Branch-Local Field Algebra, Phase Selection, and Matter Spectrum

SCQG paper 18 of 28. Paper 18 explains how Semantic Commitment Quantum Gravity (SCQG) connects its microscopic description to matter fields, particle species, gauge symmetries, masses and mixing on one physical branch. The construction requires the action, field algebra, prepared state and scale-dependent couplings to describe the same system. It distinguishes the local gauge algebra from the global gauge group and its bundle and line-operator data, which constrain the allowed charges. Anomaly conditions test whether the quantum theory preserves the symmetries required for a consistent matter description. For the stated 3 + 2 internal-channel construction, the paper derives a one-family fermion representation. When the frame symmetry is physically gauged, its determinant constraint gives (SU(3) × SU(2) × U(1))/ℤ₆. It follows the neutral fermion or topological contribution needed to complete the discrete anomaly calculation. Family selection is then treated separately. The framing test asks whether changing an auxiliary geometric frame leaves physical amplitudes unchanged. Under the stated completion and framing conditions, the family count must be divisible by three. Combining that result with the separate benchmark bound of one to five families selects three families. The paper also gives a criterion based on physical CP-violating data. The spectrum is defined through quantum correlations. Isolated positive spectral weights describe stable excitations, while complex poles of causal response describe resonances. The paper keeps these distinct from continuous spectral weight and from particles identified by finite instruments. It also treats Higgs symmetry breaking, fermion mixing, finite chiral regulators and Stoney–Planck coupling coordinates. The resulting matter data supply the later kinetic and gravitational calculations in the series. Reciprocal CPT conditions relate the allowed endpoint data; ordinary matter fields, states, signals and energy currents remain local to their branch.