Constitutive Alignment of Bulk, Shift, and Spin Process-Load Sectors with ADM Source Projections

This paper establishes a coordinate-consistent constitutive alignment between the Bulk, Shift, and Spin process-load sectors of the Signature Framework and the dominant ADM projections of an effective energy-momentum source tensor in the weak-field regime. The stationary Bulk energy density is assigned to the leading scalar energy channel. For the translational Shift sector, the field response derived in Paper II, H_Sh^(1) = v × D_B, is shown to generate a local anisotropic kinetic kernel. The resulting field momentum density satisfies the exact constitutive identity g_Sh^(1) = ∂ρ_Sh^(H) / ∂v at fixed Bulk displacement field and spatial metric. This identifies the leading Shift ADM momentum projection directly from the carrier-field dynamics and establishes equality between the corresponding ADM energy flux and the carrier Poynting flux. Integration over the spherically symmetric Omnidirectional Spherical Process-Load Domain recovers P_Sh^(1) = (4 E_Bulk / 3c²) v. For the closed-circulation Spin sector derived in Paper III, a formal metric response is defined from the Hodge-Neumann projected Spin energy. Its conversion into the ADM spatial stress projection is shown to require the complete implicit metric variation of the projected profile and the sign conventions of a four-dimensional carrier action. The resulting hierarchy provides a precise interface between the previously derived constitutive carrier sectors and weak-field ADM source projections while clearly separating established field identities from action-dependent stress closure. This work constitutes Paper IV 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 Paper II — Shift Sector: Firtl, M. A. (2026). A Constitutive Field Derivation of the Shift Sector in a Lossless Continuous Carrier Vacuum. Zenodo. doi: 10.5281/zenodo.21613055 Paper III — Spin Sector: Firtl, M. A. (2026). A Constitutive Field Derivation of the Spin Sector as the Hodge-Projected Circulation of Advected Carrier Flux. Zenodo. doi: 10.5281/zenodo.21648295 Foundation Lemma: Firtl, M. A. (2026). Foundation Lemma: Constitutional Principles and Nomenclature of the Signature Framework. Zenodo. doi: 10.5281/zenodo.20575293