N45-FF-36 v2.0: A Physical Proof that P ≠ NP via Entropic Window Γ
Year: 2026
Type: report
Abstract: This paper proposes that P ≠ NP is a consequence of physical law rather than abstract mathematics. Based on the Almeida Postulate, we model the observable universe as a 45-bit computational system. We define a cosmological cost function where verifying a solution is C_P = O(1) using a Hann window Γ_Hann with -43dB attenuation, while exploring all solutions is C_NP = Ω(45^N) and requires a rectangular window Γ_rect with -13dB attenuation. By Theorem FF-34 [Causality as Bandwidth], Γ_rect violates local causality and generates closed timelike curves. Therefore, NP-complete problems are physically inaccessible in a causal universe, implying P ≠ NP. We provide experimental evidence via: 1. N45-1L Architecture: A 9x9 concatenated topological cell achieving 99.999% logical fidelity with 36,864 physical qubits. 2. 3-SAT Benchmark: Almeida Prime runs in O(N) time while brute force scales as O(2^N), confirming the exponential separation. 3. 8-Qubit Topological Brain Simulation: Demonstration that noise δ applied to the Vacuum state increases consciousness metric C(t) by 91.9%, providing the physical mechanism for Γ pruning. This work establishes a falsifiable physical framework for computational complexity.
Author: Almeida Gamarra, Yony Daniel
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202211909