Tutorial 1: Deriving How Many Particles the Mandala Allows

Description: A guided worksheet deriving the Standard Model's 11 fundamental fermion channels from the geometry of the mandala — a regular pentagon with inscribed triangle — using only counting and symmetry. Starting from three numbers read directly off the figure (s = 5, Nᶜ = 3, χ = 2), the tutorial constructs the 125-dimensional site space, decomposes it into four type-patterns (CCC, CCW, CWW, WWW) and three symmetry types under S₃, and shows that Λ³(ℂ²) = 0 reduces the 12 candidate channels to exactly 11 — matching the 11 interior regions of the pentagon with all diagonals drawn. A postscript explains how the same χ = 2 that removes the 12th channel also encodes the particle–antiparticle distinction via boundary patch orthogonality, and why this structure predicts Dirac (not Majorana) neutrinos. Includes a fill-in worksheet and complete answer key with TikZ mandala diagrams. Keywords: Information-Pressure Theory, IPT, mandala algebra, Standard Model, particle physics, fermion generations, Young diagrams, S₃ permutation symmetry, representation theory, neutrinos, Dirac neutrinos, Majorana exclusion, antimatter, fine sectors, spectral geometry, pentagon geometry, χ = 2, tutorial, worksheet