{"id":"adaptive-computational-resolution","title":"Spending computation where approximation fails","regions":["computation","mathematical-experiments"],"question":"Can a cheap local approximation identify where expensive computation is actually needed?","formulation":"Use regularity-sensitive approximation to allocate fine computation to difficult regions of a fractal visualization.","representations":[{"name":"Uniform high-resolution computation","affords":"Provides a consistent baseline.","loses":"Spends work in regions where a simpler estimate may suffice.","epistemic_kind":"reconstruction"},{"name":"Local approximation with refinement","affords":"Allocates work using an estimated error.","loses":"An incorrect error estimator may miss precisely the difficult regions.","epistemic_kind":"reconstruction"}],"tension":"A cheap indicator must detect its own failure well enough to justify skipping expensive work.","challenge":"How are missed difficult regions counted alongside runtime savings?","development":"historical_branch","epistemic_kind":"reconstruction","evidence":["basis-adaptive-computational-resolution"],"next_move":{"text":"Benchmark against a high-resolution reference and report both false refinement decisions and final error.","epistemic_kind":"model_proposed"},"open_questions":["Can a cheap local approximation identify where expensive computation is actually needed?","How are missed difficult regions counted alongside runtime savings?"],"formal_status":"open_problem","version":1,"content_hash":"bcee4ad5d162eed572b44ffc35ee27698e85a9fcfd2b9ea5c1c2aad5b0895cb7"}