Sci - The "Transcendental" of Pi: On Closure, Representation, and the Infinite Tail of a Finished Constant

Sci - The "Transcendental" of Pi: On Closure, Representation, and the Infinite Tail of a Finished Constant Armstrong Knight — intent-tensor-theory.com The word 'transcendental' carries two precise and simultaneous meanings when applied to π. Classically (Lindemann, 1882), π is transcendental in the sense that it is not the root of any nonzero polynomial with integer coefficients — no finite algebraic construction reaches it. In the doctrine of Dimensionless Mathematics, 'transcendental' names a deeper property: π exists in the pre-geometric substrate, and dimensional representations approach it only asymptotically. This paper argues both meanings point at the same mathematical fact from different directions.…