e-Arc-Helix: Volume IV: Static-Field Prerequisite Axiomatic Closure under the a Priori Asymmetric Dependency of the Static Field (Arc Theory)

This volume presents a Hilbert-VI-style axiomatic closure certificate for arc geometry under the Static-Field Prerequisite. It avoids both a pure zero-axiom topological derivation and an empirically back-fitted verdict, developing the closure within arc geometry’s self-contained syntax. The framework adopts the A Priori Asymmetric Dependency of the Static Field: dynamic implies static, static does not imply dynamic, and static without dynamic excitation is vacuum. In this setting, H = C_proj = πD_proj is treated only as the zero-excitation metric benchmark; kappa_I is formalized as a rigid compensation-projection law, not a fitting parameter; and C_Pi remains a comparison-layer perturbation, not a source primitive. The volume proves observed-layer residual closure by replacing an unconstrained empirical remainder with an exact source-derived comparison-layer residual and uniform bound, supplemented by a residual source-note dossier and external testability register. It records a publication-facing closure while preserving layer discipline, non-circularity, and the non-promotion of comparison objects directly into source-layer primitives.