{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NSIQJE6TKQY7HDX7V57LQJBEQW","short_pith_number":"pith:NSIQJE6T","canonical_record":{"source":{"id":"1102.3931","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-02-18T22:30:01Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"1069f241f6ba223f5a8d9074788557c120617295b6ff51ad29a14d9be4ca4657","abstract_canon_sha256":"9f5bcef600b6062652117e6627d7ae17f87bb4a386ba02220d4981c70c49bd23"},"schema_version":"1.0"},"canonical_sha256":"6c910493d35431f38effaf7eb8242485a284e61d5ad7d2e4d12304c192e76564","source":{"kind":"arxiv","id":"1102.3931","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3931","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3931v2","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3931","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"NSIQJE6TKQY7","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NSIQJE6TKQY7HDX7","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NSIQJE6T","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NSIQJE6TKQY7HDX7V57LQJBEQW","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3931","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-02-18T22:30:01Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"1069f241f6ba223f5a8d9074788557c120617295b6ff51ad29a14d9be4ca4657","abstract_canon_sha256":"9f5bcef600b6062652117e6627d7ae17f87bb4a386ba02220d4981c70c49bd23"},"schema_version":"1.0"},"canonical_sha256":"6c910493d35431f38effaf7eb8242485a284e61d5ad7d2e4d12304c192e76564","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:06.544520Z","signature_b64":"/90h2ENjIuxI3tFpCZs1qs+iGgoCuMBvgKLAz2Yky9fP2/VwfFMBO6Jpch/RVdmZbYgI8R3SOltXJLVnwV5QDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c910493d35431f38effaf7eb8242485a284e61d5ad7d2e4d12304c192e76564","last_reissued_at":"2026-05-18T04:15:06.543795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:06.543795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3931","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:15:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juBx8fPytGI55hkmbMl+s9ICEtGzcdYerkNLWfoSucMLqtL5CY/GpZLbQ+xnNOTRYbeDYx9exZryVZi9ldQNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:25:31.867956Z"},"content_sha256":"441d1307d56ecb2d96333501ccaa50109814cac2801d24bb84e0d323b6a63d3c","schema_version":"1.0","event_id":"sha256:441d1307d56ecb2d96333501ccaa50109814cac2801d24bb84e0d323b6a63d3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NSIQJE6TKQY7HDX7V57LQJBEQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Social consensus through the influence of committed minorities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"B. K. Szymanski, C. Lim, G. Korniss, J. Xie, S. Sreenivasan, W. Zhang","submitted_at":"2011-02-18T22:30:01Z","abstract_excerpt":"We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p_c \\approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c \\sim \\exp(\\alpha(p)N), while for p > p_c, T_c \\sim \\ln N. We conclude with simulation results f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3931","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:15:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0+DtMJbCP7Wlbcmt0nKgi3ViSUGDcrJYyNSxStpDwPdLFVAoT7E5jRGZepdBMMo1+t2pH0B/wAvIdc4r/NQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:25:31.868656Z"},"content_sha256":"12a894ea0a9c6711e26d55b73349b58ba6a4ac66263daf6636e7b1f395da234a","schema_version":"1.0","event_id":"sha256:12a894ea0a9c6711e26d55b73349b58ba6a4ac66263daf6636e7b1f395da234a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSIQJE6TKQY7HDX7V57LQJBEQW/bundle.json","state_url":"https://pith.science/pith/NSIQJE6TKQY7HDX7V57LQJBEQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSIQJE6TKQY7HDX7V57LQJBEQW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T15:25:31Z","links":{"resolver":"https://pith.science/pith/NSIQJE6TKQY7HDX7V57LQJBEQW","bundle":"https://pith.science/pith/NSIQJE6TKQY7HDX7V57LQJBEQW/bundle.json","state":"https://pith.science/pith/NSIQJE6TKQY7HDX7V57LQJBEQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSIQJE6TKQY7HDX7V57LQJBEQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NSIQJE6TKQY7HDX7V57LQJBEQW","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":"9f5bcef600b6062652117e6627d7ae17f87bb4a386ba02220d4981c70c49bd23","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-02-18T22:30:01Z","title_canon_sha256":"1069f241f6ba223f5a8d9074788557c120617295b6ff51ad29a14d9be4ca4657"},"schema_version":"1.0","source":{"id":"1102.3931","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3931","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3931v2","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3931","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"NSIQJE6TKQY7","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NSIQJE6TKQY7HDX7","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NSIQJE6T","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:12a894ea0a9c6711e26d55b73349b58ba6a4ac66263daf6636e7b1f395da234a","target":"graph","created_at":"2026-05-18T04:15:06Z","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 show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p_c \\approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c \\sim \\exp(\\alpha(p)N), while for p > p_c, T_c \\sim \\ln N. We conclude with simulation results f","authors_text":"B. K. Szymanski, C. Lim, G. Korniss, J. Xie, S. Sreenivasan, W. Zhang","cross_cats":["cond-mat.stat-mech","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-02-18T22:30:01Z","title":"Social consensus through the influence of committed minorities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3931","kind":"arxiv","version":2},"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":"sha256:441d1307d56ecb2d96333501ccaa50109814cac2801d24bb84e0d323b6a63d3c","target":"record","created_at":"2026-05-18T04:15:06Z","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":"9f5bcef600b6062652117e6627d7ae17f87bb4a386ba02220d4981c70c49bd23","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-02-18T22:30:01Z","title_canon_sha256":"1069f241f6ba223f5a8d9074788557c120617295b6ff51ad29a14d9be4ca4657"},"schema_version":"1.0","source":{"id":"1102.3931","kind":"arxiv","version":2}},"canonical_sha256":"6c910493d35431f38effaf7eb8242485a284e61d5ad7d2e4d12304c192e76564","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c910493d35431f38effaf7eb8242485a284e61d5ad7d2e4d12304c192e76564","first_computed_at":"2026-05-18T04:15:06.543795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:06.543795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/90h2ENjIuxI3tFpCZs1qs+iGgoCuMBvgKLAz2Yky9fP2/VwfFMBO6Jpch/RVdmZbYgI8R3SOltXJLVnwV5QDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:06.544520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3931","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:441d1307d56ecb2d96333501ccaa50109814cac2801d24bb84e0d323b6a63d3c","sha256:12a894ea0a9c6711e26d55b73349b58ba6a4ac66263daf6636e7b1f395da234a"],"state_sha256":"f1e89e79431dc5e695e13f5ee1a3d7be7382f31740ab1c95ffac25f7d6eeec25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xz1Szm01i85/s2YN7Pn92uVvBPvw8P7EDroRVDHz2JpyCN3/GgxyBpmVN0aQ7PdqcEjQwnQycKyMsDF/gGY+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:25:31.871801Z","bundle_sha256":"9de7219c78c2b3fa809cf95501cac8af11e39fe5d25989a974d84e778892a132"}}