{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SUWRPH6OD22IVBDXMBF4DANIVU","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":"eced8dc5fdf626462b5a5c117954f33ac021c000dc5acff22aaf85b9e6749038","cross_cats_sorted":["physics.data-an"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2026-07-24T11:00:48Z","title_canon_sha256":"9a2ad1d7498eb08091b00bcb296d057446976d5244696b784b9d8d6ce239e4c4"},"schema_version":"1.0","source":{"id":"2607.22189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.22189","created_at":"2026-07-27T01:20:53Z"},{"alias_kind":"arxiv_version","alias_value":"2607.22189v1","created_at":"2026-07-27T01:20:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22189","created_at":"2026-07-27T01:20:53Z"},{"alias_kind":"pith_short_12","alias_value":"SUWRPH6OD22I","created_at":"2026-07-27T01:20:53Z"},{"alias_kind":"pith_short_16","alias_value":"SUWRPH6OD22IVBDX","created_at":"2026-07-27T01:20:53Z"},{"alias_kind":"pith_short_8","alias_value":"SUWRPH6O","created_at":"2026-07-27T01:20:53Z"}],"graph_snapshots":[{"event_id":"sha256:f34c047e0cb4208d70c002a941faa05026b8d90e26c71e449488c5e1516d1b3f","target":"graph","created_at":"2026-07-27T01:20:53Z","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/2607.22189/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Academic departments are the primary unit of scholarship and education at universities, and they vary vastly in their sizes. However, the consequences and natural dynamics of department size are poorly understood. Small departments face disproportionate teaching and administrative overhead per faculty member, while large ones face coordination costs and thematic incoherence. Here, we characterize and model the dynamics of academic department sizes using $14,000$ U.S.-based departments in eight academic domains. Across all domains, similar broad-tailed distributions reveal a common size range f","authors_text":"Aaron Clauset, Daniel B. Larremore, Fariba Karimi, Gerardo I\\~niguez, Jan Bachmann, Lisette Esp\\'in-Noboa","cross_cats":["physics.data-an"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2026-07-24T11:00:48Z","title":"How large should academic departments be?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22189","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:b787c4fd2334c6a14bc9c1765a552b5315060b3af9dbb7b3eb0796c8476da73c","target":"record","created_at":"2026-07-27T01:20:53Z","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":"eced8dc5fdf626462b5a5c117954f33ac021c000dc5acff22aaf85b9e6749038","cross_cats_sorted":["physics.data-an"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2026-07-24T11:00:48Z","title_canon_sha256":"9a2ad1d7498eb08091b00bcb296d057446976d5244696b784b9d8d6ce239e4c4"},"schema_version":"1.0","source":{"id":"2607.22189","kind":"arxiv","version":1}},"canonical_sha256":"952d179fce1eb48a8477604bc181a8ad3403a8efae7dabfd3e118d05688a86f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"952d179fce1eb48a8477604bc181a8ad3403a8efae7dabfd3e118d05688a86f2","first_computed_at":"2026-07-27T01:20:53.061370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T01:20:53.061370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nWobCTWrAoCgZbh7bf/SADuc3UvqZesUkU80ARgu6BYXkvABPZ3Gsj/huLJ9uIH3ZqDIxUdEj38IuJe0cSdsBw==","signature_status":"signed_v1","signed_at":"2026-07-27T01:20:53.062300Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.22189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b787c4fd2334c6a14bc9c1765a552b5315060b3af9dbb7b3eb0796c8476da73c","sha256:f34c047e0cb4208d70c002a941faa05026b8d90e26c71e449488c5e1516d1b3f"],"state_sha256":"baceccb7c20eb856f51006fc32715fbc982517792a82605af2b699aecf4d3226"}