{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HRPW25A5JSRT2JYLLQXMDWAMID","short_pith_number":"pith:HRPW25A5","schema_version":"1.0","canonical_sha256":"3c5f6d741d4ca33d270b5c2ec1d80c40f6d1f582a2c3ed48ee3bbe947187409b","source":{"kind":"arxiv","id":"2509.01424","version":1},"attestation_state":"computed","paper":{"title":"Hierarchical Maximum Entropy via the Renormalization Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Amir R. Asadi","submitted_at":"2025-09-01T12:30:23Z","abstract_excerpt":"Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is given by the exponential Gibbs-Boltzmann form, we introduce the framework of \"hierarchical maximum entropy\" to address these multilevel models. We demonstrate that Pareto optimal distributions, which maximize entropies across all levels of hierarchical transformations, can be obtained via renormalization-group procedures from theoretical physics. This is ach"},"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":"2509.01424","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-09-01T12:30:23Z","cross_cats_sorted":["cs.LG","math.IT"],"title_canon_sha256":"cc80386ef3aef303609ea979220f7a2dd7f1f9613282e3b1d12d22feee9b54ce","abstract_canon_sha256":"7b0726c13c0cee8f7c997b375451f737ffc496c9e8540a6b9bfbf1b04588d34b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:00.696255Z","signature_b64":"ExEcPMTDmmZRnDtTMwIJ66p/AdDPfIKwDwamBkfBQngHDcRH9jNhrQOJp39E5aVm2o/r//rvk1Sl4YI8BbPNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c5f6d741d4ca33d270b5c2ec1d80c40f6d1f582a2c3ed48ee3bbe947187409b","last_reissued_at":"2026-07-05T12:03:00.695592Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:00.695592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical Maximum Entropy via the Renormalization Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Amir R. Asadi","submitted_at":"2025-09-01T12:30:23Z","abstract_excerpt":"Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is given by the exponential Gibbs-Boltzmann form, we introduce the framework of \"hierarchical maximum entropy\" to address these multilevel models. We demonstrate that Pareto optimal distributions, which maximize entropies across all levels of hierarchical transformations, can be obtained via renormalization-group procedures from theoretical physics. This is ach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01424","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.01424/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":"2509.01424","created_at":"2026-07-05T12:03:00.695689+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.01424v1","created_at":"2026-07-05T12:03:00.695689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01424","created_at":"2026-07-05T12:03:00.695689+00:00"},{"alias_kind":"pith_short_12","alias_value":"HRPW25A5JSRT","created_at":"2026-07-05T12:03:00.695689+00:00"},{"alias_kind":"pith_short_16","alias_value":"HRPW25A5JSRT2JYL","created_at":"2026-07-05T12:03:00.695689+00:00"},{"alias_kind":"pith_short_8","alias_value":"HRPW25A5","created_at":"2026-07-05T12:03:00.695689+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/HRPW25A5JSRT2JYLLQXMDWAMID","json":"https://pith.science/pith/HRPW25A5JSRT2JYLLQXMDWAMID.json","graph_json":"https://pith.science/api/pith-number/HRPW25A5JSRT2JYLLQXMDWAMID/graph.json","events_json":"https://pith.science/api/pith-number/HRPW25A5JSRT2JYLLQXMDWAMID/events.json","paper":"https://pith.science/paper/HRPW25A5"},"agent_actions":{"view_html":"https://pith.science/pith/HRPW25A5JSRT2JYLLQXMDWAMID","download_json":"https://pith.science/pith/HRPW25A5JSRT2JYLLQXMDWAMID.json","view_paper":"https://pith.science/paper/HRPW25A5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.01424&json=true","fetch_graph":"https://pith.science/api/pith-number/HRPW25A5JSRT2JYLLQXMDWAMID/graph.json","fetch_events":"https://pith.science/api/pith-number/HRPW25A5JSRT2JYLLQXMDWAMID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HRPW25A5JSRT2JYLLQXMDWAMID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HRPW25A5JSRT2JYLLQXMDWAMID/action/storage_attestation","attest_author":"https://pith.science/pith/HRPW25A5JSRT2JYLLQXMDWAMID/action/author_attestation","sign_citation":"https://pith.science/pith/HRPW25A5JSRT2JYLLQXMDWAMID/action/citation_signature","submit_replication":"https://pith.science/pith/HRPW25A5JSRT2JYLLQXMDWAMID/action/replication_record"}},"created_at":"2026-07-05T12:03:00.695689+00:00","updated_at":"2026-07-05T12:03:00.695689+00:00"}