{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5AC7RTFOXGCWY4FHKJKEPB7DHA","short_pith_number":"pith:5AC7RTFO","schema_version":"1.0","canonical_sha256":"e805f8ccaeb9856c70a752544787e3380fa53b7cdb116eb83de188cd045ff21a","source":{"kind":"arxiv","id":"2510.04167","version":3},"attestation_state":"computed","paper":{"title":"Multiplicative Turing Ensembles, Pareto's Law, and Creativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math-ph","math.IT","math.MP"],"primary_cat":"cs.IT","authors_text":"Aidan Rocke, Alexander Kolpakov","submitted_at":"2025-10-05T12:04:50Z","abstract_excerpt":"We study integer-valued multiplicative dynamics driven by i.i.d. prime multipliers and connect their macroscopic statistics to universal codelengths. We introduce the Multiplicative Turing Ensemble (MTE) and show how it arises naturally -- though not uniquely -- from ensembles of probabilistic Turing machines. Our modeling principle is variational: taking Elias' Omega codelength as an energy and imposing maximum entropy constraints yields a canonical Gibbs prior on integers and, by restriction, on primes. Under mild tail assumptions, this prior induces exponential tails for log-multipliers (up"},"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":"2510.04167","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-10-05T12:04:50Z","cross_cats_sorted":["cs.CC","math-ph","math.IT","math.MP"],"title_canon_sha256":"fc8d926749088867f33cbb54edd7e08b66fc24923e8866ddd626069127d73441","abstract_canon_sha256":"2d1ad6e1072c9a40bece59715b2ca5c43fa9ed3908c7ed4150a40522e5eec9b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T00:23:04.996926Z","signature_b64":"Vg0MQFpFB14UXz9dbfg4Zqn4aoGXVG/VuT+Td2lJ+2HyFz4dsFI7AQ8ULUt7qiVm3WGlrDms/AuC+8UJp6ftDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e805f8ccaeb9856c70a752544787e3380fa53b7cdb116eb83de188cd045ff21a","last_reissued_at":"2026-07-24T00:23:04.995841Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T00:23:04.995841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicative Turing Ensembles, Pareto's Law, and Creativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math-ph","math.IT","math.MP"],"primary_cat":"cs.IT","authors_text":"Aidan Rocke, Alexander Kolpakov","submitted_at":"2025-10-05T12:04:50Z","abstract_excerpt":"We study integer-valued multiplicative dynamics driven by i.i.d. prime multipliers and connect their macroscopic statistics to universal codelengths. We introduce the Multiplicative Turing Ensemble (MTE) and show how it arises naturally -- though not uniquely -- from ensembles of probabilistic Turing machines. Our modeling principle is variational: taking Elias' Omega codelength as an energy and imposing maximum entropy constraints yields a canonical Gibbs prior on integers and, by restriction, on primes. Under mild tail assumptions, this prior induces exponential tails for log-multipliers (up"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.04167","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.04167/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2510.04167","created_at":"2026-07-24T00:23:04.996380+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.04167v3","created_at":"2026-07-24T00:23:04.996380+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.04167","created_at":"2026-07-24T00:23:04.996380+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AC7RTFOXGCW","created_at":"2026-07-24T00:23:04.996380+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AC7RTFOXGCWY4FH","created_at":"2026-07-24T00:23:04.996380+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AC7RTFO","created_at":"2026-07-24T00:23:04.996380+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/5AC7RTFOXGCWY4FHKJKEPB7DHA","json":"https://pith.science/pith/5AC7RTFOXGCWY4FHKJKEPB7DHA.json","graph_json":"https://pith.science/api/pith-number/5AC7RTFOXGCWY4FHKJKEPB7DHA/graph.json","events_json":"https://pith.science/api/pith-number/5AC7RTFOXGCWY4FHKJKEPB7DHA/events.json","paper":"https://pith.science/paper/5AC7RTFO"},"agent_actions":{"view_html":"https://pith.science/pith/5AC7RTFOXGCWY4FHKJKEPB7DHA","download_json":"https://pith.science/pith/5AC7RTFOXGCWY4FHKJKEPB7DHA.json","view_paper":"https://pith.science/paper/5AC7RTFO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.04167&json=true","fetch_graph":"https://pith.science/api/pith-number/5AC7RTFOXGCWY4FHKJKEPB7DHA/graph.json","fetch_events":"https://pith.science/api/pith-number/5AC7RTFOXGCWY4FHKJKEPB7DHA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AC7RTFOXGCWY4FHKJKEPB7DHA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AC7RTFOXGCWY4FHKJKEPB7DHA/action/storage_attestation","attest_author":"https://pith.science/pith/5AC7RTFOXGCWY4FHKJKEPB7DHA/action/author_attestation","sign_citation":"https://pith.science/pith/5AC7RTFOXGCWY4FHKJKEPB7DHA/action/citation_signature","submit_replication":"https://pith.science/pith/5AC7RTFOXGCWY4FHKJKEPB7DHA/action/replication_record"}},"created_at":"2026-07-24T00:23:04.996380+00:00","updated_at":"2026-07-24T00:23:04.996380+00:00"}