{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V22GGL42OD7MIWJSNTHHNQAFGJ","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":"dda936a987f110e3ad01ddbe83a27520a5a2e84885fd92d6d490692788e2425c","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-06T00:52:56Z","title_canon_sha256":"32d5ae7dd155c9a02dd5280895f5d9c79ee6dee67914cd1f18f63ad18c752766"},"schema_version":"1.0","source":{"id":"1501.01049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01049","created_at":"2026-05-18T02:30:00Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01049v1","created_at":"2026-05-18T02:30:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01049","created_at":"2026-05-18T02:30:00Z"},{"alias_kind":"pith_short_12","alias_value":"V22GGL42OD7M","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V22GGL42OD7MIWJS","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V22GGL42","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:5e3d78f4a17f4deb6d83c08eb05c795994f1c929b6a16c4c6eeaf90fd28f2a9e","target":"graph","created_at":"2026-05-18T02:30:00Z","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":"Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\\{p_k\\}$ for situations in which a `joiner particle' $k$ pays some form of price to enter a `community' of size $k-1$, where costs are subject to economies-of-scale (EOS). Maximizing the Boltzmann-Gibbs-Shannon entropy subject to this energy-like constraint predicts a distribution having a power-law tail; it reduces to the Boltzmann distribution in the absence of EOS. We show that th","authors_text":"Jack Peterson, Ken A. Dill, Purushottam D. Dixit","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-06T00:52:56Z","title":"A maximum entropy framework for non-exponential distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01049","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:c50b6de8b985c8891c23ef9913bcb21b45f309231e755debbbdfe9d65d8468e7","target":"record","created_at":"2026-05-18T02:30:00Z","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":"dda936a987f110e3ad01ddbe83a27520a5a2e84885fd92d6d490692788e2425c","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-06T00:52:56Z","title_canon_sha256":"32d5ae7dd155c9a02dd5280895f5d9c79ee6dee67914cd1f18f63ad18c752766"},"schema_version":"1.0","source":{"id":"1501.01049","kind":"arxiv","version":1}},"canonical_sha256":"aeb4632f9a70fec459326cce76c00532736c0bdf84c25be6ce5779f9708b0650","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeb4632f9a70fec459326cce76c00532736c0bdf84c25be6ce5779f9708b0650","first_computed_at":"2026-05-18T02:30:00.384072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:00.384072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"94svzwDISuRs04sTlA/eIb6xSdydy6xufzUtGalGZeufzoGq1E1t33F7mruxL5/G0ZTlTc3eZMYjLUSRm08MDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:00.384426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c50b6de8b985c8891c23ef9913bcb21b45f309231e755debbbdfe9d65d8468e7","sha256:5e3d78f4a17f4deb6d83c08eb05c795994f1c929b6a16c4c6eeaf90fd28f2a9e"],"state_sha256":"f803b97215899af373c91cbcc008cf40559d83cdf4a3da4468dc3f71749cd8d3"}