Chronon Field Theory I: Covariant Mass, Solitonic Matter, and Emergent U(1) A Background-Independent Foundation for QED-like Dynamics, the Coulomb Law, and Fermionic Matter with Emergent (ℏ, G, e, c)

We present a self-contained formulation of Chronon Field Theory (CFT) in which (i) a smooth, unit-norm, future-directed timelike field Φµ induces foliation, causal structure, and an emergent Lorentzian metric; (ii) a covariant local mass/energy density is defined as ρ(x) = Tµν Φ µΦµ, furnishing a unified and positive notion of inertial/gravitational mass; (iii) matter arises as topologically stable solitons with w = 1, carrying spin- 1 2 and Fermi–Dirac statistics via a Finkelstein–Rubinstein/Berry holonomy mechanism; and (iv) a U(1) gauge sector emerges from chronon holonomy, yielding Maxwell dynamics on the emergent metric and a massless “photon” as a Goldstone-like excitation. We prove positivity and conservation properties for ρ, establish existence of finite-energy soliton minimizers under mild assumptions, and state a holonomy-matching theorem that ties the FR Z2 class to the emergent spacetime U(1) connection. A key outcome is that the familiar constants of Nature are not postulated but emerge: the effective action unit ℏeff ∼ Ecτc, Newton’s constant G ∼ (c(αi , γ)Λ2 ) −1 , the elementary charge e = q0/ √ κA, and the universal light speed c = ℓΦ/τc. In the gravitational sector we recover Einstein–Maxwell on stabilized domains at two-derivative order, while allowing controlled, power-counted deviations (æther-like and higher-derivative terms) that are constrained phenomenologically. We further derive the Coulomb law on stabilized leaves, V (r) = e1*e2/(4πr), whose normalization fixes the holonomy stiffness via the observed Coulomb constant (equivalently αem), yielding κA = q0 2/(4παem). We outline collective-coordinate quantization where splittings scale with ℏeff, and identify falsifiable signatures (achromatic birefringence; exchange-phase interferometry). This paper (I) lays the foundation for non-Abelian extensions (II) and QCD-like dynamics (III).