Codon
A codon is the τ-categorical decoding atom: a triplet of nucleotide positions read non-overlappingly as a single input element of the genetic code morphism. It is not arbitrarily of length three — its width is fixed by the BSD motivic structure that needs 64 = 4³ inputs to span 20+1 outputs with the redundancy required by VI.T22 (codon degeneracy as error correction).
τ-Definition
A codon is the τ-categorical decoding atom: a triplet of nucleotide positions read non-overlappingly as a single input element of the genetic code morphism. It is not arbitrarily of length three — its width is fixed by the BSD motivic structure that needs 64 = 4³ inputs to span 20+1 outputs with the redundancy required by VI.T22 (codon degeneracy as error correction).
Categorical invariant. Domain element of the BSD motivic morphism 𝒢 (VI.D40); a triplet read as a single morphism input; one of 64 atoms of the decoding alphabet.
Primary registry anchor:
VI.D40
τ-Derivation Chain
Empirical Correlate
Biomarker: Triplet of mRNA bases (A, U, C, G); 64 possible codons (4³); 61 sense codons + 3 stop codons; AUG doubles as start signal.
Measurable range: Codon width is invariant: no known organism reads codons of length 2 or 4 in its main translation system; programmed +1/-1 frameshifts are documented but localized exceptions, not alphabet changes.
Observation method: Ribosome profiling (Ribo-seq) at single-codon resolution; toeprinting; reading-frame mutagenesis; suppressor tRNA experiments.
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel
- DNA/RNA D-sugar backbone (chirality fixed by K_χ)
- directional 5′→3′ reading frame on the chirality-fixed backbone
- triplet codon as the BSD-motivic decoding atom
Manuscript reference: manuscript-sources/book-06/part04/ch27-genetic-code.tex
Lean Coverage
Status: Planned