{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YLZPJMTLXAEXIQQNH5XN2X5OHU","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":"e2fdcbff9327c69be44127bb5a41e8b4e6dc52cadbf49a5a8caf0d28e56a7b7d","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-20T15:00:32Z","title_canon_sha256":"6c08ca64dd36681ac00cb1aadf9f402208a6cda1a5c689679ccb9ebf6be6d16b"},"schema_version":"1.0","source":{"id":"2607.18032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18032","created_at":"2026-07-21T02:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18032v1","created_at":"2026-07-21T02:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18032","created_at":"2026-07-21T02:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"YLZPJMTLXAEX","created_at":"2026-07-21T02:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"YLZPJMTLXAEXIQQN","created_at":"2026-07-21T02:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"YLZPJMTL","created_at":"2026-07-21T02:22:12Z"}],"graph_snapshots":[{"event_id":"sha256:2357cc01af1b1731687ff851144cc1c1a81b2f94644a0658c1584a2036f8f775","target":"graph","created_at":"2026-07-21T02:22:12Z","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/2607.18032/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove full replica symmetry breaking for the zero-field Sherrington-Kirkpatrick model at zero temperature: the Parisi minimizer is absolutely continuous, has a smooth density, and has support $[0,1)$. At inverse temperature $\\beta>1$, [arxiv.org/abs/2607.11756v3] recently proved that the Parisi measure has support $[0,q_\\beta]$. Here, we show $q_\\beta$ converges to $1$ as $\\beta\\to\\infty$.","authors_text":"Hong-Bin Chen","cross_cats":["cond-mat.dis-nn","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-20T15:00:32Z","title":"FRSB in the SK spin glass: convergence to full-interval support at zero temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18032","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:d357ac00a38128018b8f59664b0627487cf0e28af094b3a1c7d7f61bd5f9cb20","target":"record","created_at":"2026-07-21T02:22:12Z","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":"e2fdcbff9327c69be44127bb5a41e8b4e6dc52cadbf49a5a8caf0d28e56a7b7d","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-20T15:00:32Z","title_canon_sha256":"6c08ca64dd36681ac00cb1aadf9f402208a6cda1a5c689679ccb9ebf6be6d16b"},"schema_version":"1.0","source":{"id":"2607.18032","kind":"arxiv","version":1}},"canonical_sha256":"c2f2f4b26bb80974420d3f6edd5fae3d196a2679e80e198676a299ba45d0dfc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2f2f4b26bb80974420d3f6edd5fae3d196a2679e80e198676a299ba45d0dfc1","first_computed_at":"2026-07-21T02:22:12.630868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T02:22:12.630868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HlZmyVHQxP/mCmQsJh2ToTL2b7WzsyAkSKHfPHDR5DbkNLkSCYKAE65oZxyj3VawhCJk7P+ycwCYM62z/YMrBA==","signature_status":"signed_v1","signed_at":"2026-07-21T02:22:12.631701Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d357ac00a38128018b8f59664b0627487cf0e28af094b3a1c7d7f61bd5f9cb20","sha256:2357cc01af1b1731687ff851144cc1c1a81b2f94644a0658c1584a2036f8f775"],"state_sha256":"56efcd2b4bb32263c67dc327521fe0629f397f20dfa5c6718588b38804196544"}