{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:5NE7K3GR2HZR222Z3X5UMBBDRP","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":"6ed7163c3be5b066400173b120d6297c098acccb8767a51da3aa8758d19b49ec","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-07-13T01:45:39Z","title_canon_sha256":"669e8e8a04c436e3f34203c363f9f461721146b49b7bd2be2c3a3143ac343f69"},"schema_version":"1.0","source":{"id":"hep-th/9907089","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9907089","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9907089v5","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9907089","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"pith_short_12","alias_value":"5NE7K3GR2HZR","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"5NE7K3GR2HZR222Z","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"5NE7K3GR","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:ff29e16ec41bc2acfa9061ca876f59d306c83bdb76b7c8c5086a0d9eda72d2aa","target":"graph","created_at":"2026-05-18T02:35:54Z","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 chiral Gross-Neveu model is one of the most popular toy models for QCD. In the past, it has been studied in detail in the large-N limit. In this paper we study its small-N behavior at finite temperature in 2+1 dimensions. We show that at small N the phase diagram of this model is {\\it principally} different from its behavior at $N\\to \\infty$. We show that for a small number $N$ of fermions the model possesses two characteristic temperatures $T_{KT}$ and $T^*$. That is, at small N, along with a quasiordered phase $0<T<T_{KT}$ the system possesses a very large region of precursor fluctuation","authors_text":"Egor Babaev","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-07-13T01:45:39Z","title":"Mass generation without phase coherence in the Chiral Gross-Neveu Model at finite temperature and small N in 2+1 dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9907089","kind":"arxiv","version":5},"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:c324be564c9918224753480f10e512d19cfe30e40dbc2f5bf15f4ff87dd59c6b","target":"record","created_at":"2026-05-18T02:35:54Z","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":"6ed7163c3be5b066400173b120d6297c098acccb8767a51da3aa8758d19b49ec","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-07-13T01:45:39Z","title_canon_sha256":"669e8e8a04c436e3f34203c363f9f461721146b49b7bd2be2c3a3143ac343f69"},"schema_version":"1.0","source":{"id":"hep-th/9907089","kind":"arxiv","version":5}},"canonical_sha256":"eb49f56cd1d1f31d6b59ddfb4604238bc2b1b76bdb06a8530eb50cd96228d84a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb49f56cd1d1f31d6b59ddfb4604238bc2b1b76bdb06a8530eb50cd96228d84a","first_computed_at":"2026-05-18T02:35:54.337167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:54.337167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bqnDv4jbAkGI6vy4ORBKsDyj5OwM4RrD+eAabBjvqjf2HDUQt5k2/7pHC2QexlkpFLXoLl1wFGskguIpvp8NBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:54.337745Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9907089","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c324be564c9918224753480f10e512d19cfe30e40dbc2f5bf15f4ff87dd59c6b","sha256:ff29e16ec41bc2acfa9061ca876f59d306c83bdb76b7c8c5086a0d9eda72d2aa"],"state_sha256":"2275f32df39a6faeaf4245ff7ad417f9f25ca3ac9bfa78a2eadbb81cc21bf5bd"}