{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QQ3QNQC76GVQIGXZL7B6HMBYTO","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":"c45f4144e1366183f0be91e69b8f27cd252dac980eef8d2c7139f12f2c0cadcf","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-01-21T20:37:31Z","title_canon_sha256":"fb7b7a81fd5345c16930bbb670492ff06ad35b61d934a4a27fa5678c899eb543"},"schema_version":"1.0","source":{"id":"1101.4227","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4227","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4227v3","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4227","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"QQ3QNQC76GVQ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QQ3QNQC76GVQIGXZ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QQ3QNQC7","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:12d9ba5a0737d4e257991aeb7b744a5fdb4a25487c30d14911efb6b3f4c300bb","target":"graph","created_at":"2026-05-18T04:09:56Z","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":"We theoretically study semi-supervised clustering in sparse graphs in the presence of pairwise constraints on the cluster assignments of nodes. We focus on bi-cluster graphs, and study the impact of semi-supervision for varying constraint density and overlap between the clusters. Recent results for unsupervised clustering in sparse graphs indicate that there is a critical ratio of within-cluster and between-cluster connectivities below which clusters cannot be recovered with better than random accuracy. The goal of this paper is to examine the impact of pairwise constraints on the clustering a","authors_text":"Aram Galstyan, Armen E. Allahverdyan, Greg Ver Steeg","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-01-21T20:37:31Z","title":"Statistical Mechanics of Semi-Supervised Clustering in Sparse Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4227","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":"sha256:78fba9f954bc2d20170d580850819ae2a37ad19d29ed9cb441a6c22aafefe6ae","target":"record","created_at":"2026-05-18T04:09:56Z","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":"c45f4144e1366183f0be91e69b8f27cd252dac980eef8d2c7139f12f2c0cadcf","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-01-21T20:37:31Z","title_canon_sha256":"fb7b7a81fd5345c16930bbb670492ff06ad35b61d934a4a27fa5678c899eb543"},"schema_version":"1.0","source":{"id":"1101.4227","kind":"arxiv","version":3}},"canonical_sha256":"843706c05ff1ab041af95fc3e3b0389b917bc4c0ed0b031ae87aaeb2e22e884a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"843706c05ff1ab041af95fc3e3b0389b917bc4c0ed0b031ae87aaeb2e22e884a","first_computed_at":"2026-05-18T04:09:56.442273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:56.442273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m2YQHwsoc4oHiyVYg3oHu9j2gKds10alQe+qy7/DzX+fZHLFW6r9vRfuhcVDjkojHC72R42ZSpZ8hdL1u2DnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:56.442953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4227","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78fba9f954bc2d20170d580850819ae2a37ad19d29ed9cb441a6c22aafefe6ae","sha256:12d9ba5a0737d4e257991aeb7b744a5fdb4a25487c30d14911efb6b3f4c300bb"],"state_sha256":"cdb4aa144e717d6b8abb7fe042c7e35dc039f26daf0ea2b74d39bfd0bfecfe3f"}