Speculative theoretical programme proposes a comprehensive equation in cosmology and gravity, linking observational tests and constraints.
This record contains the complete single-PDF edition v4.0 of the Fixed-Point Stationary Universe (FPSU) Research Programme. The document consolidates the FPSU materials into one citable volume: a UV fixed-point effective-action ansatz, the Fixed-Point Stationary Universe Theory, the proposed Equation of Everything, derived predictions of UV-finite gravity and singularity softening, technical developments on running Newton coupling, modified black-hole horizons, cosmological dynamics, observational tests, falsifiability, parameter constraints, matter-sector consistency and a new conservation-law closure layer. The central proposal is that a plausible Equation of Everything should not be understood as a single elementary algebraic formula, but as a fixed-point-stabilized stationary solution of a total quantum effective action involving spacetime geometry, matter fields, gauge interactions and possible hidden sectors. The programme derives preliminary consequences from the ultraviolet fixed-point condition applied to the dimensionless Newton coupling g(k)=k^2 G(k), including the scaling G(k) approximately g*/k^2, a softened short-distance gravitational potential, modified Schwarzschild-type horizons, a Planck-scale critical mass, a possible regularized early-universe regime, observational consistency requirements and matter-sector constraints. Version v4.0 adds a conservation-law and Bianchi-consistency development. It states that running gravitational couplings are admissible only if they satisfy a covariant closure condition. In cosmology, this links the running of Newton coupling, the running of the vacuum term and matter-sector exchange. In black-hole models, it requires an effective stress tensor or action-level derivation compatible with the Bianchi identity. This work is a speculative theoretical research programme and has not been peer reviewed. It does not claim to be an experimentally confirmed final theory of physics. Its purpose is to provide a structured mathematical formulation, explicit assumptions, preliminary derivations, internal consistency conditions and falsifiability criteria for criticism, correction and possible future development.
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Davide Barbieri (2026) studied this question.