P-Theory (Planckian Crystallization) offers a systematic approach to fundamental questions in quantum mechanics, cosmology and quantum gravity based on a minimal five-dimensional extension: the fifth dimension is interpreted as world time 𝒯, orthogonal to the observed 4D spacetime, and the dynamics of "the becoming of reality" are governed by an order parameter Φ(𝒯) and two-stage crystallization (Stage I: initiation/drift; Stage II: relaxation completion). Within Stage-1 it is demonstrated how, from the axiomatic framework and statistical averaging over independent cycles Δ𝒯, key consequences arise, including a derivation of the Born rule and a universal temperature decoherence law τ_decoh(T) = ℏ/(υk_BT) with a prescribed parameter structure. Preliminary numerical comparisons are provided for the cosmological constant Λ, the anomalous magnetic moment of the muon (g-2)_μ, and estimates of vacuum stability. Substantial attention is devoted to discussion of classical paradoxes (black hole information paradox, the vacuum selection problem, the problem of time), and a plan of critical tests for the coming years is formulated together with a roadmap for subsequent stages (Stage-2/3/4), including independent fixing of input parameters via 6D Calabi–Yau geometry and operator formalization of the world-time variable. Version history: v3 (May 2026) has been substantially revised relative to v2. The prediction F5 (cosmological constant) mechanism has been completely reformulated: the one-loop KK-summation is replaced by a two-stage factorization υ_total = υ_local × υ_global, with υ_local (~1, Planck-scale thermal regime) and υ_global determined by Calabi–Yau compactification. The updated numerical estimate is Λ_Stage-1 ≈ 1.020 × 10⁻⁵² m⁻² (~7% deviation from observed), with success criterion for Stage-2 being independent KK-spectrum computation. F5 is positioned as one member of a family of SM-parameters jointly fixed by CY⁶ topology. Vacuum stability estimates are correspondingly revised: S_E ≈ 8.5 × 10⁵, N_nucleations ~ 10⁻³⁶⁸⁹⁵² [^8d]