Quaternary Coding Theory of the Biological Ledger over GF(4): Evaluation Codes, Plaquette Checks, and Conditional Syndrome Decoding

We construct explicit quaternary error-correcting codes for abstract locus, contact and lattice registers motivated by the Chrysene Formalism. Evaluation on the four affine points of GF(4) gives the Euclidean self-dual MDS code [4,2,3]₄. The five projective points give the perfect Hamming code [5,3,3]₄, whose 64 radius-one spheres partition GF(4)⁵; their tensor product is a [20,6,9]₄ array code correcting four arbitrary symbol errors. On the cubical box $B(3,3,6)$, the cycle and cut codes have parameters [117,64,4]₄ and [117,53,3]₄. Their full CSS check pair commutes and has zero logical dimension. An ideal 16-outcome syndrome instrument preserves each syndrome subspace and enables exact classical single-symbol correction. For independent symbol errors of probability p, decoded block failure is 10p²-20p³+15p⁴-4p⁵. We compare uncoded blocks at both fixed coordinate count and equal information payload, distinguish binary-logistic and four-level Gibbs calibrations, and compute their conditional splitting thresholds. At complete quaternary randomization, $p=3/4$, channel capacity is zero and decoder success is only $1/64$. Molecular encoders, Berry-phase readout and Stark control are explicit realization targets rather than consequences of code cardinalities. Executable finite verification and a scoped Lean companion accompany the constructions.