{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2OWZ6ZTYGABRU7UPDFNOND5UQX","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":"7e4ef1f5addee67479de83f873af48ca1756dc8454defcd5ffa2c39d9cfe517c","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-02T13:28:18Z","title_canon_sha256":"5e40840db1e9a983f5ad5ce976a83764230b12590e43a10fbcd1848bee44beed"},"schema_version":"1.0","source":{"id":"1709.00578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00578","created_at":"2026-05-18T00:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00578v1","created_at":"2026-05-18T00:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00578","created_at":"2026-05-18T00:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"2OWZ6ZTYGABR","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2OWZ6ZTYGABRU7UP","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2OWZ6ZTY","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:4b9843de4b36c91178509802bebbc8dfce80772f382b86e6f878926b378145ac","target":"graph","created_at":"2026-05-18T00:36:07Z","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":"Birational toggling on Gelfand-Tsetlin patterns appeared first in the study of geometric crystals and geometric Robinson-Schensted-Knuth correspondence. Based on these birational toggle relations, Einstein and Propp introduced a discrete dynamical system called birational rowmotion associated with a partially ordered set. We generalize birational rowmotion to the class of arbitrary strongly connected directed graphs, calling the resulting discrete dynamical system the $R$-system. We study its integrability from the points of view of singularity confinement and algebraic entropy. We show that i","authors_text":"Pavel Galashin, Pavlo Pylyavskyy","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-02T13:28:18Z","title":"$R$-systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00578","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":"sha256:9431e9974da0ce801965f762705ca2a4d422dac01b246784371b277d0fcf2749","target":"record","created_at":"2026-05-18T00:36:07Z","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":"7e4ef1f5addee67479de83f873af48ca1756dc8454defcd5ffa2c39d9cfe517c","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-02T13:28:18Z","title_canon_sha256":"5e40840db1e9a983f5ad5ce976a83764230b12590e43a10fbcd1848bee44beed"},"schema_version":"1.0","source":{"id":"1709.00578","kind":"arxiv","version":1}},"canonical_sha256":"d3ad9f667830031a7e8f195ae68fb485e8cf57875c8f60236801eb5c08daba54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3ad9f667830031a7e8f195ae68fb485e8cf57875c8f60236801eb5c08daba54","first_computed_at":"2026-05-18T00:36:07.605958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:07.605958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TXcxyjm/qutNR5eHZ/6PwXbdykj7C1nQirocSDdKcj3PuxJE8yBLEUjZNYnVcZfYNTXXDQdwdmqb+0zcSBPzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:07.606795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9431e9974da0ce801965f762705ca2a4d422dac01b246784371b277d0fcf2749","sha256:4b9843de4b36c91178509802bebbc8dfce80772f382b86e6f878926b378145ac"],"state_sha256":"5e3d04886d7e332ce2bc6c0ad4c5e4488d2a39d11977a3903e6584f2352b19c7"}