The Conditional Refinement, Part II: The Chrysene-Adenosine Reaction Cell, Margin Geometry and Necessary Conditions for Sufficiency

Abstract

Part I makes the standard and vertebrate mitochondrial codes two settings of one three-valued refinement and then proves that the thresholds governing it are not a function of the codon block, and that no single environmental coordinate orders the published record. It carries the reaction vessel as a black box. This paper places the account in the cell.

The predecessor theory of cage-constrained reachability for the chrysene-adenosine complex assumes the external context of a reaction inert. We change that assumption and nothing else: the hard constraint functionals become functions of the medium. A step is then available exactly when its margin — the largest slack simultaneously available to all its constraints — is positive, so reachability of a target is a maximum over reaction paths of a minimum over step margins. Because a path margin depends only on which steps occur, no bound on path length enters.

A continuously varying medium therefore carves discretely. On a connected set missing the zero sets of the step margins each margin has constant sign, so the available steps, the available paths and the reachable targets are all constant there; the discontinuities lie in the margin locus, and within a chamber the predecessor's persistence theorems hold uniformly rather than pointwise. This uses no hypothesis and no constraint functional need be nonlinear: the nonlinearity is that of max ∘ min.

Determinism is not assumed but derived off a set of codimension one, that set being where two carves balance. Under the hypothesis that one cage covers the twenty-seven published tables, the fifteen distinct resolution vectors it must realise bound the cell from below: fourteen environed constraints in a one-dimensional medium against five in two. 

What is given are necessary conditions for a cage to realise the two codes — the two environments must lie in distinct chambers at each of three half-blocks, and some hard constraint must change sign between them — together with a criterion no cage depending on the codon through its block alone can meet. Residue-sufficiency is further from reach than type-sufficiency: the theory says which target is reachable, not which residue it carries, and that gap is sixty-three witness pairs of which two classes are open questions of the corpus. One prediction is testable without any translation table — the handedness of the carved residue is constant on chambers of the oriented locus and exchanged across a wall, with a racemic region where the oriented exclusion fails.