From Cosmology to Consciousness: Emergent Gravity, Thermodynamics, and Neural Efficiency from the Fractal Density Activation Axiom

This work demonstrates that classical gravity, thermodynamics, fractal time, and principles of neural computation emerge rigorously from a single first principle: the Fractal Density Activation Axiom (FDAA). The axiom posits that physical existence is contingent upon a local multi-scale density, D(x), meeting or exceeding a universal threshold, Σ∗. From this postulate, we derive: • An inverse-square law of gravity featuring a novel r−4 potential correction that resolves singularities and explains galactic rotation without dark matter. • The laws of thermodynamics, with the arrow of time linked to an irreversible increase in a system’s activation density. • A universal fractal dimension for time, Dt ≈ 0.81, validated against diverse empirical data. • A mechanism for neural efficiency, where the brain exploits a medium-dependent effective threshold, Σ∗ eff , to filter quantum noise at synaptic scales, explaining observed fractal dynamics in neural signaling. The framework, anchored by a single calibrated constant, is shown to be consistent with empirical data across cosmological, quantum, and biological domains, offering a uniquely parsimonious and testable foundation for a unified theory.