A.6.3.NAR:5.5 - Homotopy-theory explanation boundary

A teacher turns graph-heavy mathematical material into a didactic sequence of definitions, dependencies, examples, counterexamples, theorem prerequisites, and proof-status boundaries. The ordinary note records which structures a learner can reconstruct, which proof details or generalizations are deferred, and when to return to formal statements. Recalling an analogy alone does not establish a proof or recovery of the mathematical structure being taught.

If the explanation is cited as a stable mathematical account, exact source episteme HomotopySource-X and receiving episteme HomotopyNarrative-Y concern the same mathematical EntityOfConcern; the construction records ordering and visible loss. For mathematical-lens, proof, source-use, evidence, publication, and teaching-evaluation claims, use the patterns that define or test those exact claims.