AOFT VI HEXAGONALIGHT -

AOFT VI HEXAGONALIGHT investigates the organization of physical states starting from theAlpha–Omega relation. Alpha denotes the function of difference defined in the domain under consid-eration; Omega denotes the function of coherence defined in that domain. Both are designations forfunctions and acquire their specific mathematical and physical form only through the stated statespace. The energetic realization is𝐸 = 𝛼 ⋅ Ω, 𝐸𝑥 = ΔΦ𝑥(𝑋𝑥) 𝑋𝑥, [𝐸𝑥] = J.The work develops this foundation in three connected parts. Part I explains relationality, difference,coherence, and the six canonical Joule couplings for gravitation, electricity, mechanics, thermody-namics, chemistry, and information. It distinguishes general state information from the energeticinformation axis and formulates their operational realizations. Part II proceeds from photon energy,dual state structure, and light couplings through particle creation and recombination to hydrogenbinding, the hydrogen molecule, helium closure, and the shell organization of the periodic table.Reduced mass, the Coulomb derivation, the virial balance, and the roles of spin and correlation aredeveloped explicitly. Part III specifies local and global reconstruction, the six-color geometry, Fi-bonacci potential stages, the dual mirror, the ATOMOS paths, potential-space admissibility, memoryfrom eliminated structure, and the empirical tests.The common Joule dimension connects the projections without treating them as six independentlyadditive energy reservoirs. The mechanical axis remains 𝐸𝑚 = p ⋅ v; nonrelativistically, 𝐸𝑚 = 2𝐾.Chemistry remains 𝐸𝑐 = 𝑛𝜇𝑐 with lowercase 𝑛 and a molar potential. Information remains 𝐸𝑖 =Bit 𝑘𝐵𝑇 ln 2 with an explicitly declared information process. The six color classes and the bilateralstage 21𝛼 + 21Ω = 42𝛼Ω are structural constructions. A physical selection rule or a new particle massdoes not yet follow from their numbers alone.The quantitative foundation comprises the recalculated hydrogen Coulomb binding, a reproducedcomplex plasma-dispersion root, earlier exploratory TCV findings, and a frozen synthetic dual-codevalidation. Definitions, mathematical derivations, established physics, model calculations, and em-pirical hypotheses are distinguished at the relevant statements. The independent research claimconcerns a testable organization and reconstruction of coupling paths. An additional natural mecha-nism distinguishable from reference physics requires dynamics fixed in advance and an independentprediction.