An Arity-Logical Framework Connecting Number Theory, Physical Constants, and the Continuous Manifold Abstract We propose an interpretative framework where the continuous spacetime manifold emerges from arithmetic indecidability operating on discrete prima-logical structures. Physical constants containing irrational mathematical constants (π, e, φ, δₛ, ζ(3), etc.) map coherently to phenomena requiring spatial-temporal description, while constants expressible purely as arity ratios correspond to…