{"id":"operation-order-as-coordinate","title":"Operation order as a coordinate","regions":["representation","mathematical-experiments"],"question":"Can the order of an operation itself become a coordinate of a representation?","formulation":"Represent a function across both its input and a varying derivative order, then inspect continuity, cross-sections, and discontinuities in that family.","representations":[{"name":"Separate plots at selected orders","affords":"Shows individual transformed functions.","loses":"Conceals how the family changes between chosen orders.","epistemic_kind":"reconstruction"},{"name":"A surface indexed by input and operation order","affords":"Makes variation in the operation itself visible.","loses":"Requires an explicit fractional-derivative convention, domain, and boundary conditions.","epistemic_kind":"reconstruction"}],"tension":"A continuous-looking picture cannot establish continuity of an unspecified operator family.","challenge":"Which convention and function domain make variation in derivative order well-defined?","development":"historical_branch","epistemic_kind":"reconstruction","evidence":["basis-operation-order-as-coordinate"],"next_move":{"text":"Choose one convention and a function with an analytic family; compare cross-sections with numerical approximations.","epistemic_kind":"model_proposed"},"open_questions":["Can the order of an operation itself become a coordinate of a representation?","Which convention and function domain make variation in derivative order well-defined?"],"formal_status":"open_problem","version":1,"content_hash":"f84d1b7b82811e69d264f2cdcea0e249b223add9c58e9aa26d093fa258d09134"}