Horizons-as-Dimensional-Interface Framework: A Falsifiable Unification of General Relativity and Quantum Field Theory via Curvature–Coupled Fields

This is Version 2 of the Horizons-as-Dimensional-Interface Framework (HDIF).

Horizons-as-Dimensional-Interface Framework (HDIF) introduces a falsifiable unification of general relativity (GR) and quantum field theory (QFT) by modeling spacetime as an interface equipped with curvature–memory dynamics. In this formulation, horizons are not passive boundaries but dimensional interfaces that store and re-emit geometric tension through delayed memory kernels. Curvature, field tension, and memory interact through a single geometric structure encoded in the Master Interface Equation, from which all later reduced field equations are derived.

A key advance in Version 2 is the introduction of the Master Field Formula, a GR-compatible reorganization of the interface dynamics. This effective field description expresses interface curvature as
I = G + Λ₀ g + M[W] + C + R,
where Λ₀ is a renormalized baseline curvature offset, M[W] encodes Volterra-type memory kernels, C captures nonlocal coherence, and R represents residual correlation curvature. This structure maintains full compatibility with Einstein’s equations in the zero-memory limit while providing new, testable departures from GR.

HDIF proposes that:
• Space corresponds to the equilibrium configuration of the interface.
• Matter corresponds to localized deformations of that equilibrium.
• Energy arises from differential tension at interface boundaries.
• Quantum behavior emerges from incomplete geometric reference caused by horizon memory damping.
• Probability amplitudes arise from memory-weighted correlations rather than intrinsic randomness.

This framework yields several falsifiable predictions. HDIF introduces a quantized curvature increment through the relation ΔΛ = H_q ν_h, implying discrete curvature evolution at horizon boundaries. The same mechanism leads to a new prediction: Hawking evaporation halts when curvature reaches the baseline offset Λ₀, producing stable black-hole remnants fixed by memory saturation. The resulting remnant has minimal curvature equal to Λ₀, preventing runaway evaporation and eliminating singularities.

Additional experimental signatures arise in systems where delayed curvature response can be probed. These include:
• interferometric phase shifts Δφ from curvature-memory coupling.
• small deviations in Casimir-like tension gradients.
• frequency-dependent geodesic-deviation lags.
• potential corrections to compact-object lensing profiles.

A scalar sector is introduced to represent deformation modes of the interface, obeying a memory-coupled wave equation with causal kernels. This equation explains how delayed tension feedback produces horizon-scale coherence effects, quantum-classical matching conditions, and emergent probabilistic behavior. The tensor-level memory formulation is shown to reduce to the scalar sector through a normal-mode projection, establishing a clear mathematical bridge between the full interface geometry and its phenomenological consequences.

Finally, HDIF recovers GR exactly in the limit of vanishing memory kernels, preserving energy–momentum conservation, covariance, and the classical geometric structure. The framework therefore offers a physically grounded, mathematically consistent, and experimentally falsifiable pathway to unifying curvature dynamics with quantum behavior through curvature–memory coupling.

This version supersedes the November 4, 2025 release (Version 1.0), while preserving the original conceptual foundation. It represents the most complete and precise formulation of HDIF to date.