{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PXARCWTGR52QMTH5K6WYPI674U","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":"89e6b03409e933a987cd9dfb623a53f7c7949bc1ffb8bb8421697c0fb997b17a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-08-07T08:40:09Z","title_canon_sha256":"12c9780ce76565f1fded6f509af4bd03a31dc95d58196c89973bcb316fe5b032"},"schema_version":"1.0","source":{"id":"1808.02257","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02257","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02257v2","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02257","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"PXARCWTGR52Q","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PXARCWTGR52QMTH5","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PXARCWTG","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:5e7a452772ed9dc2356dedb30cd74ed9e2af12dc28d814964baebca9090547eb","target":"graph","created_at":"2026-05-18T00:07:17Z","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":"In the paper the phase diagram of $J_1-J_2$ frustrated antiferromagnet with spin $S=1$ and single-ion anisotropy is studied on the planar quadratic lattice in the cluster approximation. The Bogolyubov inequality is adopted for the Gibbs energy calculation for the case of $2 \\times 2$ and $4 \\times 4$ clusters. On this basis, the ranges of existence of the anfiferromagnetic, superantiferromagnetic and paramagnetic phases are investigated for the antiferromagnetic nearest-neighbour ($J_1<0$) and next-nearest-neighbour ($J_2<0$) interactions. In particular, the occurrence of tricritical and tripl","authors_text":"A. Bob\\'ak, K. Sza{\\l}owski, M. \\v{Z}ukovi\\v{c}, T. Balcerzak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-08-07T08:40:09Z","title":"Phase Diagram of the $J_1$ - $J_2$ Frustrated Anisotropic Antiferromagnet with Spin $S=1$ on the Quadratic Lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02257","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":"sha256:852ac00f65a234004b4505f113890a4609242fcada4cbf0c7366fcc9bbbe2d76","target":"record","created_at":"2026-05-18T00:07:17Z","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":"89e6b03409e933a987cd9dfb623a53f7c7949bc1ffb8bb8421697c0fb997b17a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-08-07T08:40:09Z","title_canon_sha256":"12c9780ce76565f1fded6f509af4bd03a31dc95d58196c89973bcb316fe5b032"},"schema_version":"1.0","source":{"id":"1808.02257","kind":"arxiv","version":2}},"canonical_sha256":"7dc1115a668f75064cfd57ad87a3dfe5189aeb9522e680dc251ce4c1e6b75372","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dc1115a668f75064cfd57ad87a3dfe5189aeb9522e680dc251ce4c1e6b75372","first_computed_at":"2026-05-18T00:07:17.056679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:17.056679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/VFf8thWB99u9eb840dPPQ/quoZFMD4Pnn28hbLhgOIaPOvyAIUeiCz9hVhOBcdk85xQl1E0OPJ9rNg308iDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:17.057227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02257","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:852ac00f65a234004b4505f113890a4609242fcada4cbf0c7366fcc9bbbe2d76","sha256:5e7a452772ed9dc2356dedb30cd74ed9e2af12dc28d814964baebca9090547eb"],"state_sha256":"037c925811cda7319d50eebe8cf16c07b0b7f066af0c8154fa5df299ebb64399"}