AbstractWe present a systematic investigation of digital root cycles arising from triangular, Fibonacci, and tetrahedral figurate number sequences under modulo-9 reduction. Thetriangular sequence generates a unique period-9 digital root cycle 1, 3, 6, 1, 6, 3, 1, 9, 9 shared exclusively by the dodecagonal (s = 12) polygonal family. From this cycle, afinite Triplet-Window Lattice is constructed exhibiting three provable algebraicproperties: stability under positional encoding, self-mirroring under digit reversal, anda 13-encoding property unique to its Bridge subfamily. Mapping the lattice digits 1, 3, 6, 9 bijectively to the nucleotide bases G, A, C, Tdefines Anchor (DR=1) and Bridge (DR=4) codon families. Exhaustive testing of all 24possible mappings identifies a canonical mapping (1→G, 3→A, 6→C, 9→T) thatuniquely recovers the seed motif GCA, GAC, GTT and yields Anchor/Bridge usageratios ranging from 1. 10× to across nine divergent organisms (bacteria, yeast, human, archaea, virus, fly, plant, nematode). This mapping ranks third in overall signalstrength. A strict null model matching both GC content (~55. 6%) and degeneracyprofile shows the preference exceeds random expectation in most lineages (p < 0. 05 ineukaryotes, archaea, and virus). Analysis of human laminin genes reveals elevated representation of Anchor-encodedamino acids. While codon usage is shaped by multiple biochemical, translational, andevolutionary factors, these results indicate a non-trivial structural resonance betweenfigurate number symmetries and observed codon preferences under specific3 3. 3. 06×mappings. The Coherosance Framework offers a novel mathematical lens for exploringbiological information architecture and warrants further investigation.
Tony Beede Beede (Mon,) studied this question.