{"schema":"https://assignee.net/schemas/math-result-v1","schema_version":"1.0","contract_version":"math-result-v1.0","schema_documentation":"https://assignee.net/schemas","changelog_url":"https://assignee.net/changelog","publisher":{"name":"Assignee Research","url":"https://assignee.net"},"result":{"id":"39589934f7774b5cb4650fb8f9ae7b32","problem_id":"0783e13466e641dfb4ba3cb12dfdf877","problem_name":"Sum of Odd Numbers Identity","domain":"Formal Identities","statement":"For every natural number n, the sum of the first n odd positive integers equals n squared.","status":"proven","url":"https://assignee.net/math#result-39589934f7774b5cb4650fb8f9ae7b32","doi":null},"verification":{"state":"FORMAL_PROOF_VERIFIED","label":"Formal proof verified","proof_claim":true,"method":"python_computation","result":"no_counterexample","n_cases":2000,"counterexample_available":false,"cpu_seconds":0.03,"lean4_source_public":true},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/39589934f7774b5cb4650fb8f9ae7b32/manifest.json","format":"application/json"},{"type":"lean4_source","label":"Lean4 proof source","url":"https://assignee.net/math/39589934f7774b5cb4650fb8f9ae7b32/lean4","format":"text/plain"}],"interpretation":"Computational evidence is not a formal proof. Formal verification is claimed only when public Lean4 source is attached.","limitations":["Python check code, local file paths, and private execution logs are not exposed in public manifests.","Computational evidence reports bounded search only and can be invalidated by later counterexamples.","Formal proof verification requires public Lean4 source; otherwise the record remains a proof attempt or report."]}