Annotation

This work presents the first complete, internally consistent, and observationally testable fundamental theory of gravity based on the χ‑ontology and the universal χ‑equation. The theory introduces a new level of physical reality, defined by the fundamental object χ and the χ‑space Xχ, from which geometry, dynamics, entropy, topology, quantumness, and spacetime itself emerge as χ‑projections. Within this framework, General Relativity is recovered as a strict limit of χ‑dynamics, while singularities, divergences, and inconsistencies of classical and quantum gravity are eliminated by χ‑regularity.

The article develops the full mathematical structure of χ‑geometry, χ‑topology, and χ‑entropy, formulates the universal χ‑equation as a third‑level variational system, and derives the χ‑tensor Θμν as the universal source of gravitational phenomena, unifying dark matter, dark energy, inflation, and the arrow of time. χ‑black holes are constructed as regular two‑zone χ‑structures with finite cores, χ‑entropy, χ‑radiation, χ‑QNMs, and χ‑remnants. χ‑cosmology emerges as a χ‑critical regime, providing a unified explanation of inflation, acceleration, structure formation, BAO, and CMB anisotropies.

The article establishes strict observational constraints on the χ‑scale ℓχ from QNMs, lensing, black‑hole shadows, gravitational waves, ISCO shifts, pulsar timing, and cosmological data, forming a unified χ‑experimental program for current and future missions. χ‑QFT 2.0 is introduced as a quantum theory on χ‑space, from which standard QFT and quantum phenomena arise as effective χ‑projections.

The resulting framework constitutes a complete, axiomatized, mathematically rigorous, and empirically accessible theory of gravity and fundamental physics, in which geometry, quantumness, entropy, and topology are unified within a single χ‑ontological structure.