Quantum Gravity as Contextual Gluing: Coherence Defects, Categorical Renormalization, and Operational Predictions from Horizons to Scattering

This work proposes a new operational framework for quantum gravity based on contextual gluing, rather than on quantizing a spacetime metric or invoking holographic boundary constructions. The central idea is that spacetime should be understood as locally classical but globally non-strict: each observer, measurement protocol, and clock defines a valid local spacetime description, yet different contexts cannot, in general, be glued together by exact identifications. The residual mismatch between such local descriptions is interpreted as a coherence defect, which carries the genuinely quantum-gravitational degrees of freedom.

In this approach, quantum gravity is defined operationally as the theory governing how locally classical spacetime contexts relate, compare, and fail to compose strictly. The framework replaces global factorization and absolute time ordering with a network of context-dependent correspondences, whose non-closure is quantified using tools from quantum information theory, stochastic processes, and higher-categorical structures.

A key conceptual contribution is a reinterpretation of renormalizability. Instead of ultraviolet momentum flows, renormalization is formulated as refinement of operational access: improving time resolution, bandwidth, spatial localization, detector gaps, or cosmological epoch. A theory is renormalizable if the defect statistics remain closed under such refinements. This leads naturally to a categorical renormalization group, in which kernels, power spectral densities, quantum channels, and cohomology classes flow within finite-dimensional families. In this sense, quantum gravity becomes renormalizable as a theory of coherence rather than of fields.

The paper develops several worked examples demonstrating the power and generality of this framework:

• Hawking radiation and the Page curve are derived without AdS asymptotics, replica methods, or entanglement islands. A three-party Gaussian model with finite radiation memory produces a smooth Page turnover, with mutual information acting as an operational witness of coherence defects.

• Unruh radiation with incompatible clocks is treated exactly. Using Gaussian switching functions and sinusoidally modulated clock protocols, the paper derives closed-form expressions and numerical results for protocol-dependent response shifts, while preserving thermality. These effects are absent in standard treatments and arise purely from contextual ordering.

• Cosmological horizons in de Sitter spacetime are analyzed without relying on dS/CFT. The same operational pipeline yields measurable clock-protocol defects that modify detector responses while maintaining KMS structure.

• Generic slow-roll FLRW spacetimes are treated using multi-epoch analyses. Defect power spectra are inferred across cosmological epochs, and a categorical renormalization group flow is explicitly demonstrated. Scaling collapse of scattering exponents provides operational evidence for universality classes and fixed-shape behavior.

Across all examples, the framework enables an end-to-end pipeline from measured fluctuations → inferred defect statistics → physical predictions, such as phase diffusion and interferometric visibility loss. These predictions are method-independent in content and rely only on operational data and standard statistical inference.

Gravitons appear in this framework not as fundamental quanta but as emergent collective excitations near a strict-gluing infrared limit, analogous to phonons in condensed matter systems. This avoids the traditional non-renormalizability of perturbative gravity by treating metric fluctuations as effective descriptions valid only after coherence closure is established.

Overall, the work presents a coherent, internally consistent alternative to metric quantization, semiclassical gravity, and holographic dualities. It offers concrete calculations in generic spacetimes, introduces new operational observables, and opens a path toward observable quantum-gravitational effects in cosmology, horizon physics, and interferometric experiments.