The Recursion Principle, the Principal, and the Feedback Delta: IE-005 and IE-006 as the Complete Control Loop of Silver Geometry

Formalizes IE-005 (Recursion Principle and the Principal) and IE-006 (Feedback Delta) as a unified closed-loop control system within Silver Geometry. Derives the gap formula Δ(d→d+1) = 138/[(23d+29)(23d+6)], establishes the IE operation sequence as a PEMDAS-style precedence hierarchy, and demonstrates the complete IE-005/IE-006 loop through a worked arithmetic example and a first-person perceptual observation. The origin coordinate (α = 1.920 at d = 3), d=4 ecosystem attractor (α = 95/49 ≈ 1.939), and asymptotic limit (α → 2) are identified as three distinct levels of the dimensional hierarchy governing recursive dynamics, intermediate-dimensional empirical clustering, and the IE-002 ceiling respectively.…