Heavy Quark Masses from Gauge Depth: Projective Depth as Mass Amplification

We derive the current masses of the three heavy quarks (c, b, t) from the informational axiom system with zero free parameters. The central mechanism is the gauge depth coupling: a heavy quark at QCD level acquires mass proportional to the electroweak gauge depth D(2) attenuated by the projective cutoff k_max. The three formulas are: m_c = v₃ · (d · D(2))/(k_max · C(3)) · (1 + α_s/(dπ)) = 1.2686 GeV, m_b = v₃ · D(2)/k_max = 4.1766 GeV, m_t = v₂ · (1 − 1/π) = 172.74 GeV, where v₃ = M_Pl · α^g(3) and v₂ = M_Pl · α^g(2) are cascade VEVs (Theorem 82), D(2) = (k_max · d)² = 36 is the gauge depth factorization, C(3) = 10 is the arithmetic cascade depth, α_s is the strong coupling, and k_max = 2 is the projective cutoff. All three predictions lie within one standard deviation of PDG 2024 values: m_c = 1.27 ± 0.02 GeV (−0.07σ), m_b = 4.18 ± 0.03 GeV (−0.11σ), m_t = 172.57 ± 0.29 GeV (+0.59σ). The RMS error is 0.095% across a mass range spanning a factor of 136. Key structural results: (i) the factorization D(2) = (k_max · d)² = 36 reveals the gauge depth as a square of projective modes, (ii) the ratio m_b/m_c = C(3)/d = 10/3 is a pure structural prediction (experimental: 3.29, error +1.3%), (iii) the top quark mass equals the electroweak VEV minus the combined Haar depletion of SU(2)_L × U(1)_Y: m_t = v₂(1 − 1/π). All three masses are formally derived. The top quark formula uses the maximal torus rank theorem: gauge depletion equals rank(G)/(2π), and additivity follows from rank(G₁ × G₂) = rank(G₁) + rank(G₂). Each formula uses only cascade quantities (C(n), D(n), v_n), the strong coupling α_s, and the projective cutoff k_max = 2. No experimental hadronic input is required. A complete Python validation script reproducing all numerical results is provided in the appendix.