A conditional modular-charge fifth term of the Unified Equilibrium Law within QTT: E_P = (ℏc/2πℓ_P) Q_P at A7 saturation

**Abstract.** The Unified Equilibrium Law (UEL) of the Quantum Traction Theory (QTT) two-clock framework states that one framework-defined Planck four-cell carries one Planck energy through the four-term identity E_P = m_P c² = ℏω_P = ρ_(4)(4πℓ_P⁴). Conditional on the framework's Axioms A2 (Newtonian limit, ℓ̃ = ℓ_P), A4 (S¹ internal dial), A5 (visible–hidden world-cell factorization), A6 (per-address capacity), A7 (Law of Bundled Existence, fixing the saturated modular-charge budget at Q_w^bundle = 2π), and on the QTT angular modular convention Q := 2π S(ρ‖ω) — the natural choice given the geometric modular flow of Bisognano–Wichmann/Unruh type — the four-term UEL admits a fifth term with no new coupling: E_P…