Abstract
Volume I of the Temporal–Density Framework establishes the invariant α c λ = 1 as the sole foundational constraint underlying curvature, gauge structure, and physical response within a single temporal substrate. The formulation is fully dimensionless: all conventional constants arise as geometric projections of the invariant equilibrium rather than as independent physical inputs.
Gravitation and electromagnetism are unified at the field level as longitudinal and transverse expressions of the same isotropic temporal tension. Curvature, mass, impedance, and horizon structure emerge directly from the requirement that the invariant be preserved across non-uniform geometries, without introducing auxiliary fields, normalisers, or free parameters.
Gauge structure is interpreted as a hierarchy of admissibility regimes (SU(3) → SU(2) → U(1)) governing how temporal coherence may be realised under increasing degrees of freedom. Dark matter is identified as a residual coherence population formed prior to full shear admissibility, rendering it gravitationally active but electromagnetically silent.
Volume I serves as the definitive, non-historical foundation of the framework, establishing its ontology, invariant structure, and empirical testability. Subsequent volumes extend this foundation to gauge-resolved particle physics, dark-matter behaviour, and cosmological structure.