The Einstein coupling from surface addresses: 8πG/c⁴ = QΣ/ℏc, and why the 1/4 and the 8π are the same counting

One surface count, two famous coefficients This paper isolates a compact claim in Quantum Traction Theory (QTT): the coefficient \ (1/4\) in the horizon entropy law and the coefficient \ (8\) in Einstein's field-equation coupling are two readouts of the same surface address quantum, \ Q_ = 8 A². \ The source-side entropy count is \ SkB = 2 AQ_ = A4A², = 2 kBQ_ = kB4A². \ The local horizon thermodynamic route then fixes the field-equation coupling as \ ₐₓₓ = ₐ_ ₂ = 8 A²{ c = 8 GAc⁴ }. \ The same-counting closure is the short invariant: \ \, ₐₓₓ\, ₂₊₁ = 2. \ In plain language: divide one completed surface bundle by its area and one obtains the entropy density; divide the same surface bundle by \ (c\) and one obtains the gravitational coupling. The \ (1/4\) and the \ (8\) are not separate normalizations in this framework. They are the same address count read through two different laboratory windows. The numerical value leg is inherited from the companion non-gravitational Planck-length construction: \ GA=A²c³, 8 GAc⁴ = 2. 076647881210^-43\ s²\, kg^{-1\, m^-1}, \ with \ (GA\) landing \ (+0. 211\) ppm from the CODATA Newton constant, or \ (+0. 0096\) on the CODATA uncertainty. The included standard-library verification script regenerates the displayed numerical identities. Related QTT anchors: Main book: Quantum Traction Theory: Main Book v10. 01 Non-gravitational Planck-length construction: 10. 5281/zenodo. 21190193 Newton's constant in QTT: 10. 5281/zenodo. 20057430 A2 endurance to Einstein-field dynamics: 10. 5281/zenodo. 20763263 Einstein-Hilbert coefficient source paper: 10. 5281/zenodo. 20042843 Website: quantumtraction. org Corpus DOI map: quantumtraction. org/doi-map/ Included files: PDF paper, Version 1. 1. 1 Complete reconstruction ZIP containing the LaTeX source, verification script, verifier output, change note, and SHA-256 manifest