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Axiom 2.1 (Topological Understanding):
Comprehension is a continuous deformation φ: M₁ → M₂ between mental models. Complete understanding occurs when φ is a homeomorphism.
Theorem 3.1 (P=NP Allegory):
The computational complexity dichotomy maps to cognitive operations:
P ↔ Verification, pattern recognition
NP ↔ Creative generation, insightCollapse ↔ Epiphany (when verification and creation coincide)
Axiom 2.1 (Topological Understanding):
Comprehension is a continuous deformation φ: M₁ → M₂ between mental models. Complete understanding occurs when φ is a homeomorphism.
Theorem 3.1 (P=NP Allegory):
The computational complexity dichotomy maps to cognitive operations:
P ↔ Verification, pattern recognition
NP ↔ Creative generation, insight
Collapse ↔ Epiphany (when verification and creation coincide)