Projection, Degeneracy, and the Unitarity Formulation of the Black Hole Information Paradox: A Temporal Rate Ontology Analysis

The black hole information paradox admits several distinct formulations. This paper targets the unitarity formulation: the requirement that pure states evolve to pure states under quantum mechanics conflicts with Hawking's derivation of a mixed thermal density matrix for the radiation. We propose a structural reinterpretation within Temporal Rate Ontology (TRO), in which physical states are represented by directed acyclic graph (DAG) continuation structures and observables are coarse-grained projections of this structure onto a space of observational outcomes. Within this framework, the density matrix of Hawking radiation is a projection-level object: it encodes what is accessible to coarse-grained observation, not the full continuation structure of the system. We argue that this reframing is not a hidden variables position in the standard sense, because TRO does not complete quantum mechanics but replaces its ontological substrate. The island formula results (Almheiri et al. 2019; Penington 2019), which restore the Page curve dynamically, are argued to be orthogonal to TRO's contribution: they establish that information is recoverable in principle through non-local correlations, while TRO provides an ontological account of why projection degeneracy is structurally possible and why apparent loss at the observational level is compatible with preservation at the structural level. A precise condition for projection-induced degeneracy is stated and its implications for the unitarity formulation are developed.