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NSTD.2:5.1 - Worked example: choosing a path through a graph

A knowledge graph can connect concepts, dependencies, counterexamples, evidence and practice routes. To introduce part of it, choose a traversal that helps the reader encounter the necessary dependencies. The optional example note below retains those choices for a homotopy introduction.

NarrativeOrderingRule@HomotopyIntro:
  narrativeRenderingRef: HomotopyIntroNarrative@v1
  sourceStructureRefs:
    - topological space
    - path
    - deformation under constraints
    - invariant
    - example and counterexample
    - proof-status boundary
  orderingRuleKind: didactic prerequisite plus analogy-first cue
  orderRationale: learner needs visual intuition before formal return, but formal dependency must remain recoverable
  preservedSourceRelations: prerequisite relation; analogy-to-definition return; example-to-counterexample contrast
  foregroundedSourceRelations: deformation intuition and invariant question
  coarsenedOrLostSourceRelations: full proof order; advanced generality; categorical reformulation
  sourceReturnCondition: use the formal statement and proof when deciding a theorem, equivalence or proof claim
  additionalClaimReferences: `A.6.3.CSC`, `E.17.EFP`, `A.10`, `NSTD.6` when the corresponding claim is made

The introduction can begin with a picture of paths being deformed, then return to the formal definition. For example: “First picture a loop being deformed while its endpoints stay fixed. The next definition specifies which deformations are allowed.” This connects the intuitive sequence to its missing mathematical condition.