A Global Rigid Proper-Color Clock from an Adelic Scalar (v2)

Abstract | The same single adelic scalar field π(x^μ) ∈ ℝ × ℤ₂ × ℤ₃ × ℤ₅ × ℤ₇ × ℤ₁₁ that defines the global proper-time clock (Paper I) and the global proper-scale clock (Paper II) also defines a third rigid clock: the global proper-color clock. The parity sequence of the natural numbers evaluated under the adelic norm defined by the five primes {2,3,5,7,11} generates a bounded oscillating function. Generation-indexed assignment of this function yields the rational hypercharges of the Standard Model. No new axioms or free parameters are introduced beyond the observed three chiral fermion generations.