Energy Barrier Height

Energy Barrier Height is the size of the potential barrier that holds a formed structure together, which must exceed the thermal energy scale for the form to stay stable. The book lists it first among the stabilization mechanisms that keep forms alive after the field-to-form transition, alongside the Form Persistence Time, which Temporal Drag lengthens as τ𝓜 = τ_0 × (n + 1)² in deeper layers, and the decoherence time scale. Stability requires that the barrier, found by integrating the excess of potential over total energy across the barrier region, exceed thermal fluctuations. The formal statement is ΔE◫ = ∫_(x1)^(x2) [V(x) − E] dx > ħ*ωΘ, where ΔE◫ is the Energy Barrier Height, V(x) the potential energy at position x, E the total energy, x1 and x2 the edges of the barrier, dx the spatial element, ħ the reduced Planck constant and ωΘ the thermal frequency. Dimensions from the book's Where-list: ΔE◫ [J], V(x) and E [𝕄·𝕃²·𝕋⁻²], x, x1, x2, dx [𝕃], ħ [𝕄·𝕃²·𝕋⁻¹], ωΘ [𝕋⁻¹]. It connects to Form Persistence Time, Temporal Drag, Thresholds of Recursion and the Field-to-Form Transition.