Constants From Balanced Ternary

This paper is the third in a sequence. The first paper motivates the existence of a first directed distinction. The second paper proves that the balanced-ternary alphabet -1, 0, +1 is the unique minimal integer-valued state space capable of representing a directed transition intrinsically, without an external sign convention. Starting from that established alphabet, this paper asks what mathematical structure is compelled when the alphabet is subjected to its own natural operations. Under explicit structural requirements such as independence of generators, closure under composition, and preservation of intrinsic symmetry, a sequential chain of constants emerges. The paper derives: i, √2, √3, √5, φ, e, π, ln 2, ln 3, ζ (2), ζ (3), γ, Catalan’s constant G, and the lemniscate constant ϖ. Each result depends only on structure already derived. No physical interpretation is assumed or required. The claim is limited to this: given the stated structural requirements, this particular derivation chain is forced, and each constant enters at the earliest point permitted by the available structure.