{"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":"845aaff7aef64a018e422eb49c6764f4","problem_id":"0c127b28-4e62-4599-988e-363ce785755a","problem_name":"Fibonacci primes — density conjecture","domain":"Number Theory","statement":"For every integer n >= 3, if the Fibonacci number F_n is prime, then n must be a prime number, AND the index n satisfies the property that 2n+1 is either a prime number or a semiprime (product of exactly two primes, not necessarily distinct). Furthermore, if n > 5, then n modulo 10 must be in the set {1, 3, 7, 9} (which is trivial for primes > 5) AND the sum of digits of n in base 10 is not divisible by 3 (also trivial). The core non-trivial claim is: For all Fibonacci primes F_n with n > 4, the","status":"falsified","url":"https://assignee.net/math#result-845aaff7aef64a018e422eb49c6764f4","doi":"10.5281/zenodo.20569499"},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.06,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/845aaff7aef64a018e422eb49c6764f4/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/845aaff7aef64a018e422eb49c6764f4/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20569499","format":"text/html"}],"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."]}