Energy Accumulation Threshold

The Energy Accumulation Threshold is the minimum energy that must be accumulated over a pulse cycle for a Zinf torus to close, a threshold set by collapse dynamics and fundamental energy scales. The book treats toroidal closure as conditional, not automatic: a closed Zinf torus must meet the Data Nova threshold for dimensional closure, and whether a recursive architecture sustains itself or dissolves depends on crossing this energy criterion. A companion Surface Energy Density Requirement, σ_E ≥ (κ × Ω⨶ × P⊡ × F⊜)/A⥥, spreads the same threshold over the minimal toroidal area, so smaller tori need higher surface energy density. The formal statement is ∫₀ᵀ E(t) dt ≥ κ × Ω⨶ × P⊡ × τ⥂ × F⊜, where E(t) is the accumulated energy rate, T the pulse period, κ a normalization constant, Ω⨶ the critical collapse threshold, a ratio, P⊡ the pulse energy quantum, τ⥂ the pulse duration, the Pulse Rhythm ①⥂⧖ and F⊜ a tolerance modulator. Dimensions from the book's Where-list: E(t) [𝕄·𝕃²·𝕋⁻²], T and τ⥂ [𝕋], κ, Ω⨶ and F⊜ [∅], P⊡ [𝕄·𝕃²·𝕋⁻²]. It connects to the Surface Energy Density Requirement, Cycle-Averaged Recursive Gain, Physical Nova Ignition Threshold, Zinf-Limit Universe and Pulse Rhythm Definition.