{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IQ56UF7ENPGYLTJSXSC5KBTDGD","short_pith_number":"pith:IQ56UF7E","canonical_record":{"source":{"id":"1212.4303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-18T10:54:19Z","cross_cats_sorted":["math.CO","math.PR","physics.soc-ph"],"title_canon_sha256":"a411560468800aba2f782ac0cb5742b80066202b000b3267f2d45493ceacde75","abstract_canon_sha256":"3112872d6fbb93395b400b315c3f2b8d40146812f847ec00e1b42b0a1ba9e105"},"schema_version":"1.0"},"canonical_sha256":"443bea17e46bcd85cd32bc85d5066330fa3deffc33b601f3f301cf7bccf06e79","source":{"kind":"arxiv","id":"1212.4303","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4303","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4303v2","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4303","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"IQ56UF7ENPGY","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IQ56UF7ENPGYLTJS","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IQ56UF7E","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IQ56UF7ENPGYLTJSXSC5KBTDGD","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-18T10:54:19Z","cross_cats_sorted":["math.CO","math.PR","physics.soc-ph"],"title_canon_sha256":"a411560468800aba2f782ac0cb5742b80066202b000b3267f2d45493ceacde75","abstract_canon_sha256":"3112872d6fbb93395b400b315c3f2b8d40146812f847ec00e1b42b0a1ba9e105"},"schema_version":"1.0"},"canonical_sha256":"443bea17e46bcd85cd32bc85d5066330fa3deffc33b601f3f301cf7bccf06e79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:40.477817Z","signature_b64":"Zx8jUu50Z7FeRUOa4zrX7avA9UmvngXNYnCVoPjrE6OuefT7T/6eIPVxUqbuGqc4CJqZHnjkq1PNfL65FQaMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"443bea17e46bcd85cd32bc85d5066330fa3deffc33b601f3f301cf7bccf06e79","last_reissued_at":"2026-05-18T03:37:40.477299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:40.477299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4303","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":"2026-05-18T03:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r9h8G2MJtrBBtCi5uSrjcoKT4z3G43qEDHCCsV+0mAxtxtY96xSKlxVs8L88oomCeF3nQ6SXjsHcIfVJPd+jAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:33:36.129339Z"},"content_sha256":"6730daa540f4c4b2c9c21970dde5f5c9fb1ab2fb86227382049ebdc7838fec0c","schema_version":"1.0","event_id":"sha256:6730daa540f4c4b2c9c21970dde5f5c9fb1ab2fb86227382049ebdc7838fec0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IQ56UF7ENPGYLTJSXSC5KBTDGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the notion of balance in social network analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Peter Hegarty","submitted_at":"2012-12-18T10:54:19Z","abstract_excerpt":"The notion of \"balance\" is fundamental for sociologists who study social networks. In formal mathematical terms, it concerns the distribution of triad configurations in actual networks compared to random networks of the same edge density. On reading Charles Kadushin's recent book \"Understanding Social Networks\", we were struck by the amount of confusion in the presentation of this concept in the early sections of the book. This confusion seems to lie behind his flawed analysis of a classical empirical data set, namely the karate club graph of Zachary. Our goal here is twofold. Firstly, we pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4303","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":"2026-05-18T03:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t/FvIX+NohLDsG2sjBK6RqX0urKKEupzYJHo1O3aMYjUAXXjbZBGi+9oNPLWlS++sIIy38TOto4nelEtWo70Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:33:36.129699Z"},"content_sha256":"8141032bafd51817dab0f7c7ffe4e4159595c91080977cfa21883f0b5ec13fba","schema_version":"1.0","event_id":"sha256:8141032bafd51817dab0f7c7ffe4e4159595c91080977cfa21883f0b5ec13fba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IQ56UF7ENPGYLTJSXSC5KBTDGD/bundle.json","state_url":"https://pith.science/pith/IQ56UF7ENPGYLTJSXSC5KBTDGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IQ56UF7ENPGYLTJSXSC5KBTDGD/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":"2026-06-24T20:33:36Z","links":{"resolver":"https://pith.science/pith/IQ56UF7ENPGYLTJSXSC5KBTDGD","bundle":"https://pith.science/pith/IQ56UF7ENPGYLTJSXSC5KBTDGD/bundle.json","state":"https://pith.science/pith/IQ56UF7ENPGYLTJSXSC5KBTDGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IQ56UF7ENPGYLTJSXSC5KBTDGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IQ56UF7ENPGYLTJSXSC5KBTDGD","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":"3112872d6fbb93395b400b315c3f2b8d40146812f847ec00e1b42b0a1ba9e105","cross_cats_sorted":["math.CO","math.PR","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-18T10:54:19Z","title_canon_sha256":"a411560468800aba2f782ac0cb5742b80066202b000b3267f2d45493ceacde75"},"schema_version":"1.0","source":{"id":"1212.4303","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4303","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4303v2","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4303","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"IQ56UF7ENPGY","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IQ56UF7ENPGYLTJS","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IQ56UF7E","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:8141032bafd51817dab0f7c7ffe4e4159595c91080977cfa21883f0b5ec13fba","target":"graph","created_at":"2026-05-18T03:37:40Z","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":"The notion of \"balance\" is fundamental for sociologists who study social networks. In formal mathematical terms, it concerns the distribution of triad configurations in actual networks compared to random networks of the same edge density. On reading Charles Kadushin's recent book \"Understanding Social Networks\", we were struck by the amount of confusion in the presentation of this concept in the early sections of the book. This confusion seems to lie behind his flawed analysis of a classical empirical data set, namely the karate club graph of Zachary. Our goal here is twofold. Firstly, we pres","authors_text":"Peter Hegarty","cross_cats":["math.CO","math.PR","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-18T10:54:19Z","title":"On the notion of balance in social network analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4303","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":"sha256:6730daa540f4c4b2c9c21970dde5f5c9fb1ab2fb86227382049ebdc7838fec0c","target":"record","created_at":"2026-05-18T03:37:40Z","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":"3112872d6fbb93395b400b315c3f2b8d40146812f847ec00e1b42b0a1ba9e105","cross_cats_sorted":["math.CO","math.PR","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-18T10:54:19Z","title_canon_sha256":"a411560468800aba2f782ac0cb5742b80066202b000b3267f2d45493ceacde75"},"schema_version":"1.0","source":{"id":"1212.4303","kind":"arxiv","version":2}},"canonical_sha256":"443bea17e46bcd85cd32bc85d5066330fa3deffc33b601f3f301cf7bccf06e79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"443bea17e46bcd85cd32bc85d5066330fa3deffc33b601f3f301cf7bccf06e79","first_computed_at":"2026-05-18T03:37:40.477299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:40.477299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zx8jUu50Z7FeRUOa4zrX7avA9UmvngXNYnCVoPjrE6OuefT7T/6eIPVxUqbuGqc4CJqZHnjkq1PNfL65FQaMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:40.477817Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4303","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6730daa540f4c4b2c9c21970dde5f5c9fb1ab2fb86227382049ebdc7838fec0c","sha256:8141032bafd51817dab0f7c7ffe4e4159595c91080977cfa21883f0b5ec13fba"],"state_sha256":"6b80f94df1b0ce6c8d3a868fce9b9d9ef4f07bd6ef44d461b4297803681146ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"POkF3z3Eo4MCfhqSsm2j6au5HawxLK0iDo2bkdZqA+v3p+OgPq0RPHFCJMqFGXXzS/RSmztNTkvrBrKwG9AlCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:33:36.131728Z","bundle_sha256":"539f7bee13c52c8efdd6ce3df31928073e76497bcfa69b2f619cf0116f945f3a"}}