{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:CHPULJM3L2W3JR7LNEB5Z7I3CW","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":"aaa03be7e7f11b3e61f1c9433158943a30380e2c34de50d7a885fd8d39990774","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1996-02-27T00:02:50Z","title_canon_sha256":"cd7785356c484ed9af22c67b667d9c4100372532f4988cf13b230bb13939653b"},"schema_version":"1.0","source":{"id":"hep-ph/9602405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9602405","created_at":"2026-07-04T16:01:29Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9602405v1","created_at":"2026-07-04T16:01:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9602405","created_at":"2026-07-04T16:01:29Z"},{"alias_kind":"pith_short_12","alias_value":"CHPULJM3L2W3","created_at":"2026-07-04T16:01:29Z"},{"alias_kind":"pith_short_16","alias_value":"CHPULJM3L2W3JR7L","created_at":"2026-07-04T16:01:29Z"},{"alias_kind":"pith_short_8","alias_value":"CHPULJM3","created_at":"2026-07-04T16:01:29Z"}],"graph_snapshots":[{"event_id":"sha256:60f685b4680e9274e1fc6e34f94486153e33678f4398d703fdac7eeaf6b59d28","target":"graph","created_at":"2026-07-04T16:01:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-ph/9602405/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The linear O($N$) sigma model undergoes a symmetry restoring phase transition at finite temperature. We show that the nonlinear O($N$) sigma model also undergoes a symmetry restoring phase transition; the critical temperatures are the same when the linear model is treated in mean field approximation and the nonlinear model is treated to leading plus subleading order in the 1/$N$ expansion. We also carefully define and study the behavior of $f_{\\pi}$ and the scalar condensate at low temperatures in both models, showing that they are independent of field redefinition.","authors_text":"Alexander Bochkarev, Joseph Kapusta","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"1996-02-27T00:02:50Z","title":"Chiral symmetry at finite temperature: linear vs nonlinear $\\sigma$-models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9602405","kind":"arxiv","version":1},"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":"sha256:23dd66d1f3afd875fbcbc4b482870f3f6ab896e5d09f855825106b9f67ffb285","target":"record","created_at":"2026-07-04T16:01:29Z","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":"aaa03be7e7f11b3e61f1c9433158943a30380e2c34de50d7a885fd8d39990774","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1996-02-27T00:02:50Z","title_canon_sha256":"cd7785356c484ed9af22c67b667d9c4100372532f4988cf13b230bb13939653b"},"schema_version":"1.0","source":{"id":"hep-ph/9602405","kind":"arxiv","version":1}},"canonical_sha256":"11df45a59b5eadb4c7eb6903dcfd1b15bfad4117dff4747c79ea079410ea0d16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11df45a59b5eadb4c7eb6903dcfd1b15bfad4117dff4747c79ea079410ea0d16","first_computed_at":"2026-07-04T16:01:29.926066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:01:29.926066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EPWaAUVKYYbKOjUtNAE1AGaAAhXwWAesXgKetZWiTaHvCMqfQTCTO9VEq4Gq/ZZ51H+ZXU5uW4VqzAoDou0gDg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:01:29.926465Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/9602405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23dd66d1f3afd875fbcbc4b482870f3f6ab896e5d09f855825106b9f67ffb285","sha256:60f685b4680e9274e1fc6e34f94486153e33678f4398d703fdac7eeaf6b59d28"],"state_sha256":"cf24aa300f4109de063569ba49cd75792744eee329623bc8e92258c7b2da6d54"}