arXiv Preprint Outlines Covariant Hamiltonian Approach to Canonical Quantum Gravity

The work replaces external coordinate-time derivatives with Lie derivatives along an observer congruence, keeping the Hamiltonian split between evolution and configuration variables expressed as spacetime tensors. After quantization the observer-congruent brackets produce relativistic Heisenberg and Schrödinger equations parameterized by proper time; the spatial metric and its conjugate momentum are promoted to canonical operators for gravity. This yields a model the author asserts resolves cosmological and black-hole singularities plus black-hole thermodynamics. The approach synthesizes earlier Hamiltonian formulations (Dirac 1958, Arnowitt-Deser-Misner 1962) with modern observer-dependent covariant techniques seen in papers on relational quantum mechanics. Unlike loop quantum gravity's discrete spectra, the formalism retains continuous tensors while enforcing covariance through the chosen congruence; unlike string theory it stays within canonical quantization without extra dimensions. No numerical predictions or explicit operator spectra are provided, leaving falsifiability unclear. A first strengthening step would be derivation of concrete, testable deviations in black-hole evaporation rates or early-universe power spectra that differ measurably from standard semiclassical results within the next five years of observational data.