Quantum Topological Dynamics of Black Hole Horizons: A First-Principles Derivation and Observable Signatures

This paper presents a propositional model aimed at reformulating the physical structure of black hole horizons within a framework of quantum topological dynamics. The model emerges from a cumulative sequence of theoretical attempts and prior papers seeking a deeper understanding of the relationship between quantum information, spacetime geometry, and horizon structure.

The work departs from the fundamental field of primary differentiation, understood here as a physical field preceding the conventional geometric description of spacetime. This field is not defined as a standard dynamical function, but rather as a primitive differential structure endowed with its own internal consistency constraints. It is not assumed a priori to be metric or causal; instead, it is treated as a pre-measurement entity whose properties are derived from a principle of structural consistency.

Within this perspective, we show how imposing consistency conditions on the primary differentiation naturally drives the field from a local analytic description toward a global topological formulation. This transition is not a formal choice, but a direct consequence of the breakdown of local descriptions at horizons, where traditional variables (metric, coordinates, and local time) lose their ability to fully encode physical information. In this context, the black hole horizon is reinterpreted as a dynamical topological object, on which quantum information is encoded through topological classes (cohomological and homotopy classes) rather than local degrees of freedom.

The model is based on deriving consistency relations that are forcibly implied by the invariance of the topological structure under dynamical transformations. This allows, in principle, the extraction of testable predictions, particularly concerning the behavior of quantum perturbations near horizons, the transfer of information, and a reinterpretation of certain phenomena traditionally attributed to quasi-thermal radiation mechanisms.

This paper does not claim completeness or definitive physical validity. Rather, it is presented as an open structural framework, intended to expand the domain of inquiry from local geometric descriptions toward a deeper topological space that may be more appropriate for physics at the extreme limits of validity of general relativity and quantum field theory.

The present work is the cumulative outcome of several earlier papers and attempts addressing:

the definition of time and causal structure derived from light,

cosmic differentiation as a structural mechanism,

nonlocal transformations at horizons,

and the limitations of metric-based descriptions in extreme regimes.

On this basis, we issue an explicit call for international collaboration with academic researchers in theoretical physics, mathematical topology, quantum gravity, and quantum information theory, with the goals of:

refining the mathematical formulation of the model,

connecting it with existing frameworks (such as loop quantum gravity or holographic approaches),

proposing observational or numerical scenarios to test its implications,

and developing it within an open, collective research program.We believe that the primary value of this work may lie—regardless of its ultimate physical realization—in its structural and mathematical richness, and in its potential to open new avenues for thinking about the nature of horizons, information, and the very structure of spacetime itself.