Mathematical Framework

Formal mathematical framework of the Informational Singularity Hypothesis (HSI). This component contains the core theoretical formalism, including: - Level 0 (Φ): The primordial informational field defined as Φ = ({R_α : α ∈ ℕ}, ⪯) ⊂ Ω, generated through deterministic stratified AND-collapse from absolute Nothingness (∅₀). Decay frame: D_α = (Acc_α)ABS. - Level 1 (H): The Primordial Holographic Field H = Σ P_k(Φ) · ω_k, where emergent patterns P_k and rules ω_k self-organize from the collapse dynamics. Includes the Order Energy functional ℰ[ω]. - Level 2 (Ψ): The Fundamental Geometric Field Ψ = Σ c_i · φ_i, with the transformation functor ℱ: H → Ψ mapping informational structures to physical geometry via f(ω_k → φ_i) and g(P_k → c_i). - Falsifiability criterion: If no mapping ℱ can reproduce basic empirical features of physics (Lorentz invariance, gauge symmetries, conservation laws), the hypothesis must be considered incomplete or erroneous.