Chapter 29: ι_τ Confirmed — The Archimedean-Non-Archimedean Bridge

Book I introduced the master constant ι_τ = 2/(π + e) ≈ 0.341304 as a structural mediator between the B and C channels (I.D24, Book I). At that stage, neither π nor e was earned: ι_τ was a formal ratio awaiting numerical content. Chapters and earned π and e from the τ-framework itself, and the relevant chapter established the bipolar unit j. This chapter closes the circle. We confirm ι_τ = 2/(π + e) with earned π and e, establish the Archimedean-Non-Archimedean Bridge between ultrametric refinement (D-depth) and Euclidean resolution (ABC angular precision), and prove the Refinement-Resolution Duality: the statement that these two measurement processes are dual descriptions of the same structural process. The chapter also explains why τ accesses transcendental constants without importing ℝ.