A Constitutive Field Derivation of the Shift Sector in a Lossless Continuous Carrier Vacuum

We derive the leading translational Shift response of the Signature Framework from the stationary three-dimensional Bulk field of a continuous, lossless carrier. An active uniform translation of the Bulk displacement profile produces the unique source-free first-order conjugate response H_Sh⁽¹⁾ = v × D_B, subject to solenoidality, vanishing normal conjugate flux at the reaction surface, finite energy, and decay at spatial infinity. Because the stationary Bulk configuration has no conjugate component, its first-order inductive energy cross-term vanishes identically. The induced field nevertheless carries a first-order momentum-load density g_Sh⁽¹⁾ = S_Sh⁽¹⁾ / c², whose integral over a spherical Omnidirectional Spherical Process-Load Domain is P_Sh⁽¹⁾ = (4E_B / 3c²)v. The associated leading conjugate energy is therefore L_Sh⁽ᴴ⁾ = ½ P_Sh⁽¹⁾ · v = ⅔ E_B v² / c². The coefficient κ_Sh = 4E_B / (3c²) is identified strictly as a conjugate-sector response coefficient. Higher-order capacitive and stress closures are not included in this first-order field construction. This work constitutes Paper II of the Bulk–Shift–Spin development within the Signature Framework. Related Publications:– Paper I (Bulk Sector): Firtl, M. A. (2026). A Constitutive Derivation of Stationary Bulk Fields from a Topological Boundary-Flux Invariant. Zenodo. doi: 10.5281/zenodo.21612107– Foundation Lemma: Firtl, M. A. (2026). Foundation Lemma: Constitutional Principles and Nomenclature of the Signature Framework. Zenodo. doi: 10.5281/zenodo.20575293