{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:V22GGL42OD7MIWJSNTHHNQAFGJ","short_pith_number":"pith:V22GGL42","schema_version":"1.0","canonical_sha256":"aeb4632f9a70fec459326cce76c00532736c0bdf84c25be6ce5779f9708b0650","source":{"kind":"arxiv","id":"1501.01049","version":1},"attestation_state":"computed","paper":{"title":"A maximum entropy framework for non-exponential distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.soc-ph","authors_text":"Jack Peterson, Ken A. Dill, Purushottam D. Dixit","submitted_at":"2015-01-06T00:52:56Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.01049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-06T00:52:56Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"32d5ae7dd155c9a02dd5280895f5d9c79ee6dee67914cd1f18f63ad18c752766","abstract_canon_sha256":"dda936a987f110e3ad01ddbe83a27520a5a2e84885fd92d6d490692788e2425c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:00.384426Z","signature_b64":"94svzwDISuRs04sTlA/eIb6xSdydy6xufzUtGalGZeufzoGq1E1t33F7mruxL5/G0ZTlTc3eZMYjLUSRm08MDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeb4632f9a70fec459326cce76c00532736c0bdf84c25be6ce5779f9708b0650","last_reissued_at":"2026-05-18T02:30:00.384072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:00.384072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A maximum entropy framework for non-exponential distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.soc-ph","authors_text":"Jack Peterson, Ken A. Dill, Purushottam D. Dixit","submitted_at":"2015-01-06T00:52:56Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01049","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.01049","created_at":"2026-05-18T02:30:00.384127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.01049v1","created_at":"2026-05-18T02:30:00.384127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01049","created_at":"2026-05-18T02:30:00.384127+00:00"},{"alias_kind":"pith_short_12","alias_value":"V22GGL42OD7M","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"V22GGL42OD7MIWJS","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"V22GGL42","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ","json":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ.json","graph_json":"https://pith.science/api/pith-number/V22GGL42OD7MIWJSNTHHNQAFGJ/graph.json","events_json":"https://pith.science/api/pith-number/V22GGL42OD7MIWJSNTHHNQAFGJ/events.json","paper":"https://pith.science/paper/V22GGL42"},"agent_actions":{"view_html":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ","download_json":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ.json","view_paper":"https://pith.science/paper/V22GGL42","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.01049&json=true","fetch_graph":"https://pith.science/api/pith-number/V22GGL42OD7MIWJSNTHHNQAFGJ/graph.json","fetch_events":"https://pith.science/api/pith-number/V22GGL42OD7MIWJSNTHHNQAFGJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/action/storage_attestation","attest_author":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/action/author_attestation","sign_citation":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/action/citation_signature","submit_replication":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/action/replication_record"}},"created_at":"2026-05-18T02:30:00.384127+00:00","updated_at":"2026-05-18T02:30:00.384127+00:00"}