A modular-charge fifth face of the Unified Equilibrium Law in Quantum Traction Theory: E_P = (ℏc/2πℓ_P) Q_P at A7 saturation

Abstract

Reading Planck energy as a completed modular-charge budget Version: 3.8 Concept DOI: 10.5281/zenodo.19975260 Author: Ali Attar Website: quantumtraction.org \[ \boxed{ E_P=m_Pc^2=\hbar\omega_P =\rho_A^{(4)}\!\left(4\pi\ell_A^4\right) =\frac{\hbar c}{2\pi\ell_A}Q_P, \qquad Q_P=2\pi. } \] The paper reads mass, frequency, completed-event four-capacity, and A7-saturated modular capacity as faces of one endpoint budget. Version 3.8 makes the fourth face auditable rather than merely dimensionally recognizable: \[ \boxed{ \Delta V_A^{(4)}=24\left(\frac{\pi}{6}\ell_A^3\right)\ell_A=4\pi\ell_A^4, \qquad |\mathcal O_3^+|=24. } \] The external standard ingredients are the ball volume and the proper orientation count. The QTT-native object is the completed address-event product measure and its fourth-face role. The fifth face then uses the separately declared A7 modular saturation \(Q_P=2\pi\); the release does not reclassify ordinary low-energy Landauer erasure as the same object. Public anchors Quantum Traction Theory: Main Book Completed-Event Four-Capacity Theorem QTT Lexicon QTT Derivation Atlas The release package exposes one PDF preview. Source, verification material, metadata, and a SHA-256 manifest are bundled in the reconstruction ZIP.