High-Dimensional Symmetric Invariant Field Theory: A Unified Geometric Framework for Gravitation, Gauge Interactions, and Quantum Mechanics

This deposit presents a geometric framework in which general relativity and quantum mechanics are unified as projections of a single classical sixteen-dimensional geometry, and in which gravity and the gauge interactions are unified structurally as index-blocks of one metric. The parent field equation is not postulated but forced: given three independently motivated conditions, Lovelock's theorem admits only a finite family, and in four dimensions only two terms survive identically. The sixteen-dimensional metric carries 136 independent components, which sort by index range into ten Einstein equations, forty-eight Yang–Mills equations, and seventy-eight moduli equations — one equation for one object, from which gravity and the gauge fields emerge together rather than being placed side by side. Several quantities follow with no adjustable parameter. The gauge group SU(3)×SU(2)×U(1) is obtained exactly, twelve hidden dimensions supplying twelve isometries and forty-eight off-diagonal metric components giving twelve gauge four-vectors; the counting would not close with eleven or thirteen. Three chiral generations follow from a topological invariant. The cosmological constant is derived to within twelve per cent of observation, and the gravitational-to-strong coupling hierarchy to 0.13 per cent. Quantum mechanics is obtained by geometrization rather than quantization. The quantum potential is shown to equal a curvature scalar through a Fisher action whose metric variation yields an identically conserved tensor, so the bridge equation joining gravity to the quantum sector is consistent for two independent reasons — the contracted Bianchi identity on one side, Noether's second theorem on the other. Contents. Bohmian Mechanics Derived (19 pp) is self-contained and can be assessed without the cosmology; it derives the four ingredients of de Broglie–Bohm mechanics from one structure. The Concise Summary (41 pp) and Full Summary (52 pp) are progressively fuller overviews. The Monograph (151 pp) contains the complete development. LaTeX sources are included. Declared inputs, open problems, and results established as unreachable in principle — including the numerical convergence of the gauge couplings with gravity — are stated explicitly throughout.