
This work examines the possibility that three constants usually treated as conceptually independent, the geometric constant π, the cosmological constant Λ, and Newton’s gravitational constant G, may admit a common boundary geometric origin. The starting point is a spherical radiative boundary whose topology, flux projection, phase space organization, and harmonic spectral summation combine into the dimensionless invariant π³/15 This invariant is then projected onto the cosmological horizon, yielding the relations ΛR_H² = π³/15 Ω_Λ = π³/45 When the horizon is resolved holographically through the standard Planck area relation N = A_H / ℓ_P² with ℓ_P² = ħG / c³ Newton’s constant appears as the parameter governing the microscopic closure of the same geometry, with the holographic cell count N determining the Planck scale resolution of the horizon. In this picture, π characterizes the spherical boundary geometry, Λ represents its cosmological projection, and G completes its microscopic holographic description. The proposal is not presented as a complete dynamical theory of gravity, but as a geometric reconstruction suggesting that part of the normalization of cosmological and gravitational parameters may originate in a common radiative boundary structure.
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