{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z2YY57GCIMKOLPYD4UBYRXVWPZ","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":"e4a8bffc772eb50c68b4522b15a2e61a180ff6b28502b2696de5e4b8550987f9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-17T05:34:07Z","title_canon_sha256":"06e10608d5964cfcf62472c5516879d096b75d8b9ca6c99d486ccfcc61d3e2e4"},"schema_version":"1.0","source":{"id":"1207.3883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3883","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3883v2","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3883","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"pith_short_12","alias_value":"Z2YY57GCIMKO","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z2YY57GCIMKOLPYD","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z2YY57GC","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:a557c8803a19a81af1e570778377d15f7ce8f4f57682b034bc1fe528a5b57ea1","target":"graph","created_at":"2026-05-18T03:19:46Z","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":"It has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical Boltzmann weights in a number of lattice models. Remarkably, the solutions of these linear equations also solve the Yang-Baxter equations. We extend this analysis for the Z_N model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a quadratic equation in the Boltzmann weights and for three rhombi a cubic equation. The two-rhombus equation implies the inversion relations","authors_text":"I. T. Alam, M. T. Batchelor","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-17T05:34:07Z","title":"Integrability as a consequence of discrete holomorphicity: the Z_N model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3883","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":"sha256:8855fda0cd8db9814a490eba63b36242b8817e2cab4cc9f2ccf5b7a83b7b755b","target":"record","created_at":"2026-05-18T03:19:46Z","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":"e4a8bffc772eb50c68b4522b15a2e61a180ff6b28502b2696de5e4b8550987f9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-07-17T05:34:07Z","title_canon_sha256":"06e10608d5964cfcf62472c5516879d096b75d8b9ca6c99d486ccfcc61d3e2e4"},"schema_version":"1.0","source":{"id":"1207.3883","kind":"arxiv","version":2}},"canonical_sha256":"ceb18efcc24314e5bf03e50388deb67e4e9009018bf4a7ab6dd713212f6c239c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceb18efcc24314e5bf03e50388deb67e4e9009018bf4a7ab6dd713212f6c239c","first_computed_at":"2026-05-18T03:19:46.063856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:46.063856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c6oz4XZA1eTcjML5cYzTJNj3ijZXVK96Qheq8KpVFeoyWep7byv+mzWcflFuAEKHP3BDz2dex0sRT3bgrMx+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:46.064494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8855fda0cd8db9814a490eba63b36242b8817e2cab4cc9f2ccf5b7a83b7b755b","sha256:a557c8803a19a81af1e570778377d15f7ce8f4f57682b034bc1fe528a5b57ea1"],"state_sha256":"ff4972a6e03883bb8224b47ab5fb050044906ed1e707fd97c407f826b0b685f6"}