{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EGNWXYX6TGYTICXBUTK5FVNVH2","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":"77b464ee91a5b5ebfcae8949603d1b552dded2fbaa2fe9d376ea53c579f646ee","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-28T12:37:47Z","title_canon_sha256":"c0007870b642309c99be605d35717009ed3031ed0bd3061c5f674965ee593737"},"schema_version":"1.0","source":{"id":"1803.10561","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10561","created_at":"2026-05-18T00:18:08Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10561v2","created_at":"2026-05-18T00:18:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10561","created_at":"2026-05-18T00:18:08Z"},{"alias_kind":"pith_short_12","alias_value":"EGNWXYX6TGYT","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EGNWXYX6TGYTICXB","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EGNWXYX6","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:833bc3632d9e421800e6b666b387ecc497989926f667e19d6bb7bff7b91b8c44","target":"graph","created_at":"2026-05-18T00:18:08Z","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 consider generalizations of parity polytopes whose variables, in addition to a parity constraint, satisfy certain ordering constraints. More precisely, the variable domain is partitioned into $k$ contiguous groups, and within each group, we require that $x_i \\geq x_{i+1}$ for all relevant $i$. Such constraints are used to break symmetry after replacing an integer variable by a sum of binary variables, so-called binarization. We provide extended formulations for such polytopes, derive a complete outer description, and present a separation algorithm for the new constraints. It turns out that ","authors_text":"Dominik Ermel, Matthias Walter","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-28T12:37:47Z","title":"Parity Polytopes and Binarization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10561","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":"sha256:107251a02ef521927953d8fbf231cafa3373bce6861f50f38374bb5ca3ea1f69","target":"record","created_at":"2026-05-18T00:18:08Z","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":"77b464ee91a5b5ebfcae8949603d1b552dded2fbaa2fe9d376ea53c579f646ee","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-28T12:37:47Z","title_canon_sha256":"c0007870b642309c99be605d35717009ed3031ed0bd3061c5f674965ee593737"},"schema_version":"1.0","source":{"id":"1803.10561","kind":"arxiv","version":2}},"canonical_sha256":"219b6be2fe99b1340ae1a4d5d2d5b53e8de2774aa585b193d7fcadf1fdb51910","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"219b6be2fe99b1340ae1a4d5d2d5b53e8de2774aa585b193d7fcadf1fdb51910","first_computed_at":"2026-05-18T00:18:08.971874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:08.971874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LJjwNOyvySqWkEHRpTdnbQUzr1v1FCsq+vJdxn2e/DC0Ln7/C8bBEm0A+JpxlJy+Hi+GxRlex8FG0dbhp4j3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:08.972543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10561","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:107251a02ef521927953d8fbf231cafa3373bce6861f50f38374bb5ca3ea1f69","sha256:833bc3632d9e421800e6b666b387ecc497989926f667e19d6bb7bff7b91b8c44"],"state_sha256":"559bf3ba8b9f14a81753f8306eb17c823dda165abf5a5e6f913b4eaad2e906d6"}