{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YC5TQNVK6JUPQTXO4TMOGIIA65","short_pith_number":"pith:YC5TQNVK","canonical_record":{"source":{"id":"1205.5893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-26T16:28:13Z","cross_cats_sorted":[],"title_canon_sha256":"d1b60665aefda8c509452a7f05a4466a80975ecdfa1bfe066b17f7a6f142e5e1","abstract_canon_sha256":"bfd1d77f21bdd4f9e8a6de40be7a37ef2cb118fd9db9aee7efa2474413e8cac8"},"schema_version":"1.0"},"canonical_sha256":"c0bb3836aaf268f84eeee4d8e32100f76dffc28908fe370cab7911172306bfce","source":{"kind":"arxiv","id":"1205.5893","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5893","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5893v2","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5893","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"YC5TQNVK6JUP","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YC5TQNVK6JUPQTXO","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YC5TQNVK","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YC5TQNVK6JUPQTXO4TMOGIIA65","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-26T16:28:13Z","cross_cats_sorted":[],"title_canon_sha256":"d1b60665aefda8c509452a7f05a4466a80975ecdfa1bfe066b17f7a6f142e5e1","abstract_canon_sha256":"bfd1d77f21bdd4f9e8a6de40be7a37ef2cb118fd9db9aee7efa2474413e8cac8"},"schema_version":"1.0"},"canonical_sha256":"c0bb3836aaf268f84eeee4d8e32100f76dffc28908fe370cab7911172306bfce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:48.977379Z","signature_b64":"ZCoSXio1O33LcPZ5eJuciAmjZI83bRgoFnurO4Hzv059Ti7R7TyJE9wboqtb71TfTTKNAJ+8ZdQqNo8sH+/rBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0bb3836aaf268f84eeee4d8e32100f76dffc28908fe370cab7911172306bfce","last_reissued_at":"2026-05-18T03:46:48.976562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:48.976562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5893","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUbvrC7ID7/kIRsLdKcxdtNUt2C3yeZP+8ZSPLuxjgTWBfcunx0ZJOsiw31ABxzNRNqTphFGevjS8RDGiGQgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:04:35.614636Z"},"content_sha256":"0862163b78ae409bf1be7e78d58a437e56031a2709ec8fa100dab5e93b4b8368","schema_version":"1.0","event_id":"sha256:0862163b78ae409bf1be7e78d58a437e56031a2709ec8fa100dab5e93b4b8368"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YC5TQNVK6JUPQTXO4TMOGIIA65","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical manifold of the Potts model: Exact results and homogeneity approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"F. Y. Wu, Wenan Guo","submitted_at":"2012-05-26T16:28:13Z","abstract_excerpt":"The $q$-state Potts model has stood at the frontier of research in statistical mechanics for many years. In the absence of a closed-form solution, much of the past efforts have focused on locating its critical manifold, trajectory in the parameter $\\{q, e^J\\}$ space where $J$ is the reduced interaction, along which the free energy is singular. However, except in isolated cases, antiferromagnetic (AF) models with $J<0$ have been largely neglected. In this paper we consider the Potts model with AF interactions focusing on deducing its critical manifold in exact and/or closed-form expressions.\n  "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5893","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aeGU4Ldxne9QAC7lN1KFr9mOocmrwS3qgqHXniB46vEFr3b19aLO55QNu4pY67XLYJ5cbh6d0JZ4MHDv3KViBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:04:35.614976Z"},"content_sha256":"e09df976e5a115b672920fbd189f04a6af780c2d5007a1f36f11d64666b165e0","schema_version":"1.0","event_id":"sha256:e09df976e5a115b672920fbd189f04a6af780c2d5007a1f36f11d64666b165e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YC5TQNVK6JUPQTXO4TMOGIIA65/bundle.json","state_url":"https://pith.science/pith/YC5TQNVK6JUPQTXO4TMOGIIA65/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YC5TQNVK6JUPQTXO4TMOGIIA65/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T07:04:35Z","links":{"resolver":"https://pith.science/pith/YC5TQNVK6JUPQTXO4TMOGIIA65","bundle":"https://pith.science/pith/YC5TQNVK6JUPQTXO4TMOGIIA65/bundle.json","state":"https://pith.science/pith/YC5TQNVK6JUPQTXO4TMOGIIA65/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YC5TQNVK6JUPQTXO4TMOGIIA65/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YC5TQNVK6JUPQTXO4TMOGIIA65","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":"bfd1d77f21bdd4f9e8a6de40be7a37ef2cb118fd9db9aee7efa2474413e8cac8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-26T16:28:13Z","title_canon_sha256":"d1b60665aefda8c509452a7f05a4466a80975ecdfa1bfe066b17f7a6f142e5e1"},"schema_version":"1.0","source":{"id":"1205.5893","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5893","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5893v2","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5893","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"YC5TQNVK6JUP","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YC5TQNVK6JUPQTXO","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YC5TQNVK","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:e09df976e5a115b672920fbd189f04a6af780c2d5007a1f36f11d64666b165e0","target":"graph","created_at":"2026-05-18T03:46:48Z","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":"The $q$-state Potts model has stood at the frontier of research in statistical mechanics for many years. In the absence of a closed-form solution, much of the past efforts have focused on locating its critical manifold, trajectory in the parameter $\\{q, e^J\\}$ space where $J$ is the reduced interaction, along which the free energy is singular. However, except in isolated cases, antiferromagnetic (AF) models with $J<0$ have been largely neglected. In this paper we consider the Potts model with AF interactions focusing on deducing its critical manifold in exact and/or closed-form expressions.\n  ","authors_text":"F. Y. Wu, Wenan Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-26T16:28:13Z","title":"Critical manifold of the Potts model: Exact results and homogeneity approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5893","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":"sha256:0862163b78ae409bf1be7e78d58a437e56031a2709ec8fa100dab5e93b4b8368","target":"record","created_at":"2026-05-18T03:46:48Z","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":"bfd1d77f21bdd4f9e8a6de40be7a37ef2cb118fd9db9aee7efa2474413e8cac8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-26T16:28:13Z","title_canon_sha256":"d1b60665aefda8c509452a7f05a4466a80975ecdfa1bfe066b17f7a6f142e5e1"},"schema_version":"1.0","source":{"id":"1205.5893","kind":"arxiv","version":2}},"canonical_sha256":"c0bb3836aaf268f84eeee4d8e32100f76dffc28908fe370cab7911172306bfce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0bb3836aaf268f84eeee4d8e32100f76dffc28908fe370cab7911172306bfce","first_computed_at":"2026-05-18T03:46:48.976562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:48.976562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZCoSXio1O33LcPZ5eJuciAmjZI83bRgoFnurO4Hzv059Ti7R7TyJE9wboqtb71TfTTKNAJ+8ZdQqNo8sH+/rBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:48.977379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5893","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0862163b78ae409bf1be7e78d58a437e56031a2709ec8fa100dab5e93b4b8368","sha256:e09df976e5a115b672920fbd189f04a6af780c2d5007a1f36f11d64666b165e0"],"state_sha256":"a861555e5b5e912c6f06e69c7aa45d83cdf8c76b8cc7e12eb91d1e70d16ca2f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nAqd2vMiS/fFJF0lJ/yks7CKIdSHKO4INU1yZWAdpW8QbGpOfQZbW6IAkWgKTbAkw+db3nI3ci5DEW2fYVtkDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:04:35.616813Z","bundle_sha256":"cae4945dd9809cd8d43ecfd28acc0771257ac8939d792a3681b5b9f4b1431d95"}}