EnvironmentCoupling
plain-language theorem explainer
EnvironmentCoupling packages the number of environmental modes N and coupling strength g (bounded in [0,1]) as the input record for decoherence calculations in Recognition Science QFT. Researchers formalizing first-principles decoherence from the Gap-45 threshold and phi-ladder scaling would cite this structure when building the quantum-to-classical transition. The declaration is a plain structure definition with no lemmas or computational reduction.
Claim. An environment coupling is a record consisting of a natural number $N$ (number of modes) and a real number $g$ satisfying $0 ≤ g ≤ 1$ (coupling strength), used to compute the decoherence timescale via $τ_0 × φ^{-N g}$.
background
The QFT.Decoherence module derives decoherence timescales from the Gap-45 threshold, the approximate ratio 10^45 between Planck time and biological scales that separates coherent quantum regimes from classical ones. Quantum coherence persists below this threshold; exceeding it entangles the system with the environment and produces decoherence. The structure supplies the parameters N and g that enter the formula $τ_decoherence ≈ τ_0 × φ^{-N g}$, where φ is the golden ratio and τ_0 is the fundamental tick.
proof idea
Structure definition that directly declares the fields modes : ℕ, strength : ℝ and the proposition strength_bound : 0 ≤ strength ∧ strength ≤ 1. No upstream lemmas are invoked; the declaration serves as the type for downstream definitions such as decoherenceTime.
why it matters
EnvironmentCoupling supplies the typed parameters required by decoherenceTime and the monotonicity theorems decoherence_decreases_with_modes and decoherence_decreases_with_coupling. It realizes the Gap-45 mechanism inside the Recognition Science framework by tying mode count and coupling strength to exponential suppression through φ, consistent with the phi-ladder and eight-tick octave. The structure closes the interface between the classical bridge and QFT, enabling the quantum_classical_dichotomy theorem.
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