{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DI2RJGDBVWU7W4SEGPM3KATQMS","short_pith_number":"pith:DI2RJGDB","canonical_record":{"source":{"id":"1307.4035","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-15T18:07:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"98e6b778b7a4c2773979bf1c71db95485103fb1fe0d4ba913b70bf3568039fba","abstract_canon_sha256":"caaaa7b26ccc8fd4c60fc35a623528348130c48d34c0403dfe2cbc6951cfe9f8"},"schema_version":"1.0"},"canonical_sha256":"1a35149861ada9fb724433d9b502706484a20837b85e0136fb62e8c273c19e49","source":{"kind":"arxiv","id":"1307.4035","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4035","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4035v2","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4035","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"DI2RJGDBVWU7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DI2RJGDBVWU7W4SE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DI2RJGDB","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DI2RJGDBVWU7W4SEGPM3KATQMS","target":"record","payload":{"canonical_record":{"source":{"id":"1307.4035","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-15T18:07:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"98e6b778b7a4c2773979bf1c71db95485103fb1fe0d4ba913b70bf3568039fba","abstract_canon_sha256":"caaaa7b26ccc8fd4c60fc35a623528348130c48d34c0403dfe2cbc6951cfe9f8"},"schema_version":"1.0"},"canonical_sha256":"1a35149861ada9fb724433d9b502706484a20837b85e0136fb62e8c273c19e49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:59.032196Z","signature_b64":"qIlB83I4RcnmJAubiAEvf2Iuk4JO+juaVYyZ02LM4k1sgpITIyyzcb7uozJIf7u7V0qIG3aVwlSFDyL2+f/UAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a35149861ada9fb724433d9b502706484a20837b85e0136fb62e8c273c19e49","last_reissued_at":"2026-05-18T01:59:59.031605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:59.031605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.4035","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":"2026-05-18T01:59:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZvDkZdsUl7vbv3ecFNK9YpOBvFCN8RCWMOpu4lCn4wXiILVG19Gsq2rGGHR+6bZNskP2+xEsTbAqW9tES1XAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:22:12.911068Z"},"content_sha256":"1e3dcacc75e64fd99ef6ebb1cadcf7249f76d5de5acf99aeff3e20c3097c388d","schema_version":"1.0","event_id":"sha256:1e3dcacc75e64fd99ef6ebb1cadcf7249f76d5de5acf99aeff3e20c3097c388d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DI2RJGDBVWU7W4SEGPM3KATQMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Majority Dynamics and the Retention of Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Omer Tamuz, Ran J. Tessler","submitted_at":"2013-07-15T18:07:42Z","abstract_excerpt":"We consider a group of agents connected by a social network who participate in majority dynamics: each agent starts with an opinion in {-1,+1} and repeatedly updates it to match the opinion of the majority of its neighbors.\n  We assume that one of {-1,+1} is the \"correct\" opinion S, and consider a setting in which the initial opinions are independent conditioned on S, and biased towards it. They hence contain enough information to reconstruct S with high probability. We ask whether it is still possible to reconstruct S from the agents' opinions after many rounds of updates.\n  While this is not"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4035","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":"2026-05-18T01:59:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mC0x0ih+1qtd2ib1885bFXSF2XwU1s2G50BkKKb3k1N4E9Jph53XTQw2EYw5kAlsjR/+JryLwSbWof2zqA+iBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:22:12.911427Z"},"content_sha256":"b06cf7412cffada26b62f3e4e943fd785d777d31f084451780a7be876066dff6","schema_version":"1.0","event_id":"sha256:b06cf7412cffada26b62f3e4e943fd785d777d31f084451780a7be876066dff6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DI2RJGDBVWU7W4SEGPM3KATQMS/bundle.json","state_url":"https://pith.science/pith/DI2RJGDBVWU7W4SEGPM3KATQMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DI2RJGDBVWU7W4SEGPM3KATQMS/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":"2026-06-05T09:22:12Z","links":{"resolver":"https://pith.science/pith/DI2RJGDBVWU7W4SEGPM3KATQMS","bundle":"https://pith.science/pith/DI2RJGDBVWU7W4SEGPM3KATQMS/bundle.json","state":"https://pith.science/pith/DI2RJGDBVWU7W4SEGPM3KATQMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DI2RJGDBVWU7W4SEGPM3KATQMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DI2RJGDBVWU7W4SEGPM3KATQMS","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":"caaaa7b26ccc8fd4c60fc35a623528348130c48d34c0403dfe2cbc6951cfe9f8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-15T18:07:42Z","title_canon_sha256":"98e6b778b7a4c2773979bf1c71db95485103fb1fe0d4ba913b70bf3568039fba"},"schema_version":"1.0","source":{"id":"1307.4035","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4035","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4035v2","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4035","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"DI2RJGDBVWU7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DI2RJGDBVWU7W4SE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DI2RJGDB","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:b06cf7412cffada26b62f3e4e943fd785d777d31f084451780a7be876066dff6","target":"graph","created_at":"2026-05-18T01:59:59Z","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 consider a group of agents connected by a social network who participate in majority dynamics: each agent starts with an opinion in {-1,+1} and repeatedly updates it to match the opinion of the majority of its neighbors.\n  We assume that one of {-1,+1} is the \"correct\" opinion S, and consider a setting in which the initial opinions are independent conditioned on S, and biased towards it. They hence contain enough information to reconstruct S with high probability. We ask whether it is still possible to reconstruct S from the agents' opinions after many rounds of updates.\n  While this is not","authors_text":"Omer Tamuz, Ran J. Tessler","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-15T18:07:42Z","title":"Majority Dynamics and the Retention of Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4035","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":"sha256:1e3dcacc75e64fd99ef6ebb1cadcf7249f76d5de5acf99aeff3e20c3097c388d","target":"record","created_at":"2026-05-18T01:59:59Z","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":"caaaa7b26ccc8fd4c60fc35a623528348130c48d34c0403dfe2cbc6951cfe9f8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-15T18:07:42Z","title_canon_sha256":"98e6b778b7a4c2773979bf1c71db95485103fb1fe0d4ba913b70bf3568039fba"},"schema_version":"1.0","source":{"id":"1307.4035","kind":"arxiv","version":2}},"canonical_sha256":"1a35149861ada9fb724433d9b502706484a20837b85e0136fb62e8c273c19e49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a35149861ada9fb724433d9b502706484a20837b85e0136fb62e8c273c19e49","first_computed_at":"2026-05-18T01:59:59.031605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:59.031605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qIlB83I4RcnmJAubiAEvf2Iuk4JO+juaVYyZ02LM4k1sgpITIyyzcb7uozJIf7u7V0qIG3aVwlSFDyL2+f/UAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:59.032196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4035","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e3dcacc75e64fd99ef6ebb1cadcf7249f76d5de5acf99aeff3e20c3097c388d","sha256:b06cf7412cffada26b62f3e4e943fd785d777d31f084451780a7be876066dff6"],"state_sha256":"4eb89a2c55e162ab3e974f1aed106d84167796c63d4016d94a7f9d7f77b7260d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5Tn5/BGPT2z9Fg3u9MUfIN+mxe8thAwMQQuckmszIDCN3WpRohMUI5BSt/zKsa5XvTxFeg7ZY+c4VUJU4DUAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:22:12.913683Z","bundle_sha256":"2912165ee958e97024b80c5802b94b8cfceecffe2c80fe788a8db3bafe9e2b79"}}