{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:DXEXUDPWQM5TDLFUY52FJAC3V6","short_pith_number":"pith:DXEXUDPW","schema_version":"1.0","canonical_sha256":"1dc97a0df6833b31acb4c77454805bafa65557a50216520192727452a4e9d61b","source":{"kind":"arxiv","id":"1201.0412","version":1},"attestation_state":"computed","paper":{"title":"The effect of clusterings on the equilibrium states of local majority-rule: Occurrence probability and robustness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jinn-Wen Wu, Ming-Chang Huang, Yu-Pin Luo","submitted_at":"2012-01-02T01:48:34Z","abstract_excerpt":"The equilibrium states associated with the local majority-rule are divided into three classes, the states of system-wide coordination, the trapped states, and the states of period-2. The effect of clustering coefficient on the occurrence probability of the states of three classes is analyzed numerically for Watts-Strogatz and scale-free networks. We further study the effect of clustering coefficient on the robustness for the states of each class by proposing a stochastic local majority-rule. The states of period-2 are found to be easy to break up, and the trapped states are most robust among t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.0412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-01-02T01:48:34Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"b19f1656611925e9304366743149c89ed44f24638743fb2f40e9edfaa9d3edbc","abstract_canon_sha256":"0118d8e0dca14a1d05c8a1c95a014ba1e88eb821d5d42e5b8a932b4414a150ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:17.586285Z","signature_b64":"ZMVVInPWlaLcVhjoo062a8GjQ3ar6TFywpTQVfAAZ9BMOW30GckGhCSXbrF+MCng+rfYopiUoAabQADIuNfZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dc97a0df6833b31acb4c77454805bafa65557a50216520192727452a4e9d61b","last_reissued_at":"2026-05-18T04:05:17.585619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:17.585619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The effect of clusterings on the equilibrium states of local majority-rule: Occurrence probability and robustness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jinn-Wen Wu, Ming-Chang Huang, Yu-Pin Luo","submitted_at":"2012-01-02T01:48:34Z","abstract_excerpt":"The equilibrium states associated with the local majority-rule are divided into three classes, the states of system-wide coordination, the trapped states, and the states of period-2. The effect of clustering coefficient on the occurrence probability of the states of three classes is analyzed numerically for Watts-Strogatz and scale-free networks. We further study the effect of clustering coefficient on the robustness for the states of each class by proposing a stochastic local majority-rule. The states of period-2 are found to be easy to break up, and the trapped states are most robust among t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0412","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1201.0412","created_at":"2026-05-18T04:05:17.585745+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.0412v1","created_at":"2026-05-18T04:05:17.585745+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0412","created_at":"2026-05-18T04:05:17.585745+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXEXUDPWQM5T","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXEXUDPWQM5TDLFU","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXEXUDPW","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6","json":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6.json","graph_json":"https://pith.science/api/pith-number/DXEXUDPWQM5TDLFUY52FJAC3V6/graph.json","events_json":"https://pith.science/api/pith-number/DXEXUDPWQM5TDLFUY52FJAC3V6/events.json","paper":"https://pith.science/paper/DXEXUDPW"},"agent_actions":{"view_html":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6","download_json":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6.json","view_paper":"https://pith.science/paper/DXEXUDPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.0412&json=true","fetch_graph":"https://pith.science/api/pith-number/DXEXUDPWQM5TDLFUY52FJAC3V6/graph.json","fetch_events":"https://pith.science/api/pith-number/DXEXUDPWQM5TDLFUY52FJAC3V6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6/action/storage_attestation","attest_author":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6/action/author_attestation","sign_citation":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6/action/citation_signature","submit_replication":"https://pith.science/pith/DXEXUDPWQM5TDLFUY52FJAC3V6/action/replication_record"}},"created_at":"2026-05-18T04:05:17.585745+00:00","updated_at":"2026-05-18T04:05:17.585745+00:00"}