Timecharge-Relativistic Cosmology and the Horizon Duality Principle

A timecharge-relativistic cosmology is proposed in which time is not a universal parameter but a local scalar field τ(x) ∈ [−1, +1] that defines the thermodynamic and causal arrow of time within any given universe. Black hole event horizons are temporal boundaries — surfaces where τ passes through zero and reverses sign, connecting parent and child universes across what standard general relativity describes as singularities. We show that singularities do not exist in this framework: every apparent singularity is a τ = 0 zero-crossing, a smooth field transition between timecharge states governed by a double-well potential. Timecharge is conserved globally across the fractal multiverse through an entropy-weighted conservation law Σ Tᵢ · Sᵢ = 0, where weights are Bekenstein-Hawking entropies. The model exhibits a wave-particle duality: τ is continuous internally (the wave face) and discrete ±1 externally across horizons (the particle face). Major consequences include: the equivalence of cosmological endpoints and black hole singularities as identical τ = 0 events; the reinterpretation of cosmic expansion and gravitational attraction as the same dynamics experienced from opposite timecharge orientations; a possible timecharge origin for dark energy predicting w ≠ −1; complete information preservation through timecharge encoding in child universe initial conditions; and structured non-Gaussian signatures in the CMB encoding parent black hole infall history. Four observational predictions are advanced: timecharge radiation as a breathing-mode gravitational wave signal detectable by LISA; black hole merger mass spectrum suppression testable with current LIGO data; dark energy equation of state deviation from w = −1 testable by Euclid and Vera Rubin Observatory; and CMB non-Gaussianity with preferred directional structure testable against existing Planck data. The highest ambition of this paper is: if we are to be wrong — and in degrees we almost certainly are — to be wrong in ways that teach us something new or improve our confidence in current thinking.