{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Y6SSQDKHTVQ5Q4D2FQG7DHEOKC","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":"f3861f703e20d9c366c7e615f0d958515b671a66842157ad0d2ad9eb70d2536f","cross_cats_sorted":["cond-mat.stat-mech","cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-05-26T04:42:53Z","title_canon_sha256":"2c788c5fa81e789058d5f210bf6af62adfc0dfde4669a42453c73f21b3af18d8"},"schema_version":"1.0","source":{"id":"1505.06802","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06802","created_at":"2026-05-18T01:22:39Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06802v3","created_at":"2026-05-18T01:22:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06802","created_at":"2026-05-18T01:22:39Z"},{"alias_kind":"pith_short_12","alias_value":"Y6SSQDKHTVQ5","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y6SSQDKHTVQ5Q4D2","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y6SSQDKH","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:05d318feb5babdc2e6854674830689c7df24b607e97b0e305f23e4d3b052b749","target":"graph","created_at":"2026-05-18T01:22:39Z","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 study the solution space structure of model RB, a standard prototype of Constraint Satisfaction Problem (CSPs) with growing domains. Using rigorous the first and the second moment method, we show that in the solvable phase close to the satisfiability transition, solutions are clustered into exponential number of well-separated clusters, with each cluster contains sub-exponential number of solutions. As a consequence, the system has a clustering (dynamical) transition but no condensation transition. This picture of phase diagram is different from other classic random CSPs with ","authors_text":"Fuzhou Gong, Pan Zhang, Tian Liu, Wei Xu","cross_cats":["cond-mat.stat-mech","cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-05-26T04:42:53Z","title":"Solution space structure of random constraint satisfaction problems with growing domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06802","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":"sha256:57c07a5bdf9afed1b9d08c157c244fca195635c15bf83fa71b13c1692733268c","target":"record","created_at":"2026-05-18T01:22:39Z","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":"f3861f703e20d9c366c7e615f0d958515b671a66842157ad0d2ad9eb70d2536f","cross_cats_sorted":["cond-mat.stat-mech","cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-05-26T04:42:53Z","title_canon_sha256":"2c788c5fa81e789058d5f210bf6af62adfc0dfde4669a42453c73f21b3af18d8"},"schema_version":"1.0","source":{"id":"1505.06802","kind":"arxiv","version":3}},"canonical_sha256":"c7a5280d479d61d8707a2c0df19c8e5082f321dfc87505a7acdaee8022160f3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7a5280d479d61d8707a2c0df19c8e5082f321dfc87505a7acdaee8022160f3e","first_computed_at":"2026-05-18T01:22:39.987214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:39.987214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z5oPhtHvH/7W+hKdFIiY4/LmyBAfehMoBXhI5Dljxa7zBwDHmd270RH4zQIqZINtOygo2j1kkD8TMDoESTLWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:39.987644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06802","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57c07a5bdf9afed1b9d08c157c244fca195635c15bf83fa71b13c1692733268c","sha256:05d318feb5babdc2e6854674830689c7df24b607e97b0e305f23e4d3b052b749"],"state_sha256":"1d0f48525ff9e962265c02091e4345f78582838f187993e832c1db2c1dcef1f8"}