{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:YREAME4V6IHTBBIZK7QTGEJ2ZX","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":"473ea288089e11c6e9786e1ed833ee36a6b001810a30b9ae08e964d3871f25f4","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-12-11T20:47:36Z","title_canon_sha256":"d03a0d71de11f15a377d704d83a7236558283dd6ee8901760beef26b5c3d9a54"},"schema_version":"1.0","source":{"id":"cond-mat/9712129","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9712129","created_at":"2026-05-18T01:39:32Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9712129v3","created_at":"2026-05-18T01:39:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9712129","created_at":"2026-05-18T01:39:32Z"},{"alias_kind":"pith_short_12","alias_value":"YREAME4V6IHT","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"YREAME4V6IHTBBIZ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"YREAME4V","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:0f28c4b2027a6aba380e88e9c47894926d51be55eb35ed16a0b185f3bf505e05","target":"graph","created_at":"2026-05-18T01:39:32Z","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":"While the Gibbs states of spin glass models have been noted to have an erratic dependence on temperature, one may expect the mean over the disorder to produce a continuously varying ``quenched state''. The assumption of such continuity in temperature implies that in the infinite volume limit the state is stable under a class of deformations of the Gibbs measure. The condition is satisfied by the Parisi Ansatz, along with an even broader stationarity property. The stability conditions have equivalent expressions as marginal additivity of the quenched free energy. Implications of the continuity ","authors_text":"M. Aizenman (Princeton University), P. Contucci (Princeton University)","cross_cats":["cond-mat.dis-nn","math-ph","math.MP"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-12-11T20:47:36Z","title":"On the Stability of the Quenched State in Mean Field Spin Glass Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9712129","kind":"arxiv","version":3},"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":"sha256:69a86be1e5e4a6d400fc507d037c34c0d9ec1d0f7162e57673fc6d805b42b3be","target":"record","created_at":"2026-05-18T01:39:32Z","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":"473ea288089e11c6e9786e1ed833ee36a6b001810a30b9ae08e964d3871f25f4","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-12-11T20:47:36Z","title_canon_sha256":"d03a0d71de11f15a377d704d83a7236558283dd6ee8901760beef26b5c3d9a54"},"schema_version":"1.0","source":{"id":"cond-mat/9712129","kind":"arxiv","version":3}},"canonical_sha256":"c448061395f20f30851957e133113acddafd6f7b912a75186bd13ee1ee0c001d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c448061395f20f30851957e133113acddafd6f7b912a75186bd13ee1ee0c001d","first_computed_at":"2026-05-18T01:39:32.752179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:32.752179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IvB1MA+HhfJKZqvGknSMa7D9zgOgOCTXAVAUKLZiQYsnKDFftzOeuTSTn5FITuErCuUrz6Gq53K5Wvc43P8fBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:32.752676Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9712129","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69a86be1e5e4a6d400fc507d037c34c0d9ec1d0f7162e57673fc6d805b42b3be","sha256:0f28c4b2027a6aba380e88e9c47894926d51be55eb35ed16a0b185f3bf505e05"],"state_sha256":"c684bb27693168a713d391c1d9647445a98ac3d1adb90c743b6a4055e87963e4"}