Informational Singularity Intersection (ISI) Hypothesis: Physical Constants as Dimensional Singularities and Fractional Operator Hierarchies

We propose the Informational Singularity Intersection (ISI) Hypothesis: physical reality emerges as the intersection of singularities across multiple dimensions, where each dimension is infinite in its own metric but appears finite to observers constrained to lower-dimensional projections. We introduce five Intersection Projection Axioms (IPA-1 through IPA-5). IPA-1 states that all fundamental physical constants represent projection singularities — each is infinite in its own dimension, appearing finite only through stereographic-type projection onto our observational manifold. IPA-2 extends this to information: the base unit of information (the d_bit) is an infinite-dimensional quantum superposition pre-measurement. IPA-3 generalises the fractal dimension parameter from d ∈ [0,1] to d ∈ [0,∞) for every dimension. We demonstrate that the arithmetic operator hierarchy maps onto a continuous α-axis (α = 2 − d_H, where d_H is the Hausdorff dimension), connecting classical calculus (α=1), quantum mechanics (α=0, d_H=2, as confirmed by Feynman path integrals), and the ISI singularity (α→−∞). Time is reframed not as a dimension but as emergent ordering arising at the d_H=1 boundary. Consciousness is proposed as a self-referential fixpoint of the d_H reduction process (IPA-5). Experimental grounding is provided by the recent observation of negative weak values for photon dwell time (Angulo et al., Physical Review Letters, 2026, DOI: 10.1103/gjfq-k9dv), interpreted here as a projection crossing the Riemann sphere pole.