{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:OKCJMNMFL25CIONFBK2KYFZH7N","short_pith_number":"pith:OKCJMNMF","schema_version":"1.0","canonical_sha256":"72849635855eba2439a50ab4ac1727fb54736957ebc95393a51f73334cfc2f52","source":{"kind":"arxiv","id":"1105.3664","version":2},"attestation_state":"computed","paper":{"title":"Approximate Solutions of Functional Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Cosmas Zachos, Thomas Curtright, Xiang Jin","submitted_at":"2011-05-18T15:43:36Z","abstract_excerpt":"Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by construction of approximate continuous functional iterates for x/(1-x), sin x, and {\\lambda}x(1-x). Simple functional conjugation by these functions, and their inverses, substantially improves the numerical accuracy of formal series approximations for their continuous iterates."},"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":"1105.3664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-18T15:43:36Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"0aced1a2d05bfacdc3582b98f0362a9a0bc36af4a6b7f80ee07cb78d774715c8","abstract_canon_sha256":"50ba45e16e45d5345546d8191015dc8cc7bc10e0764f7df57742b85e25a79b12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:59.361742Z","signature_b64":"bEeH0xHhI/MaC1MmYpgjBRSjWVhW4bSuzHkwh6ACxIE68ZGA5XZ/8YAPwgCjQNBL4txfsGdDgLHjbVUCU6NYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72849635855eba2439a50ab4ac1727fb54736957ebc95393a51f73334cfc2f52","last_reissued_at":"2026-05-18T02:21:59.360976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:59.360976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate Solutions of Functional Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Cosmas Zachos, Thomas Curtright, Xiang Jin","submitted_at":"2011-05-18T15:43:36Z","abstract_excerpt":"Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by construction of approximate continuous functional iterates for x/(1-x), sin x, and {\\lambda}x(1-x). Simple functional conjugation by these functions, and their inverses, substantially improves the numerical accuracy of formal series approximations for their continuous iterates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3664","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":""},"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":"1105.3664","created_at":"2026-05-18T02:21:59.361097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.3664v2","created_at":"2026-05-18T02:21:59.361097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3664","created_at":"2026-05-18T02:21:59.361097+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKCJMNMFL25C","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKCJMNMFL25CIONF","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKCJMNMF","created_at":"2026-05-18T12:26:37.096874+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/OKCJMNMFL25CIONFBK2KYFZH7N","json":"https://pith.science/pith/OKCJMNMFL25CIONFBK2KYFZH7N.json","graph_json":"https://pith.science/api/pith-number/OKCJMNMFL25CIONFBK2KYFZH7N/graph.json","events_json":"https://pith.science/api/pith-number/OKCJMNMFL25CIONFBK2KYFZH7N/events.json","paper":"https://pith.science/paper/OKCJMNMF"},"agent_actions":{"view_html":"https://pith.science/pith/OKCJMNMFL25CIONFBK2KYFZH7N","download_json":"https://pith.science/pith/OKCJMNMFL25CIONFBK2KYFZH7N.json","view_paper":"https://pith.science/paper/OKCJMNMF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.3664&json=true","fetch_graph":"https://pith.science/api/pith-number/OKCJMNMFL25CIONFBK2KYFZH7N/graph.json","fetch_events":"https://pith.science/api/pith-number/OKCJMNMFL25CIONFBK2KYFZH7N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKCJMNMFL25CIONFBK2KYFZH7N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKCJMNMFL25CIONFBK2KYFZH7N/action/storage_attestation","attest_author":"https://pith.science/pith/OKCJMNMFL25CIONFBK2KYFZH7N/action/author_attestation","sign_citation":"https://pith.science/pith/OKCJMNMFL25CIONFBK2KYFZH7N/action/citation_signature","submit_replication":"https://pith.science/pith/OKCJMNMFL25CIONFBK2KYFZH7N/action/replication_record"}},"created_at":"2026-05-18T02:21:59.361097+00:00","updated_at":"2026-05-18T02:21:59.361097+00:00"}