The Generation Structure of Fermions: Particles as Completed Closure Cycles in a Sea of Light

The synthesis paper (main paper 9) of the Dimension Generation series. The central claim inverts default and exception: the default state of the system is a sea of light — the zero-square-sum closure (fully coherent shared modes) is the axiom itself, so nothing needs to be created for light to exist. Particles are the exception: rare events in which a chain of exchanges happens to complete a register's closure cycle and becomes a recurring closure. The first branching is parity (odd harmonics = fermionic, even = bosonic); the second is address capture (rational addresses m/n on finite registers); matter and antimatter are counted in pairs by the closure geometry itself (lambda^62 = -1, lambda^124 = +1, a 2:1 double cover). There is only one interaction — the universal exchange collision, whose per-collision flow splits identically into exactly two terms — and the kinds of force are aliases of the kinds of particle, which are aliases of wave shape (four independent axes: parity, binding, coherence, hair). The photon is the hair-free, fully shared even-difference mode: boson by parity, massless by full coherence (det Gamma = 0, a Cauchy-Schwarz identity), chargeless by absence of hair, free by absence of address. Abundance follows from counting: among M = N(N-1)/2 relational waves at resolution N, the closure-capable integer-ratio pairs are a fraction f(N) = 2(ln N + 2 gamma - 2)/N — matter is extremely rare yet strictly nonzero, and the observed baryon-to-photon ratio ~ 6e-10 reads as a fossil of the resolution N ~ 10^11 at arrest. Derivation and synthesis only: no new numerical experiments, no figures; every quantitative fact maps one-to-one to published papers and committed reproduction packages. Ten open problems are stated explicitly in three tiers, including the address-selection problem (60 coprime addresses; why 23/124), the boson spectrum, and the mass dictionary. Japanese and English versions included.