{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RU3ZT7QJSWLG4YSXQTMKMP2EEI","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":"d428630b6020cdb94a882a83e425002f9b9f0bfc0f939cc9eb6d7d0d72781640","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2025-07-03T13:53:20Z","title_canon_sha256":"868552ca3ad8d579793b5cbf59e11b1831ecde3001489e397350cb39a6cf0cee"},"schema_version":"1.0","source":{"id":"2507.02627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.02627","created_at":"2026-07-05T11:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"2507.02627v1","created_at":"2026-07-05T11:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.02627","created_at":"2026-07-05T11:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"RU3ZT7QJSWLG","created_at":"2026-07-05T11:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"RU3ZT7QJSWLG4YSX","created_at":"2026-07-05T11:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"RU3ZT7QJ","created_at":"2026-07-05T11:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:07e179e3b61f4f618ddd7f65cb544f9c65142b8f06b123ace1674e0dc3a6db97","target":"graph","created_at":"2026-07-05T11:31:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.02627/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the generalised friendship paradox, focussing on the number of triangles at a vertex as the relevant attribute. We show that, contrary to the setting where the attribute is the number of edges at a vertex or the number of wedges at a vertex, the average friendship-bias of the number of triangles at a vertex is not always non-negative. We identify classes of finite deterministic graphs for which the bias is non-negative, and provide examples of finite deterministic graphs for which it is not. For certain classes of sparse and dense random graphs, we compute the scaling of the bias i","authors_text":"Bishakh Bhattacharya, Frank den Hollander, Nitya Gadhiwala, Pradeeptha R Jain, Tejashree Subramanya","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2025-07-03T13:53:20Z","title":"The Triangle Friendship Paradox"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.02627","kind":"arxiv","version":1},"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":"sha256:60528fe0922a3f08eadb8eb23780c17b2e6206c6a1c13de0d39162cff38eeefd","target":"record","created_at":"2026-07-05T11:31:31Z","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":"d428630b6020cdb94a882a83e425002f9b9f0bfc0f939cc9eb6d7d0d72781640","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2025-07-03T13:53:20Z","title_canon_sha256":"868552ca3ad8d579793b5cbf59e11b1831ecde3001489e397350cb39a6cf0cee"},"schema_version":"1.0","source":{"id":"2507.02627","kind":"arxiv","version":1}},"canonical_sha256":"8d3799fe0995966e625784d8a63f442232807f68a92e353a781cd5deb6aa7c6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d3799fe0995966e625784d8a63f442232807f68a92e353a781cd5deb6aa7c6c","first_computed_at":"2026-07-05T11:31:31.991541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:31.991541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mcNSXDsIJcpOJQsCJAJuphjkENOUJUoW1aCe2BnQ8gThkaMEfZcxvaP7EpIYr/PGE+qdmB3Qgpeuh3Zl4DltDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:31.992007Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.02627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60528fe0922a3f08eadb8eb23780c17b2e6206c6a1c13de0d39162cff38eeefd","sha256:07e179e3b61f4f618ddd7f65cb544f9c65142b8f06b123ace1674e0dc3a6db97"],"state_sha256":"e25d0a10c4ded21b7fb433fb08b651585ca0d89e4bfe14b27bd3262ceb10b237"}