Finite 48-State Symbol Dynamics on a Fibonacci Modulo-9 Lattice

We study a finite 48-state symbol system built on the 24-periodic Fibonacci residue sequence modulo 9. The residue lattice is defined by M (r, c) = sᵣ sc 9, where s is one full Pisano period and the values are partitioned into three exact classes: NIL = \0, 3, 6\, PAR = \1, 4, 7\, and ANT = \2, 5, 8\. On this lattice, we impose a fixed 48-symbol ordering and an adopted internal geometric partition of symbols into four labels (fermion-like, gauge-like, CKM-like, and scalar-like). We report four exact finite results: (i) The first eight seed positions match F (1) through F (8) 9 exactly, with the first five positions natively producing the Fibonacci seed 1, 1, 2, 3, 5. (ii) The 12 NIL (vacuum) symbols are exactly and exclusively those with index k 3 4. (iii) The discrete row structure is sharply segregated under the adopted labels: Row 4 is pure gauge-like (5/5), Row 6 contains four CKM-like symbols (4/5), and Row 7 is pure scalar-like (7/7). (iv) The induced class algebra on the lattice provides an exact discrete scattering table (e. g. , NIL absorbs every class, PAR ANT ANT, and ANT ANT PAR). Consistent with prior papers in this series, all mathematical findings are explicitly claim-bounded. We do not claim a historical origin for the symbol order, nor an empirical derivation of the full Standard Model. This paper records precise correspondence structures without converting them into a broader causal thesis.