Particle Physics from Topological Saturation: Mass, Charge, and Radius from the ℂP¹ ↪ ℂP² Embedding

This paper proposes that the Standard Model’s fundamental particles are classified by a hierarchy of complex projective spaces: the electron by ℂP¹, the quark by ℂP², and the proton by the full group U(3) containing three antisymmetrically confined quarks. From the single natural embedding ℂP¹ → ℂP², the paper recovers six experimentally confirmed quantities: (i) the proton-to-electron mass ratio mₚ/mₑ = 6π⁵ ≈ 1836.12, explaining the 1951 observation of Lenz;(ii) the proton charge radius relation rₚ = 4λ̄ₚ, equivalent to the Trinhammer–Bohr U(3) result;(iii) the up quark electric charge Qᵤ = 2/3 as the ratio c₁(CP¹)/c₁(CP²);(iv) the down quark charge Q_d = 1/3 as the complementary ratio;(v) the Koide lepton mass relation at ppm accuracy; and(vi) the baryon decuplet mass spacing Δm_s = 3π⁴mₑ ≈ 149 MeV. The paper argues that these results are not independent numerical coincidences but consequences of a single geometric hierarchy ℂP¹ → ℂP² → U(3). The central physical principle is generative exhaustion: rest mass is identified with the total irreversible depletion of a compact internal configuration space. This selects the Kähler top form ωⁿ, rather than the Liouville-normalized form ωⁿ/n!, as the physically relevant volume measure. Under that selection, the proton mass formula becomes 6π⁵ rather than 6π⁵/8. The framework further provides structural explanations for color confinement, baryon number quantization, the absence of strong interactions for leptons, and CPT invariance of baryon masses. It is presented as part of a broader programme in which physical time emerges from irreversible record formation on compact Kähler manifolds.