Sparse Local Operators on the Codon Hamming Graph: Blind Cross-Family Prediction, Symmetry Breaking, and the Empirical Boundary of High-Dimensional Geometry

Paper 070 provides a reproducible re-evaluation of the relationship between codons and high-dimensional geometry. The 64 codons form the known Hamming graph H(3,4), realizable as a nine-dimensional product of three tetrahedra. Rather than treating this representation as a biological cause, the study tests a blinded cross-family prediction task: all synonymous codons of the target amino-acid family are removed before their within-family usage distribution is predicted from position-specific Hamming neighbors elsewhere in the codon table. The target-family masking rule reduces 36 directed edge types to an exact rank-33 operator with three structural zero types. A stability refit yields a threshold-dependent 17-type support. On 699 separate UCI/CUTG aggregate profiles, this support outperforms a seven-type model, uniform Core64, and a third-base-centered factor tree across most or all evaluable kingdom groups, while offering no meaningful improvement over a previously frozen 20-type model. The accompanying topology and tensor audit identifies the exact valid structure—an anisotropic local Kronecker-sum operator—and rejects stronger interpretations not supported by the data. In particular, the results do not establish E8, 600-cell, persistent-homology, low-rank MPS, category-theoretic, or noncommutative biological mechanisms. The result is positioned as an exact combinatorial finding and an externally retained statistical discovery candidate requiring a third pristine confirmation dataset and molecular covariate decomposition.