
We present Inverse Time Limit Theory (ITLT), a geometric framework based on the principle that spacetime curvature saturates at a fundamental density scale: ρ* = βMₚ⁴ This principle provides a minimal extension of Einstein gravity without modifying the Einstein–Hilbert action or introducing additional fields. In the static, spherically symmetric sector, it yields a regular black hole solution described by the metric function f(r) = 1 − (2Mr²)/(r³ + a), where a = M/ρ* This spacetime is free of curvature singularities, contains a finite-curvature core, and asymptotically recovers the Schwarzschild solution. All curvature invariants remain finite, and the spacetime is geodesically complete.The same curvature saturation principle extends naturally to homogeneous cosmology, leading to a modified Friedmann equation in which the Hubble parameter remains finite at arbitrarily high densities. This eliminates the classical Big Bang curvature divergence while preserving standard cosmological evolution in the low-density limit. The theory predicts the existence of a universal curvature bound, nonsingular black hole interiors, and Planck-scale remnant formation.ITLT provides a unified and purely geometric mechanism for singularity resolution in both gravitational collapse and cosmology, governed by a single universal curvature scale, while remaining fully consistent with Einstein gravity in the weak-curvature regime.
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