{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WRRBIQQRKHYGMQTFRPTLVDNVIX","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":"3d45b27d18cf9878eb0c53b43963bbd9ec9b3b7ef41368e0eeb7bec65323ae79","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-19T00:55:11Z","title_canon_sha256":"62e157bf81557a015f7248532b2447162ba3b910f169147f4a337a66af636870"},"schema_version":"1.0","source":{"id":"1704.05570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05570","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05570v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05570","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"WRRBIQQRKHYG","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WRRBIQQRKHYGMQTF","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WRRBIQQR","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:953d7907830692d4585206625bc3bd030dc19b2d84d6733516313c2ab3fd5fbe","target":"graph","created_at":"2026-05-18T00:46:07Z","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":"Zamolodchikov periodicity is a property of $T$- and $Y$-systems, arising in the thermodynamic Bethe ansatz. Zamolodchikov integrability was recently considered as its affine analog in our joint work with P. Pylyavskyy. Here we prove periodicity and integrability for similar discrete dynamical systems based on the cube recurrence, also known as the discrete BKP equation. The periodicity part was conjectured by Henriques in 2007.","authors_text":"Pavel Galashin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-19T00:55:11Z","title":"Periodicity and integrability for the cube recurrence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05570","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":"sha256:72d03f9a429773cee2902d6e64fc942b3504c25889c2a145084f1977fb4872a1","target":"record","created_at":"2026-05-18T00:46:07Z","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":"3d45b27d18cf9878eb0c53b43963bbd9ec9b3b7ef41368e0eeb7bec65323ae79","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-19T00:55:11Z","title_canon_sha256":"62e157bf81557a015f7248532b2447162ba3b910f169147f4a337a66af636870"},"schema_version":"1.0","source":{"id":"1704.05570","kind":"arxiv","version":1}},"canonical_sha256":"b46214421151f06642658be6ba8db545d7f52469fe782d78303eab81b9685ee0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b46214421151f06642658be6ba8db545d7f52469fe782d78303eab81b9685ee0","first_computed_at":"2026-05-18T00:46:07.101617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:07.101617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LpnFKqIKh9PnxF+irDS693G0HJpt4DrRPEyXhfSe3cfa6EEJHoWdwpp0Nys1sO6Jt9OKtuPt2IjJ2QkwPXIWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:07.102283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72d03f9a429773cee2902d6e64fc942b3504c25889c2a145084f1977fb4872a1","sha256:953d7907830692d4585206625bc3bd030dc19b2d84d6733516313c2ab3fd5fbe"],"state_sha256":"d056f7af3a992e5988fcac58c725938dac5d6b6dc4f2d207972b91c227b2ef0c"}