NSTD.5:5.2 - Worked example: an engaging homotopy image with its limiting condition

A homotopy lesson uses the image of a loop “slipping around a hole”. The image is engaging and memorable, but it may cause learners to think all deformations are allowed. NSTD.5 protects the formal boundary:

NarrativeEngagementBoundary@HomotopyLoopImage:
  engagementDevice: vivid analogy
  protectedSourceStructureRefs: deformation under constraints, invariant, formal definition, proof-status boundary
  intendedEffect: sustain attention through abstraction
  persuasionOrHarmRisk: low, unless used to make a false certainty claim
  sourceFidelityRisk: analogy replaces condition-bound definition
  precisionBackoff: state where analogy stops and return to formal statement
  evaluationReturn: learner marks allowed and blocked deformation conditions