Mass Ratio Correction and Quantum Oscillation in the Fine Structure Constant: The Role of mₑ/mₚ and e (Paper III of III)

Building on Paper II (1/αᵢdeal = 24π²/√3 = 136. 757), we derive two physical corrections that bring the prediction to 14. 9 ppb precision. 1/α = 24π²/√3 + √3/6· (1 − mₑ/mₚ − 1/ (4e²) ) = 137. 035 999 121 CODATA 2018: 137. 035 999 084. Discrepancy: +2. 0×10⁻⁷ (14. 9 ppb). ─── First correction: CODATA precision mass measurements ── The electron and proton are the two long-lived stable charged particles in nature. Both carry identical electromagnetic charge; both satisfy the TGA stability condition. Since they share the same outer electromagnetic coupling frequency, their difference is entirely in the inner fermionic energy — encoded in the mass ratio mₑ/mₚ. Using CODATA 2018: mₑ = 0. 510 998 950 00 MeV (±1. 5×10⁻¹⁰) mₚ = 938. 272 088 16 MeV (±3. 1×10⁻¹⁰) δ₁ = √3/6· (1 − mₑ/mₚ) = +0. 288 518 → 1/α⁽¹⁾ = 137. 046 (71 ppm) ─── Second correction: quantum oscillation and Euler's number e ── The TGA projection is a continuous existence payment process: the fermion pays its existence cost at every moment, like continuous compounding. The natural base of this process is Euler's number e: lim (n→∞) (1 − 1/n) ⁿ = 1/e = 0. 367879. . . The zero-point oscillation amplitude is identified numerically as Aω ≈ 1/e: δ₂ = −√3/6·1/ (4e²) = −0. 009 767 Verification: |δ₂|/τG (e) = 0. 033841 vs 1/ (4e²) = 0. 033834 (agreement 0. 021%) ─── Precision progression ─────────────────────────────── Topology only (Paper II): 136. 757 2034 ppm + CODATA masses: 137. 046 71 ppm + quantum correction e: 137. 035 999 121 14. 9 ppb (4800× improvement) ─── Physical implications ─────────────────────────────── (1) Gravity is not a force — both the electron and proton are equally stable despite a factor of 1836 difference in TGA projection magnitude. Stability depends on existence of the patch, not its size. (2) The strong force requires no independent mediators — both particles share the identical stability mechanism. ─── Series information ────────────────────────────────── Paper III of III. Published simultaneously with: - Paper I: Overview and main result (1/α = 137. 035 999 121, 14. 9 ppb) - Paper II: Geometric derivation of 24π²/√3 (no mass input)