{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:V22GGL42OD7MIWJSNTHHNQAFGJ","short_pith_number":"pith:V22GGL42","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"},"canonical_sha256":"aeb4632f9a70fec459326cce76c00532736c0bdf84c25be6ce5779f9708b0650","source":{"kind":"arxiv","id":"1501.01049","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:V22GGL42OD7MIWJSNTHHNQAFGJ","target":"record","payload":{"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"},"canonical_sha256":"aeb4632f9a70fec459326cce76c00532736c0bdf84c25be6ce5779f9708b0650","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"},"source_kind":"arxiv","source_id":"1501.01049","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CiUSmcvSvJ+jIkgN0N/dQdlkInBzdjaBTbQ9ncsdYkzl9IWjtaG8mtrir6nvbWMItf8ReCMeZzxcFAukmQHcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T06:56:58.140564Z"},"content_sha256":"c50b6de8b985c8891c23ef9913bcb21b45f309231e755debbbdfe9d65d8468e7","schema_version":"1.0","event_id":"sha256:c50b6de8b985c8891c23ef9913bcb21b45f309231e755debbbdfe9d65d8468e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:V22GGL42OD7MIWJSNTHHNQAFGJ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HNEbpJRuJN4p/ZMwIB6JBXtcG4tWxCvpU1q8CfDd4uZMyOYicRp4qeQZshxme1wF/xbkfZcJUfJYn8VcCnyZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T06:56:58.140953Z"},"content_sha256":"5e3d78f4a17f4deb6d83c08eb05c795994f1c929b6a16c4c6eeaf90fd28f2a9e","schema_version":"1.0","event_id":"sha256:5e3d78f4a17f4deb6d83c08eb05c795994f1c929b6a16c4c6eeaf90fd28f2a9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/bundle.json","state_url":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/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":"2026-05-24T06:56:58Z","links":{"resolver":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ","bundle":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/bundle.json","state":"https://pith.science/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V22GGL42OD7MIWJSNTHHNQAFGJ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IHPiTkppSVnNGqcb/1aw3vhGcMYUlrR0kk5ev01mrstpUkidnRGnoh491DPB/GQj1sCAPEzdSDJ2dMdnu+IeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T06:56:58.144032Z","bundle_sha256":"8d804785c19686ae86e09e86f0d6877d3b2ef84efad93019b4c99d394c52f402"}}