Exotic Weil Self-Intersection Across All Nine Heegner Fields (Paper 57, Constructive Reverse Mathematics Series)

[This paper is a companion to Paper 56: it uses the same Lean 4 framework and the same formula, applied to the six remaining class-number-1 fields. The two papers share a single Zenodo record structure but maintain separate Lean bundles, and are kept separate to preserve the research audit trail.] Paper 57 of the Constructive Reverse Mathematics and Arithmetic Geometry series. We complete the exotic Weil self-intersection computation of Paper 56 across all nine imaginary quadratic fields with class number 1 (Baker–Heegner–Stark). For each field K = ℚ(√-d), d ∈ {1, 2, 3, 7, 11, 19, 43, 67, 163}, we pair K with a cyclic Galois totally real cubic F and compute the self-intersection degree of the primitive exotic Weil class on the resulting CM abelian fourfold. The formula deg(w₀ · w₀) = √disc(F) is verified in all nine cases: d=1: deg=9 | d=2: deg=19 | d=3: deg=7 | d=7: deg=13 | d=11: deg=37 | d=19: deg=61 | d=43: deg=79 | d=67: deg=163 | d=163: deg=97 The degree sequence consists of prime conductors with a single exception (9 = 3²). The number 163 — the largest Heegner number — appears both as a d-value (yielding degree 97) and as a degree value (from d = 67). By Baker–Heegner–Stark, no further class-number-1 examples exist; the theorem's natural domain is exhausted. Lean 4 / Mathlib formalization: 3 modules, ~785 lines, 2 principled axioms (discriminant equation, Galois diagonality), zero sorry gaps. All nine 3×3 determinants verified by native_decide over ℚ. KEYWORDS: exotic Weil class, self-intersection, CM abelian fourfold, field discriminant, Heegner number, class number 1, Baker–Heegner–Stark, cyclic cubic conductor, Lean 4, formal verification, constructive reverse mathematics NOTES: AI-assisted formalization using Claude (Anthropic) for Lean 4 code generation under human direction. All mathematical content specified by the author; every theorem verified by the Lean 4 type checker. Built with Lean 4 v4.29.0-rc1 and Mathlib. Reproducible via 'lake build'. Code available exclusively on Zenodo.