Sector Paper XV — The Unified Theory of Everything - Derivation of GR, QFT, Standard Model, Tensor Sector, and Cosmology from the δI Substrate

Sector Paper XV — The Unified Theory of Everything: Derivation of GR, QFT, Standard Model, Tensor Sector, and Cosmology from the δI Substrate Sector Paper XV presents the complete correspondence‑layer derivation showing that General Relativity, Quantum Field Theory, the Standard Model, the extended tensor‑bosonic sector, and cosmology are not independent theories but regime‑specific projections of a single primitive informational object: the δI‑substrate. Every familiar physical quantity—metric, curvature, propagator, field, mass, coupling, tensor mode, and cosmological parameter—is shown to arise as a forced‑emergent projection of correlation geometry. The paper defines the unified projection architecture in which geometric, identity‑structure, renormalisation, density‑regime, and global‑evolution projections map the primitive correlation functional I(x, x′) into the full physics stack. In the geometric regime, spacetime metric, Levi‑Civita connection, Riemann curvature, Einstein tensor, geodesics, and gravitational waves appear as symmetric, low‑energy projections of correlation curvature. In the excitation regime, quantum fields, commutation relations, propagators, and particle excitations arise from oscillatory and discrete modes of the correlation kernel. In the identity‑structure regime, fermions, gauge fields, Higgs behaviour, Yukawa couplings, and mass hierarchies emerge from parity‑biased correlation modes and curvature coefficients. In the tensor‑bosonic regime, rank‑2 and rank‑3 tensor modes appear as density‑conservation and correlation‑gradient modes in high‑density regimes. In the cosmological regime, expansion history, curvature evolution, structure growth, lensing, and vacuum‑sector behaviour arise from global correlation flow. These derivations are unified by a total projection identity P_total acting on I(x, x′), demonstrating that GR, QFT, SM, tensor physics, and cosmology are not separate frameworks but five manifestations of one underlying correlation geometry. The correspondence layer is shown to be complete: once the projection identities are fixed, geometry, quantum fields, gauge structure, tensor modes, and cosmology follow necessarily and cannot be removed from the substrate description. Sector XV is released alongside Sector XIIII as part of the dual‑paper closure of the classical and modern physics eras. Together, they provide the primitive correlation object and the unified projection identity, completing the public correspondence layer of the Unified Information Substrate and collapsing the apparent fragmentation of physics into a single informational foundation.