{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HJTMIA7FAJFSRFGIBSTL2N3KZ3","short_pith_number":"pith:HJTMIA7F","schema_version":"1.0","canonical_sha256":"3a66c403e5024b2894c80ca6bd376acedb1bdf0b6f28277ce46adafebc85150a","source":{"kind":"arxiv","id":"2509.05567","version":2},"attestation_state":"computed","paper":{"title":"Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","nlin.AO","physics.data-an"],"primary_cat":"physics.soc-ph","authors_text":"Hui Li, Yanxin Li","submitted_at":"2025-09-06T02:49:21Z","abstract_excerpt":"Understanding and predicting the evolution of across complex systems remains a fundamental challenge due to the absence of unified and computationally testable frameworks. Here we propose the Recursive Hierarchical Network(RHN), conceptualizing evolution as recursive encapsulation along a trajectory of node $\\to$ module $\\to$ system $\\to$ new node, governed by gradual accumulation and abrupt transition. Theoretically, we formalize and prove the law of functional evolution, revealing an irreversible progression from structure-dominated to regulation-dominated to intelligence-dominated stages. E"},"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":"2509.05567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-09-06T02:49:21Z","cross_cats_sorted":["cs.SI","nlin.AO","physics.data-an"],"title_canon_sha256":"bf5536ec3e8579a0496705c7fd63d67c3c6dcbabc5f776b72ce873c1b3ec9217","abstract_canon_sha256":"43f56b4da076fbfefab948bbceeecc8be3c44e814d5f755a69f7692a914fb34a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:04:56.973235Z","signature_b64":"u5jR+yWvs/cznxDEb9km9WWEVuAvnRjpe9slRz377o41qcgagKZiqyR+zwSPxP9BLr7+6lbbCA6kDzVUedgKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a66c403e5024b2894c80ca6bd376acedb1bdf0b6f28277ce46adafebc85150a","last_reissued_at":"2026-05-20T01:04:56.972393Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:04:56.972393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","nlin.AO","physics.data-an"],"primary_cat":"physics.soc-ph","authors_text":"Hui Li, Yanxin Li","submitted_at":"2025-09-06T02:49:21Z","abstract_excerpt":"Understanding and predicting the evolution of across complex systems remains a fundamental challenge due to the absence of unified and computationally testable frameworks. Here we propose the Recursive Hierarchical Network(RHN), conceptualizing evolution as recursive encapsulation along a trajectory of node $\\to$ module $\\to$ system $\\to$ new node, governed by gradual accumulation and abrupt transition. Theoretically, we formalize and prove the law of functional evolution, revealing an irreversible progression from structure-dominated to regulation-dominated to intelligence-dominated stages. E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05567","kind":"arxiv","version":2},"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/2509.05567/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":"2509.05567","created_at":"2026-05-20T01:04:56.972496+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.05567v2","created_at":"2026-05-20T01:04:56.972496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05567","created_at":"2026-05-20T01:04:56.972496+00:00"},{"alias_kind":"pith_short_12","alias_value":"HJTMIA7FAJFS","created_at":"2026-05-20T01:04:56.972496+00:00"},{"alias_kind":"pith_short_16","alias_value":"HJTMIA7FAJFSRFGI","created_at":"2026-05-20T01:04:56.972496+00:00"},{"alias_kind":"pith_short_8","alias_value":"HJTMIA7F","created_at":"2026-05-20T01:04:56.972496+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/HJTMIA7FAJFSRFGIBSTL2N3KZ3","json":"https://pith.science/pith/HJTMIA7FAJFSRFGIBSTL2N3KZ3.json","graph_json":"https://pith.science/api/pith-number/HJTMIA7FAJFSRFGIBSTL2N3KZ3/graph.json","events_json":"https://pith.science/api/pith-number/HJTMIA7FAJFSRFGIBSTL2N3KZ3/events.json","paper":"https://pith.science/paper/HJTMIA7F"},"agent_actions":{"view_html":"https://pith.science/pith/HJTMIA7FAJFSRFGIBSTL2N3KZ3","download_json":"https://pith.science/pith/HJTMIA7FAJFSRFGIBSTL2N3KZ3.json","view_paper":"https://pith.science/paper/HJTMIA7F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.05567&json=true","fetch_graph":"https://pith.science/api/pith-number/HJTMIA7FAJFSRFGIBSTL2N3KZ3/graph.json","fetch_events":"https://pith.science/api/pith-number/HJTMIA7FAJFSRFGIBSTL2N3KZ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HJTMIA7FAJFSRFGIBSTL2N3KZ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HJTMIA7FAJFSRFGIBSTL2N3KZ3/action/storage_attestation","attest_author":"https://pith.science/pith/HJTMIA7FAJFSRFGIBSTL2N3KZ3/action/author_attestation","sign_citation":"https://pith.science/pith/HJTMIA7FAJFSRFGIBSTL2N3KZ3/action/citation_signature","submit_replication":"https://pith.science/pith/HJTMIA7FAJFSRFGIBSTL2N3KZ3/action/replication_record"}},"created_at":"2026-05-20T01:04:56.972496+00:00","updated_at":"2026-05-20T01:04:56.972496+00:00"}