{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:B3T7DNQSGGYJVX6Y4IWLHDTUSY","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":"1172f6de2cd58ff7ff76848020d2a9c223a94ad0a0349b503273c946fb41b6a8","cross_cats_sorted":["math-ph","math.KT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-09T03:28:06Z","title_canon_sha256":"2aee766a30cad2a302aac55e2738a5c396e67f7844648ce5490917edd0101362"},"schema_version":"1.0","source":{"id":"2007.04533","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.04533","created_at":"2026-07-05T02:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"2007.04533v2","created_at":"2026-07-05T02:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.04533","created_at":"2026-07-05T02:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"B3T7DNQSGGYJ","created_at":"2026-07-05T02:04:09Z"},{"alias_kind":"pith_short_16","alias_value":"B3T7DNQSGGYJVX6Y","created_at":"2026-07-05T02:04:09Z"},{"alias_kind":"pith_short_8","alias_value":"B3T7DNQS","created_at":"2026-07-05T02:04:09Z"}],"graph_snapshots":[{"event_id":"sha256:cab328c215583816a982da090fa948307b2d67b3e48e25e76d973a8673a0dbaa","target":"graph","created_at":"2026-07-05T02:04:09Z","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/2007.04533/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct an integrable colored six-vertex model whose partition function is a double Grothendieck polynomial. This gives an integrable systems interpretation of bumpless pipe dreams and recent results of Weigandt [arXiv:2003.07342] relating double Grothendieck polynomias with bumpless pipe dreams. For vexillary permutations, we then construct a new model that we call the semidual version model. We use our semidual model and the five-vertex model of Motegi and Sakai to given a new proof that double Grothendieck polynomials for vexillary permutations are equal to flagged factorial Grothendie","authors_text":"Travis Scrimshaw, Valentin Buciumas","cross_cats":["math-ph","math.KT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-09T03:28:06Z","title":"Double Grothendieck polynomials and colored lattice models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.04533","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:e8a8a9aafca5b62801f4587fcce86eff4f2d6166ed02d20c8ae021c50f41abc1","target":"record","created_at":"2026-07-05T02:04:09Z","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":"1172f6de2cd58ff7ff76848020d2a9c223a94ad0a0349b503273c946fb41b6a8","cross_cats_sorted":["math-ph","math.KT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-09T03:28:06Z","title_canon_sha256":"2aee766a30cad2a302aac55e2738a5c396e67f7844648ce5490917edd0101362"},"schema_version":"1.0","source":{"id":"2007.04533","kind":"arxiv","version":2}},"canonical_sha256":"0ee7f1b61231b09adfd8e22cb38e74963e6c8c191b46d1099f50922ba36eece5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ee7f1b61231b09adfd8e22cb38e74963e6c8c191b46d1099f50922ba36eece5","first_computed_at":"2026-07-05T02:04:09.292726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:04:09.292726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tev1nZxkeU6P+YiyAQlEc+ngfezP+228HJQ5xJeKfPtkV6zeIX8kIZXDmobg7ICshnpVU0m8wHVbYLnCavxBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:04:09.293217Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.04533","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8a8a9aafca5b62801f4587fcce86eff4f2d6166ed02d20c8ae021c50f41abc1","sha256:cab328c215583816a982da090fa948307b2d67b3e48e25e76d973a8673a0dbaa"],"state_sha256":"37a3f926540fc77f8387e5989ab941d1f2decbadb3d87df43e85f52cd1133b7b"}