{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XGFQIITQ3LFJPKPDTMYIS6BKVI","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":"408802766d08ba74707197e7a8757aba99661ba4e62bdf5b46a64dd05037274b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-12T19:57:51Z","title_canon_sha256":"6fb60d89e53f989838f3cf7fe15d7a706ad0eabdaceb8eaaa85d43c4205a8d11"},"schema_version":"1.0","source":{"id":"1510.03414","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03414","created_at":"2026-05-18T01:12:07Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03414v2","created_at":"2026-05-18T01:12:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03414","created_at":"2026-05-18T01:12:07Z"},{"alias_kind":"pith_short_12","alias_value":"XGFQIITQ3LFJ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XGFQIITQ3LFJPKPD","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XGFQIITQ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:e3bddbbd5bd24d615f7d23a55c375e59fdf3e5f4a9e6ccbfc9ace3a0844603ea","target":"graph","created_at":"2026-05-18T01:12:07Z","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 show that the Parisi formula of the mixed $p$-spin model is a concave function of the squared inverse temperature. This allows us to derive a new expression for the Parisi formula that involves the inverse temperature and the Parisi measure as Legendre conjugate variables.","authors_text":"Antonio Auffinger, Wei-Kuo Chen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-12T19:57:51Z","title":"The Legendre structure of the Parisi formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03414","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":"sha256:7d8aa33809911fac0f697106c61821ab0d5ee4cd718570fa33a4ae21c30f3870","target":"record","created_at":"2026-05-18T01:12:07Z","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":"408802766d08ba74707197e7a8757aba99661ba4e62bdf5b46a64dd05037274b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-12T19:57:51Z","title_canon_sha256":"6fb60d89e53f989838f3cf7fe15d7a706ad0eabdaceb8eaaa85d43c4205a8d11"},"schema_version":"1.0","source":{"id":"1510.03414","kind":"arxiv","version":2}},"canonical_sha256":"b98b042270daca97a9e39b3089782aaa01a80ce8f51d08e3c5421d4b06b97bab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b98b042270daca97a9e39b3089782aaa01a80ce8f51d08e3c5421d4b06b97bab","first_computed_at":"2026-05-18T01:12:07.796889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:07.796889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yjkLJI9tJAkYpRSC7XiEfS9FwkQKDTtCOW0NubAjHi4yNBnlGfumvS75bWCUljPZ2MeRscxxpIORTRCbPlxeAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:07.797438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03414","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d8aa33809911fac0f697106c61821ab0d5ee4cd718570fa33a4ae21c30f3870","sha256:e3bddbbd5bd24d615f7d23a55c375e59fdf3e5f4a9e6ccbfc9ace3a0844603ea"],"state_sha256":"326513701d282ea0fcceb280426108ad1efd38e9f264b5fe731c7866039d39c2"}