Gap Scaling Across Domains The 400/11 Formula Connecting Geometric and Chaotic Residues

Description This paper derives an exact relationship between two fundamental gaps: the K_AUD gap (√2 × ln(2) to unity) and the Feigenbaum gap (δ to 14/3). The ratio ρ = 400/11 − 1/2500 − 1/939939, with error < 4 × 10⁻¹⁴, encodes the prime architecture connecting geometric and chaotic residues. The formula uses only the closure cycle (4), H₄ primes (2, 3, 5), the boundary prime (7), the 142857 intruders (11, 13), and a palindromic guardian (313) — no external constants needed. Update — 4 May 2026 (v1.0.2, link cleanup pass 5 May 2026 v1.0.3): Two changes — no mathematical content changed beyond a single-digit table value. (a) Typography correction in Table 3 (Section 4): displayed value of −1/939939…