Planckian Crystallization Theory (P-Theory): The Architecture of Emerging Reality, Born's Rule, and the Unification of Fundamental Interactions

Rustam Vladimirovich Akhmetzianov

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Planckian Crystallization Theory (P-Theory): The Architecture of Emerging Reality, Born's Rule, and the Unification of Fundamental Interactions

R. V. Akhmetzianov

2026-05-07

https://doi.org/10.24108/preprints-3115038

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: v2 (May 2026) has been substantially revised following a series of internal reviews; compared to version 1, v2 expands and strengthens the axiomatic/stage-based framework and the rigor map of statements, details the minimal unitarity conditions of the reduced dynamics and the plan for independent parameter verification (including explicit construction of critical tests and more comprehensive appendices with dimensional consistency, normalization tables, and quantitative estimates of vacuum decay via the Euclidean bounce action). Additionally: The article has been translated into English

Ссылка для цитирования:

Akhmetzianov R. V. 2026. Planckian Crystallization Theory (P-Theory): The Architecture of Emerging Reality, Born's Rule, and the Unification of Fundamental Interactions. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115038

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