RZS Series: Relational Topological Quasiparticles

I present a discrete-relational construction within the Relational Zero State framework, in which microjump weights define the operational geometry for a postulated effective weighted-gauge sector. My goal is not to claim a derivation of fundamental particles, a continuum limit, or anyonic exchange statistics. Instead, I show that this effective sector supports a reproducible particle-like regime: localized gauge-covariant topological defects remain stable, respond coherently to Gauss-consistent boosts, keep low core deformation, and admit operational mass and response tensors. I call the static object a Weighted Relational Gauge Vortex and the mobile nearly rigid regime a Relational Topological Quasiparticle regime. The manuscript documents the construction, the gauge-invariant charge, the Gauss projection, negative mobility controls, finite-size ensembles up to size 128, rectangular-lattice tests, a minimal phase map, non-extensive operational-mass scaling, and a static two-defect sector. The central claim is deliberately limited: given this postulated weighted-gauge sector on an RZS microjump substrate, the model exhibits reproducible, operational, discrete-relational quasiparticles.