{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5CY3LAUPLAPECNGJU5VDDKCHYT","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":"601bfde5fa000cbca75488213607899cd14972c15a9353220f9d595d797e3ca7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-26T04:48:49Z","title_canon_sha256":"8b9130baa3a396b61df19b023b42f43098a7c182a450583e304afee79eab8ab9"},"schema_version":"1.0","source":{"id":"1310.7071","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7071","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7071v2","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7071","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"pith_short_12","alias_value":"5CY3LAUPLAPE","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5CY3LAUPLAPECNGJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5CY3LAUP","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:58f99ad01d0f964e6bfc9f4d7d949200117720f9b0e0a0ebe11a218b96d63db9","target":"graph","created_at":"2026-05-18T02:30:47Z","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":"We study the effects of the environment described by the Tsallis nonextensive statistics on physical quantities using an optimization method in the case of small deviation from the Boltzmann-Gibbs statistics. The $x^4$ model is used and the density operator is restricted to be a gaussian form. The variational parameter is the frequency $\\Omega$ of a particle in the optimization method. We obtain an approximate expression of free energy and of the expectation value of $\\beta m \\Omega^2 x^2 /2$, where $\\beta$ is the inverse of the temperature and $m$ is the mass of a particle. Numerically, the o","authors_text":"Masamichi Ishihara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-26T04:48:49Z","title":"Application of optimization method to the $x^4$ model in the Tsallis nonextensive statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7071","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:ea43f131d4a97c5cabbec761b4eab2d23a6a2ecd62aeabd2e29fce5e61992a52","target":"record","created_at":"2026-05-18T02:30:47Z","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":"601bfde5fa000cbca75488213607899cd14972c15a9353220f9d595d797e3ca7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-26T04:48:49Z","title_canon_sha256":"8b9130baa3a396b61df19b023b42f43098a7c182a450583e304afee79eab8ab9"},"schema_version":"1.0","source":{"id":"1310.7071","kind":"arxiv","version":2}},"canonical_sha256":"e8b1b5828f581e4134c9a76a31a847c4cec2d969eac13dbd58a618ac2ff84f95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8b1b5828f581e4134c9a76a31a847c4cec2d969eac13dbd58a618ac2ff84f95","first_computed_at":"2026-05-18T02:30:47.584286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:47.584286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u1fVxEwLDxcukjZhPoSD0hALd9C/s/uUTyJoQlhlnKPpr5vjxxV84deaXMPFxWkPXJmOjJCpP/6aVHHx9A3DBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:47.584736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7071","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea43f131d4a97c5cabbec761b4eab2d23a6a2ecd62aeabd2e29fce5e61992a52","sha256:58f99ad01d0f964e6bfc9f4d7d949200117720f9b0e0a0ebe11a218b96d63db9"],"state_sha256":"7fbb0eeda94fbfcb396974b6f5a136bb4fb3be81f5e0698a9a96f459826ac094"}