Matter from the Fundamental Spatial Structure.

In the Stochastic Rupture (SR) framework, space emerges from stacked two-dimensional holographic sheets and matter from defects in their structure. We explore a single question: if such a sheet can close on itself, the closed surfaces fall into a small number of topological classes (sphere, torus, projective plane, Klein bottle), and we propose that these classes correspond to categories of elementary matter sphere to lepton, torus to quark, projective plane to spin. The correspondence reproduces several qualitative facts of one generation without further assumption: leptons carry no colour (the sphere has no non-contractible cycle), quarks are conned and come in three colours (the torus tube can wind around each of three emergent spatial axes),and spin is the Z2 of non-orientability. We then present the charge content as a 2 × 2 structure, a dynamical selector for sphere versus torus based on the impact angle at saturation (with 45◦ as the parameter-free divide), and the sheet dynamics that x colour to three through Plateau's laws. We propose that the closed eight-corner cube cell acts as a conning box for a baryon's tori, admitting exactly three one per perpendicular spatial axis so that the three quarks of a baryon, and the three colours, are anchored in the dimensionality of space (d = 3), a fourth coloured constituent being geometrically impossible. For the three generations a separate, ordinal question we propose that they arise from the assembly of the sheet: jigsaw-like tabs on its edges link sheets in a chain that closes the cube corner at three (the angular-defect bound δ = 360◦ − 90◦n, convex only for n = 1, 2, 3), giving both a cap at three and a mass ordering by chain length. We note that this cube corner is the same object as the coordination-three egg-box vacuum cell of a companion proposal [5], as a single universe requires. Throughout we are explicit that this is a taxonomy and an assembly picture, not a dynamical derivation: it does not yield mass values, the sheet-to-particle map is proposed rather than derived, and the mechanisms are recorded to invite examination and falsication.