Coarsenings of the Genetic Code by the Twenty Registry Classes of a Chrysene Stack: A Partition Criterion, a Filter Selection, and the Double-Sided Encoding Hypothesis

The predecessor classifies the marker assignments of a chrysene stack of six sites into twenty frame classes and expressly declines to identify them with any twenty-element set, combinatorial or biological. We ask under what condition such an identification is possible, and what follows from one. Fixing a four-letter secondary alphabet with a distinguished partition into two classes of two, we show that the twenty classes admit a bijection to the twenty amino acids respecting the placement of codons by the standard genetic code precisely when that partition is amino from keto; for purine against pyrimidine the Hall deficiency is one and for Watson-Crick it is two, and in each case the obstruction is exhibited as a set of classes sharing too few neighbours, no amino acid being unmatched in every maximum matching. The result depends only on the partition and not on which of the eight admissible letter assignments is chosen, and the invariance is proved rather than observed. The admissible bijections number one hundred and twenty-eight; five of the twenty assignments are the same in all of them, one of the five being forced by a single class's own adjacency. Five physical filters select one bijection uniquely, by a margin of 0.17%, of which three of the five are individually decisive. The resulting table and the standard genetic code are related by two block operators whose composite reproduces all sixty-four codons. What the construction does not establish is stated before it rather than after. The adjacency whose matchings are counted is built from the standard genetic code, so the table selected is a coarsening of that code onto the twenty classes and not a derivation of it: left unconstrained over all 20! bijections the same filters prefer a map of higher total that violates the adjacency at sixteen of twenty classes. Neither block operator is determined by anything constructed here, and both are given by exhibition. Existence of a coarsening is not rare, holding for seventy per cent of codes carrying the standard degeneracy profile. The coincidence between the class count and the three-letter multiset count at N=3 is refuted on three grounds and used nowhere. Under a named hypothesis that the amino acid a cluster produces is attributable to the assembly rather than to the reading of it, the assignment factors through the twenty classes and code degeneracy becomes frame multiplicity; the same hypothesis then yields fibres of sizes two and four, which the standard code does not have, so the two-step relation is not generated by the frame. Five assignments are predicted independently of the filters, and one of them by a single measurement.