Version 2.0.2 update summary Updated Bibliography Version 2.0.1 update summary Addition of an appendixed cascade regimes table. - No other alterations. Version 2.0 update summary (Volume 2) This release represents a substantial revision of Volume 2. The volume has been fully restructured to reflect the fixed ontological ordering of the Temporal–Density Framework and no longer develops matter, dark matter, or horizon structure through dynamical or cosmological narratives. The revised formulation establishes an admissibility-ordered account of pre-geometric structure, introducing distinct coherence regimes that give rise to generative topology, relational extension, and dispersive spatial realisation. Matter and dark matter are redefined as outcomes of completed and incomplete coherence under invariant constraint, and electromagnetism is identified as the necessary bridge enabling volumetric addressability. The treatment of horizons has been rewritten to distinguish clearly between the initiation and termination of volumetric coherence, removing singularity-based interpretations and scale assumptions. All legacy parameters, transitional heuristics, and dynamical proxies from earlier versions have been removed. Version 2.0 supersedes all prior releases of Volume 2 and aligns it consistently with the Core Paper and Volume 1 of the framework. v1.1.1 — Clarification of Gauge Admissibility and Pre-Lorentzian Structure This revision refines the chronological admissibility of the Temporal Triad within the gauge cascade. In particular, the role of linear density and Lorentzian shear is restricted to the $U(1)$ domain, with earlier $SU(3)$ and $SU(2)$ regimes reformulated in terms of curvature, coherence, and geometric continuity rather than density accounting. Several sections have been streamlined to remove redundant parametrisation and to clarify that baryonic and dark–matter partitions arise from coherence contraction under confinement, not from pre-Lorentzian threshold conditions. Version 1.1.0 — Update Summary This update aligns Volume 2 with the final three-volume structure of the Temporal–Density Framework. The title, bibliography, and footer have been standardised to match Volumes 1 and 3, including updated cross-references, DOI links, and project information. No scientific content has been altered: all equations, derivations, and results remain identical to the previous release. Changes include:• Consistent title and formatting across all three volumes• Updated bibliography entries pointing to Volumes 1 and 3• Standardised footer with project site and ORCID• Minor layout and style corrections for inter-volume continuity This release brings Volume 2 into full alignment with the published framework and prepares it for integration with the tdft.co.uk reference archive. v1.0.2 Update Summary This version introduces a fully integrated derivation of Hawking radiation within the Temporal–Density Framework (TDFT).The new Section 7.6 reformulates horizon evaporation as a coherence-mismatch phenomenon of the temporal substrate, replacing the need for geometric singularities in GR. Hawking temperature is shown to arise as the SI projection of the substrate’s saturation dynamics. The update also clarifies the physical status of black holes within TDFT: horizons are non-radiative temporal-saturation surfaces, and black-hole interiors remain inert, gauge-silent regions at the universal density floor. This resolves the long-standing conceptual tension between particle–based Hawking emission and the intrinsic structure of the temporal substrate. Additional refinements include: a new QFT–TDFT correspondence section (7.5), improved logical weaving between gauge collapse, substrate saturation, and horizon physics, updated predictions and observational consequences, consolidated terminology and tightened cross-references. No changes were made to quantitative demonstrations or empirical predictions; all remain stable under the new horizon formalism. Minor Revision (v1.0.1):Corrected section-transition phrasing in §4, compacted large figure caption for clarity, harmonised cross-references, and aligned flow with the developed gauge-cascade ordering.No scientific content or equations have changed.

This volume develops the ontological origins of matter, dark matter, and horizon structure within the Temporal–Density Framework, extending the invariant foundation established in the core formulation. It introduces an admissibility-ordered account of pre-geometric structure, describing how successive coherence regimes give rise to generative topology, relational freedom, and ultimately dispersive spatial realisation. Matter and dark matter are treated not as products of dynamical evolution or collapse, but as distinct outcomes of completed and incomplete coherence under invariant constraint. Dark matter is identified with fully closed generative structure, while baryonic matter emerges through extended relational coherence that becomes electromagnetically addressable only after the onset of U(1) admissibility. Electromagnetism is described as the coherence bridge that enables volumetric realisation and atomic structure, rather than as an independent interaction. The volume also clarifies the ontological role of horizons. The U(1) horizon is shown to mark the initiation of dispersive volumetric coherence, while black-hole horizons mark its termination. Although both share the same linear-density condition, their functions are categorically distinct. No singularities, scale assumptions, or temporal narratives are invoked. This work is non-dynamical and non-cosmological in scope. It does not propose a history of the universe or a mechanism of formation in time, but instead establishes the conditions under which different forms of physical description become admissible. Related Works This volume forms part of a chronologically organised research programme developing the Temporal–Density Framework from first principles: J. P. Hughes,The Temporal–Density Framework (Volume 0): Axiomatic Geometry from a Single Constraint,Zenodo (2025).DOI: 10.5281/zenodo.17904884Establishes the foundational geometric ontology and invariant constraint underlying the framework. J. P. Hughes,The Temporal–Density Framework (Volume 1): Dimensionless Unification and Empirical Predictions,Zenodo (2025).DOI: 10.5281/zenodo.17597722Develops the invariant triad, dimensionless field dynamics, and initial empirical consequences. J. P. Hughes,The Temporal–Density Framework (Volume 2): Unified Origins of Matter, Dark Matter, and Horizon Geometry,Zenodo (2025).DOI: 10.5281/zenodo.17666466Describes the geometric origin of matter, dark matter, and horizon structure within the same ontology. J. P. Hughes,The Temporal–Density Framework (Volume 3): Geometric Entropy and the Origin of Cosmic Structure,Zenodo (2025).DOI: 10.5281/zenodo.17716678Extending the framework to galactic, cluster, and cosmological scales. Author: J.P.Hughes ORCID: 0009-0005-7543-3681 Project site: tdft.co.uk