Can gravitational geometry arise as a collective response without postulating a fundamentalgraviton? We investigate this possibility within the Principium Geometricum (PG) program, inwhich local sectors are restrictions of a global state and toroidal phase and breathing variablesare proposed as underlying degrees of freedom. A local normalization Φ = ZΘ yields K = K0Z2and β = β0Z, preserving β2/K. An exact change-of-variable test shows, however, that thisidentity alone produces no new gravitational observable: when all gradient terms are retained, Z cancels from the physical potential Ψ = βΘ. A physical toroidal mechanism must therefore modify the source energy or introduce independently derived interactions. Conditional on universal clock coupling, the source is total energy, and a static gapless sector yields a Poisson equation and inverse-square acceleration. A reciprocal exponential metric reproduces the static weak-field coefficients γ = β = 1, but its exterior Einstein tensor is nonzero at nonlinear order. The construction thus provides an effective framework and a precise set of consistency tests, rather than a completed quantum theory of gravity. Its central open problem is to derive source energies, constitutive coefficients, and gravitational dynamics from the same microscopic theory. A fundamental graviton is not assumed; emergent graviton-like excitations are neither derived nor excluded.