Inverted Hypersphere Cosmology: First Principles from a Single Axiom

We develop the foundational layer of Inverted Hypersphere Cosmology (IHC), a framework that begins from a single axiom—that a state of non-existence is not self-consistent—and asks what minimal structure a self-referential reality must possess. We argue that consistency forces a non-preferential superposition whose natural geometric carrier is the real projective space RP^4 = S^4 / Z_2, and we show that a chain of uniqueness arguments then fixes, with no adjustable parameters, a sequence of structural quantities: the spatial dimension n = 4; the golden ratio varphi as the self-similarity constant of the collapse hierarchy, via its maximal irrationality (Hurwitz); a shell count N = 33 = 3M with M = 11 from Fibonacci spectral stability on RP^4; and a Z_3 triality structure yielding three generations. From this geometry we derive parameter-free values for the dark-energy fraction Omega_Lambda = (5 - sqrt(5))/4, the Weinberg angle sin^2 theta_W = (3/8) varphi^(-1), the electron mass ratio m_e / m_P = varphi^(-78) * 33^(-4) * e^(-alpha), and the coherence coefficient beta_coh = 6 cos(pi/23), together with the vanishing of the strong-CP angle as a topological consequence of the RP^4 identification. The anti-periodicity of the cohesion field forced by this identification is shown to place twisted-sector resonances at half-integer positions of the golden shell ladder. Throughout we maintain an explicit separation between quantities genuinely derived from the axiom and those imported as empirical anchors; the framework requires a single dimensionful input, and we make precise which dimensionless ratios are fixed around it.