Emergent Spacetime Rigidity and the Regularization of the Big Bang Singularity

We show that a Planck-scale rigidity principle for spacetime, expressed as upper bounds on curvature invariants, replaces the initial cosmological singularity with a finite Planckian core. In this framework, the Friedmann dynamics approaches a de Sitter-like plateau at early times, ensuring geodesic completeness and a well-defined thermodynamic arrow (gσ ≥ 0). The same structural bound unifies the treatment of black-hole and big-bang cores, which become mathematically indistinguishable (ℓ_P^{2k} I_k ≤ O(1), S_max = A_core/4G). We discuss consistency with observational constraints and the connection to late-time dark energy through the rigidity energy density ρ_rig ∝ 1/L^2. This paper belongs to a broader program where rigidity, entropy, and scale form universal invariants across possible universes.