dc59b5a33e3a793a128238d7f37b9b4e869b60293c88423fea1a5df5ffc94b86","target":"graph","created_at":"2026-05-18T00:29:01Z","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":"An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by lower bounds on the number of integer variables that are required by traditional MIP formulations, we present a more general mixed-integer branching formulation framework. Our approach maintains favorable algorithmic properties of traditional MIP formulations: in particular, amenability to branch-and-bound and branch-and-cut algorithms. Our main technical result gives an explicit linear inequality description for both t","authors_text":"Joey Huchette, Juan Pablo Vielma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T19:09:57Z","title":"A mixed-integer branching approach for very small formulations of disjunctive constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10132","kind":"arxiv","version":2},"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":"sha256:271e81fb798bcf1309f5563090fd13836582f94394cd459caf49827aafdec559","target":"record","created_at":"2026-05-18T00:29:01Z","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":"6348dc24af930626ba67e6cb85a57fe8ac2d75c666c00730aad868fa5b4333bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-28T19:09:57Z","title_canon_sha256":"eacb4caf49a33ebf18a48d8520c53a8c80120f01d7ffc998f08e030303f0e4bf"},"schema_version":"1.0","source":{"id":"1709.10132","kind":"arxiv","version":2}},"canonical_sha256":"4dedd67ec0865255519df6c99347530ff5b73d08cfed609cb6cd164799e05213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dedd67ec0865255519df6c99347530ff5b73d08cfed609cb6cd164799e05213","first_computed_at":"2026-05-18T00:29:01.120482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:01.120482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z0RU0J4ExdjoHb1Km8uoOiqD59qr19Jf3T9BKWipQ1Wh3qqE02nIDGtbm3qD0rAEkCjIDmL4RYAEN3SG4G51Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:01.120955Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10132","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:271e81fb798bcf1309f5563090fd13836582f94394cd459caf49827aafdec559","sha256:dc59b5a33e3a793a128238d7f37b9b4e869b60293c88423fea1a5df5ffc94b86"],"state_sha256":"60cc59577c19358908546f03a5305c4506120364d02c8de4cd0a7788074a9fa4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u68GQgobVcNLG4Rt0QZLHofHibPS6BdrrzxzrUEtbGLNQ9twrEEPHqwkgcmGoePsG5YYYiy8VlRJuFlBveg6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:17:48.981184Z","bundle_sha256":"e80d91d07329a4c136f117ce090eac8048bf87b22713bd77e893209903e2d604"}}