{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WJKK2WJGC7OCGOR3YJYFNB7Q54","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":"59d8a6be83cc2631a2c717cf3b46c80dd232ee5b18c5c64732276aaee8c4495b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-01-13T00:12:05Z","title_canon_sha256":"d484d97d3ad534ffb1b13aed51e347c3ba6cace61a4733631a167939b17dd46f"},"schema_version":"1.0","source":{"id":"2601.10749","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.10749","created_at":"2026-05-29T01:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"2601.10749v6","created_at":"2026-05-29T01:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.10749","created_at":"2026-05-29T01:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"WJKK2WJGC7OC","created_at":"2026-05-29T01:05:01Z"},{"alias_kind":"pith_short_16","alias_value":"WJKK2WJGC7OCGOR3","created_at":"2026-05-29T01:05:01Z"},{"alias_kind":"pith_short_8","alias_value":"WJKK2WJG","created_at":"2026-05-29T01:05:01Z"}],"graph_snapshots":[{"event_id":"sha256:ff76f3561fa624ef655af566887a145107934a5a03c89957dd958aaf6f2f46ac","target":"graph","created_at":"2026-05-29T01:05:01Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The exact solution of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field is derived. The partition function and the spontaneous magnetization are obtained."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the 2D model with next-nearest interactions is equivalent to a triangular Ising model plus an interaction along the z axis, so that 3D Ising solution methods can be directly modified and applied."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Exact partition function and spontaneous magnetization obtained for the 2D Ising model with next-nearest interactions via transfer-matrix methods adapted from 3D Ising approaches."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The exact solution is derived for the two-dimensional Ising model with next-nearest-neighbor interactions at zero magnetic field, yielding closed-form partition function and spontaneous magnetization."}],"snapshot_sha256":"f3a492511844b7e8481bc12ea53b7436e1584a557071cc2ef3c10702233a7890"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"61175123682eca79e41c211afbfa318d86e240cade43a01e742b561d871c0e46"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2601.10749/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The exact solution of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field is derived. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic representation, transfer tensor representation and schematic representation, to inspect nontrivial topological structures in this system. The system is equivalent to a triangular Ising model plus an interaction along the z axis, so that the approaches developed for the 3D Ising model are modified to be appropriable for solving the exact solution of the 2D Ising model with th","authors_text":"Zhidong Zhang","cross_cats":[],"headline":"The exact solution is derived for the two-dimensional Ising model with next-nearest-neighbor interactions at zero magnetic field, yielding closed-form partition function and spontaneous magnetization.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-01-13T00:12:05Z","title":"Exact solution of a two-dimensional (2D) Ising model with the next nearest interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.10749","kind":"arxiv","version":6},"verdict":{"created_at":"2026-05-16T15:25:36.168007Z","id":"5fd503e4-56e4-413c-8704-3b6276afc8f0","model_set":{"reader":"grok-4.3"},"one_line_summary":"Exact partition function and spontaneous magnetization obtained for the 2D Ising model with next-nearest interactions via transfer-matrix methods adapted from 3D Ising approaches.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The exact solution is derived for the two-dimensional Ising model with next-nearest-neighbor interactions at zero magnetic field, yielding closed-form partition function and spontaneous magnetization.","strongest_claim":"The exact solution of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field is derived. The partition function and the spontaneous magnetization are obtained.","weakest_assumption":"That the 2D model with next-nearest interactions is equivalent to a triangular Ising model plus an interaction along the z axis, so that 3D Ising solution methods can be directly modified and applied."}},"verdict_id":"5fd503e4-56e4-413c-8704-3b6276afc8f0"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fa44f0f213edec9f0d657245cdc9ca4d3707fab531e9c8567988e922da11bebb","target":"record","created_at":"2026-05-29T01:05:01Z","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":"59d8a6be83cc2631a2c717cf3b46c80dd232ee5b18c5c64732276aaee8c4495b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-01-13T00:12:05Z","title_canon_sha256":"d484d97d3ad534ffb1b13aed51e347c3ba6cace61a4733631a167939b17dd46f"},"schema_version":"1.0","source":{"id":"2601.10749","kind":"arxiv","version":6}},"canonical_sha256":"b254ad592617dc233a3bc2705687f0ef22ceb52857f8be38ee767156674d8bf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b254ad592617dc233a3bc2705687f0ef22ceb52857f8be38ee767156674d8bf5","first_computed_at":"2026-05-29T01:05:01.873449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:01.873449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fxGymBA7Rv0nFe9Dn8+KD5UVOrrKA17IxM9hpA2J9X70zArecsGZbqqS+aijFCfcb/21LSR2BtO1JrBoxeCXCA==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:01.874281Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.10749","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa44f0f213edec9f0d657245cdc9ca4d3707fab531e9c8567988e922da11bebb","sha256:ff76f3561fa624ef655af566887a145107934a5a03c89957dd958aaf6f2f46ac"],"state_sha256":"e8e7992e67e61ddf56ffd6604e1de94951c0cf5c3b6ebbb508b702d4e5e1e604"}