Abstract We propose a formal distinction between Abstract Computation (Turing Machines on infinite tapes) and Physically Realizable Computation. We demonstrate that while P=?NP remains an open question in ZFC, the inclusion is physically impossible in any universe governed by thermodynamic laws. We establish the Thermodynamic Censorship Principle: efficiently solving worst-case NP-Complete problems requires physical resources that scale exponentially with problem size to combat thermal noise. By analyzing the Spectral Gap Closure via the Parisi-Talagrand framework, we prove that the readout time for NP-hard solutions exceeds physical limits, establishing Pphys ≠ NPphys. Derivation from the Master EquationThis resolution emerges as the spectral gap limit of the Tamesis Kernel Hamiltonian: H = ∑ Jij σi σj + μ ∑ Ni + λ ∑ (ki - k̄)2 + TS For constraint satisfaction problems (CSP) on a frustrated graph GN, the readout time follows τ ≥ Δ(N)-2. The key result, derived via the Talagrand (2006) proof of the Parisi formula applied to the Kernel's energy landscape, is: Δ(N) ∼ e-αN ⇒ P ≠ NP See the foundational framework: The Computational Architecture of Reality (DOI: 10.5281/zenodo.18407409). I. Introduction: The Category ErrorHistorically, attempts to resolve P vs NP have failed because they treat computation as a purely logical process. We identify "No-Go Zones" (Relativization, Natural Proofs, Algebrization) where mathematical abstraction hits physical reality. Our approach introduces physical axioms that formalize the cost of computation. II. The Physics of NP: Spectral Gap AnalysisLemma 3.1 (Spectral Gap Closure — Talagrand 2006): For worst-case NP-Complete instances (Spin Glasses), the minimum spectral gap Δ(N) between the ground state and the first excited state vanishes exponentially: Δ(N) ∼ e-αN This is a proven mathematical theorem following from the rigorous proof of the Parisi formula. III. Thermodynamic CensorshipTheorem 3.2: To distinguish the ground state signal from thermal noise, the readout time τ follows the Linear Response Limit: τreadout ∝ 1/Δ(N)² ∼ e2αN Since the required time scales exponentially, NPphys ⊈ Pphys. IV. The Three Independent ClosuresThe resolution proceeds through three independent closures: Closure A (Spectral Gap): Talagrand (2006) and Panchenko (2013) proved the ultrametric structure of spin glasses, implying exponential gap closure. This is rigorous mathematics, not conjecture. Closure B (Topological Universality): All NP-Complete problems map to the same universality class. Hardness is intrinsic to the constraint structure, not the encoding. Different representations yield identical scaling. Closure C (Physical Computation Axiom): Under ZFC + PCA (Landauer erasure, Finite speed of light, Thermal noise), the statement P ≠ NP becomes a provable theorem. ConclusionComputational Complexity is a Physical Phenomenon. The "hardness" of NP problems is not a combinatorial accident, but a manifestation of the Third Law of Thermodynamics. You cannot build a perpetual motion machine of knowledge. ∴ P ≠ NP is inevitable in any physically realizable computation.
Douglas H. M. FULBER (Thu,) studied this question.