minEnergyFluctuation
plain-language theorem explainer
minEnergyFluctuation defines the minimum energy fluctuation at the fundamental tick duration τ₀ as ħ/(2τ₀) in RS-native units. Researchers deriving vacuum effects or zero-point energy from temporal discreteness would cite it when grounding QFT fluctuations in the Recognition Science time lattice. The definition is a direct one-line expression using the imported constants hbar and tau0.
Claim. The minimum energy fluctuation at the fundamental timescale satisfies $ΔE_{min} = ħ/(2τ₀)$, where $τ₀$ is the duration of one recognition tick and $ħ$ is the reduced Planck constant in RS-native units.
background
The QFT.VacuumFluctuations module derives vacuum fluctuations from the discreteness of time at scale τ₀. The constant τ₀ is the fundamental time unit (duration of one tick) in RS-native units. The reduced Planck constant satisfies ħ = E_coh · τ₀ = φ^{-5} in these units, as recorded in the Constants module.
proof idea
This is a one-line definition that directly applies the imported constants hbar and tau0. It instantiates the uncertainty bound ΔE · Δt ≥ ħ/2 at the minimal interval Δt = τ₀.
why it matters
This definition supplies the energy scale for the zero-point energy section and supports sibling declarations on Casimir pressure and virtual particle lifetimes. It realizes the module target of deriving vacuum fluctuations from τ₀ discreteness rather than continuum field quantization. The construction connects to the eight-tick octave that enforces the minimal time step in the Recognition Science chain.
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