Correlational Theory V1 - pt 3.

This work proposes that physical law is not a primitive ingredient of reality but an inevitable structural consequence of stability under extremization of a closed energy form defined on a non-factorizable domain. We assume neither fundamental spacetime nor fundamental dynamical equations. Instead, we postulate the existence of a closable, strongly local quadratic form on a domain that admits no global factorization. The associated gradient semigroup defines a canonical self-adjoint generator whose structure enforces locality, second-order differential behavior, dimensional criticality, and curvature dynamics. Under minimal structural assumptions, we show that:(i) geometry emerges from the quadratic principal symbol of the generator,(ii) four-dimensionality arises from marginal stability of the heat kernel expansion,(iii) Einstein-type dynamics follows from stationarity of the induced action,(iv) non-commutative residual structure yields quantum behavior,(v) internal symmetries arise as stabilizers of the minimal energy sector. Thus, classical and quantum physics emerge from a unified stability principle rather than from independent axioms.