{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6VAQ4FBMW6TMSWRG5UZTTMP7WF","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":"258a6c4fce8b29a3f81e04ebf37321a784e4cc57e3b5dbd4e14eda511b3703f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-01T18:17:03Z","title_canon_sha256":"3fed717664e4e08cad2b6e51bc7276db88e8e15bfdb06aa6439546b1ee65ac0c"},"schema_version":"1.0","source":{"id":"1108.0379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0379","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0379v2","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0379","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"6VAQ4FBMW6TM","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6VAQ4FBMW6TMSWRG","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6VAQ4FBM","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:678aea59d201190616a4b5085813e8f242ceb9375d4eb763a5816c74af67fbd3","target":"graph","created_at":"2026-05-18T04:07:29Z","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"},"paper":{"abstract_excerpt":"In this paper we obtain a new family of identities for random measures on the unit ball of a separable Hilbert space which arise as the asymptotic analogues of the Gibbs measures in the Sherrington-Kirkpatrick and $p$-spin models and which are known to satisfy the Ghirlanda-Guerra identities. We give several applications of the new identities to structural results for such measures.","authors_text":"Dmitry Panchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-01T18:17:03Z","title":"A new representation of the Ghirlanda-Guerra identities with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0379","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":"sha256:78df0e0278d0e9d96caf4e9ed5f787e37cb8bcd6c1a65d1316a447c54e18caf5","target":"record","created_at":"2026-05-18T04:07:29Z","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":"258a6c4fce8b29a3f81e04ebf37321a784e4cc57e3b5dbd4e14eda511b3703f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-01T18:17:03Z","title_canon_sha256":"3fed717664e4e08cad2b6e51bc7276db88e8e15bfdb06aa6439546b1ee65ac0c"},"schema_version":"1.0","source":{"id":"1108.0379","kind":"arxiv","version":2}},"canonical_sha256":"f5410e142cb7a6c95a26ed3339b1ffb178f47a4eb9699e343225b51e7efc50ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5410e142cb7a6c95a26ed3339b1ffb178f47a4eb9699e343225b51e7efc50ad","first_computed_at":"2026-05-18T04:07:29.082087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:29.082087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t5QBuNSrOgHgF3iFE1VzrWnNazsgYfN+oewzWxgzz7OS+Uv1AklHYhZqGhXbw1rpRNp3Ak6Zo1Za0ohl2Kn0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:29.082761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78df0e0278d0e9d96caf4e9ed5f787e37cb8bcd6c1a65d1316a447c54e18caf5","sha256:678aea59d201190616a4b5085813e8f242ceb9375d4eb763a5816c74af67fbd3"],"state_sha256":"9c86e8f635012704ea94e4888dc482bccf95de3a1cc3d897790d3bc64c44bf8f"}