{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NZ4OOK6HEWZMQXFFZQA4SGR6KE","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":"47bd3e21ac064883749f980709cda171fbd6a381c74c68875dde26f7090815b5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-17T09:15:39Z","title_canon_sha256":"f778baab8c051b7ff29fb83fcb3d76e4f34e28b748f21b690294047683af7a1b"},"schema_version":"1.0","source":{"id":"2605.17338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17338","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17338v1","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17338","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"NZ4OOK6HEWZM","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"pith_short_16","alias_value":"NZ4OOK6HEWZMQXFF","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"pith_short_8","alias_value":"NZ4OOK6H","created_at":"2026-05-20T00:03:52Z"}],"graph_snapshots":[{"event_id":"sha256:37683af422f621a0aed94270fc64cbe10d6b9410bbd8b38f3dad48eae56315c7","target":"graph","created_at":"2026-05-20T00:03:52Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"For any translation-invariant joint Gibbs measure on disorder, two spin replicas, and CMR bond variables on Z^d, the blue subgraph contains at most two infinite connected components; if two exist, then they lie in a common infinite grey cluster and belong to opposite overlap-parity classes."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The blue-bond process lacks insertion tolerance and positive association, so the proof must rely on the full joint measure together with a finite-box merge operation and the mass-transport bound on ends of translation-invariant subgraphs rather than standard Burton-Keane or random-cluster arguments (abstract, paragraph on main obstacle)."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Proves that the blue subgraph in the CMR representation of the short-range Edwards-Anderson model has at most two infinite clusters, which must lie in one grey cluster with opposite overlap parity if both are infinite."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The blue subgraph in the two-replica CMR representation of the Edwards-Anderson spin glass has at most two infinite connected components."}],"snapshot_sha256":"c5ce70c01d8f28e12cb4a648d0e3c6f724f372357cc10682a376fbad69bbd16b"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"0d1c724862889404e4b4114d6ac373c37b99aa2b9236c01ac312a73d5dae40b6"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.674469Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T22:52:24.793560Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.804042Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.739037Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.17338/integrity.json","findings":[],"snapshot_sha256":"3790d07e71ca9778d4f41e36f8ba4c1ac38c64636a39ee22f3247d5845bc0597","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The two-replica Chayes-Machta-Redner (CMR) representation is one of the main proposed geometric signatures of spin-glass order in the short-range Edwards-Anderson model. Mean-field arguments and recent numerics suggest that the low-temperature phase should exhibit two macroscopic blue clusters carrying opposite overlap signs. We prove a rigorous structural constraint in this direction. For any translation-invariant joint Gibbs measure on disorder, two spin replicas, and CMR bond variables on Z^d, the blue subgraph contains at most two infinite connected components; if two exist, then they lie ","authors_text":"Yan Ru Pei","cross_cats":["math-ph","math.MP"],"headline":"The blue subgraph in the two-replica CMR representation of the Edwards-Anderson spin glass has at most two infinite connected components.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-17T09:15:39Z","title":"At Most Two Infinite Blue Clusters in the CMR Representation of the Edwards-Anderson Spin Glass"},"references":{"count":12,"internal_anchors":0,"resolved_work":12,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Oliver Redner, Jon Machta, and Lincoln F. Chayes. Graphical representations and cluster algorithms for critical points with fields.Physical Review E, 58(3):2749–2752, 1998","work_id":"0b691a20-96e1-4163-99ce-72a87ef348c9","year":1998},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"J. Machta, C. M. Newman, and D. L. Stein. The percolation signature of the spin glass transition.Journal of Statistical Physics, 130:113–128, 2007","work_id":"089eeaa9-10a4-4018-a658-3e44a29a24de","year":2007},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Cluster percolation in the two-dimensional Ising spin glass.Physical Review E, 107(5):054103, 2023","work_id":"90673ce2-e728-4d3c-83a4-83bc2ed6603c","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Cluster percolation in the three-dimensional±Jrandom- bond Ising model.Physical Review E, 113(2):024139, 2026","work_id":"b73f6a36-0ba1-4b87-9b97-13d3746e1b58","year":2026},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Graphical representations for Ising systems in external fields.Journal of Statistical Physics, 93:17–32, 1998","work_id":"953f748d-0011-46e7-98d5-e4cc3e6278b5","year":1998}],"snapshot_sha256":"3df44d84390f2186d993cb90ee5274979021142e15adacfeb635c0211ea62884"},"source":{"id":"2605.17338","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:46:24.075405Z","id":"90c8c680-c404-4fa5-87ad-0291815bb397","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves that the blue subgraph in the CMR representation of the short-range Edwards-Anderson model has at most two infinite clusters, which must lie in one grey cluster with opposite overlap parity if both are infinite.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The blue subgraph in the two-replica CMR representation of the Edwards-Anderson spin glass has at most two infinite connected components.","strongest_claim":"For any translation-invariant joint Gibbs measure on disorder, two spin replicas, and CMR bond variables on Z^d, the blue subgraph contains at most two infinite connected components; if two exist, then they lie in a common infinite grey cluster and belong to opposite overlap-parity classes.","weakest_assumption":"The blue-bond process lacks insertion tolerance and positive association, so the proof must rely on the full joint measure together with a finite-box merge operation and the mass-transport bound on ends of translation-invariant subgraphs rather than standard Burton-Keane or random-cluster arguments (abstract, paragraph on main obstacle)."}},"verdict_id":"90c8c680-c404-4fa5-87ad-0291815bb397"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:99f2d1147fa860cb88c00dd95b20d9e0923008fca1812b463ca8ac35bf6ba830","target":"record","created_at":"2026-05-20T00:03:52Z","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":"47bd3e21ac064883749f980709cda171fbd6a381c74c68875dde26f7090815b5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-17T09:15:39Z","title_canon_sha256":"f778baab8c051b7ff29fb83fcb3d76e4f34e28b748f21b690294047683af7a1b"},"schema_version":"1.0","source":{"id":"2605.17338","kind":"arxiv","version":1}},"canonical_sha256":"6e78e72bc725b2c85ca5cc01c91a3e5132aa2eff1b9f94e669fe4f4eccea9ee9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e78e72bc725b2c85ca5cc01c91a3e5132aa2eff1b9f94e669fe4f4eccea9ee9","first_computed_at":"2026-05-20T00:03:52.964425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:52.964425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vp7PMqjZEn9B4xSxl4J3xRXKNyNfy5nOv/yCLj9AoPgUU9kEIhaH7Mv0sQi5qHy867M0OCkXQn5x3PYtc033Cg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:52.965259Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99f2d1147fa860cb88c00dd95b20d9e0923008fca1812b463ca8ac35bf6ba830","sha256:37683af422f621a0aed94270fc64cbe10d6b9410bbd8b38f3dad48eae56315c7"],"state_sha256":"ce944de2b180df58d12c93ed8a21d59427de69be88fe529800fc98b31775e0ca"}