IRS as Emergent Structure from Exceptional-Group Topology: Primordial and Mediated Emergence via the Recursion-Invariant Functor

Drawing on the categorical foundation for closed recursive self-reference [1] and the algebraic-geometric unification of E8 through SU (3), SU (2), U (1), and H4 symmetries, this paper refines the Infinity Resonance System (IRS) as a macroscopicemergent description constrained by exceptional-group topology. IRS constructs are presented in a derivational hierarchy with primordial and mediated emergence layers from seven fundamental invariants extracted by the Recursion-Invariant Functor(RIF) on a category of exceptional-octonionic objects. Primordial (topological) emergence yields IRS fundamentals directly from invariants along the chain H4 → E8 ⊃E7 × SU (2) ⊃ E6 × U (1) ⊃ SU (3)3 × U (1). Mediated emergence produces mediatedfeatures—including Non-Localised Resonance Waves (NRW) and Localised Resonance States (LRS)—via interactions and compositions of primaries. Black Holes as algebraic local saturation fixed points arise from recursive symmetry descent alongthe fixed exceptional chain while Vacuum as a finite-capacity entropy sink is mediated by the E8 manifold bulk (J = 0 scalar topology), where decoherent shards lack phase coherence for angular momentum. Modes aligned with H4 are partially recovered via a Galois-type feedback loop, while non-aligned modes accumulate in the vacuum, eventually forming global algebraic horizons. We use ’primordial’ for immediate topological derivations and ’mediated’ for sub-sequent internal elaborations.