{"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":"342d5e78b226469c959b9ff910369ab3","problem_id":"0c127b28-4e62-4599-988e-363ce785755a","problem_name":"Fibonacci primes — density conjecture","domain":"Number Theory","statement":"For every index n > 4 such that the Fibonacci number F_n is prime, the index n itself must be a prime number that can be expressed as the sum of two squares (i.e., n is a Pythagorean prime or n=2). Consequently, no Fibonacci prime exists at an index n where n is a prime congruent to 3 modulo 4.","status":"falsified","url":"https://assignee.net/math#result-342d5e78b226469c959b9ff910369ab3","doi":null},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.03,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/342d5e78b226469c959b9ff910369ab3/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/342d5e78b226469c959b9ff910369ab3/paper.pdf","format":"application/pdf"}],"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."]}