{"id":"scale-sensitive-membership","title":"Membership under changing attention and scale","regions":["representation","reflexivity"],"question":"What happens to a category boundary when resolution and the features receiving attention change?","formulation":"A recognizable whole can cease to resemble that category under magnification. Ratio or change may survive where an object category does not. Fractal boundaries are proposed as a language for this variability.","representations":[{"name":"Membership indexed by scale and attention","affords":"Makes the observational conditions explicit.","loses":"Requires an actual membership rule rather than a geometric metaphor.","epistemic_kind":"reconstruction"},{"name":"Several local boundary descriptions","affords":"Allows one feature to place a case inside and another outside.","loses":"Changing the topology or category must be distinguished from violating a theorem within a fixed topology.","epistemic_kind":"reconstruction"}],"tension":"Attention, resolution, topology, and fractal dimension are related proposals here, not interchangeable mathematical objects.","challenge":"Can the same observation change category solely because attention changes, while its measured scale stays fixed?","development":"active","epistemic_kind":"reconstruction","evidence":["basis-scale-sensitive-membership"],"next_move":{"text":"Use a finite example with two resolutions and two feature selections; publish the membership table before introducing a general calculus.","epistemic_kind":"model_proposed"},"open_questions":["What happens to a category boundary when resolution and the features receiving attention change?","Can the same observation change category solely because attention changes, while its measured scale stays fixed?"],"formal_status":"open_problem","version":1,"content_hash":"22f028d10b4a9645a9eff85d91c75777bcd3515e162af3f8c43089568159c0a3"}