The q-dRIS Framework: A Unified Structure for Quantum Mechanics, General Relativity, and the Standard Model

A unified description of quantum mechanics, general relativity, and the Standard Model re- quires a mathematical structure capable of supporting non-commutativity, internal symmetries, causal consistency, and the absence of singularities across all physical scales. Starting from a minimal set of structural constraints—finite informational resolution, global causality, observ- ability, and variational coherence—this work shows that the only admissible algebraic foundation is the octonionic algebra O, and that physical observables must arise from its maximal associa- tive projection H1 ⊕H2. The residual octonionic associator induces a fundamental cycle time h0, which defines an observer-independent limit of temporal resolution and determines the spectral cutoff of a bilateral right-acting quaternionic Laplace transform (QLT). Rewriting the metric in logarithmic form yields a continuous but blurred Lorentzian man- ifold, compatible with QLT quantization. From this structure, we construct the q-dRIS La- grangian in its non-projected (unitary) and projected (observable) forms. Variation of the non-projected Lagrangian produces a single master wave equation whose Laplace transform de- fines a meromorphic transfer function Z(z). The poles, zeros, and branch exponents of Z(z) reproduce, without free parameters, the full particle spectrum of the Standard Model, the elec- troweak scale, the observed dark-matter-like inertial excess, the cosmological constant, and the regularized structure of black-hole horizons. We show that the q-dRIS class of transfer functions is rigid: any infinitesimal perturbation of poles, zeros, or exponents leads to divergence of the action functional or loss of global analyticity. Under the structural constraints, q-dRIS is therefore the unique stable solution. A falsification protocol is provided, based on measurable deviations in the predicted spectral structure. This work presents q-dRIS as a complete and internally quantized geometric framework in which quantum mechanics and general relativity emerge as effective limits of a single underlying dynamical structure.