Amino Acid
An amino acid is the τ-categorical decoding output: a single element of the codomain of the BSD motivic morphism 𝒢. The standard 20-element output set is not arbitrary — its size is fixed by the iota-tau axis count along the hydrophobicity dimension (VI.T_NAA), and its L-handedness is fixed by the K_χ chirality channel.
τ-Definition
An amino acid is the τ-categorical decoding output: a single element of the codomain of the BSD motivic morphism 𝒢. The standard 20-element output set is not arbitrary — its size is fixed by the iota-tau axis count along the hydrophobicity dimension (VI.T_NAA), and its L-handedness is fixed by the K_χ chirality channel.
Categorical invariant. Codomain element of the BSD motivic morphism 𝒢 (VI.D40); one of 20 rational points + 1 stop signal carrying handedness fixed by VI.L18.
Primary registry anchor:
VI.D40
τ-Derivation Chain
Empirical Correlate
Biomarker: 20 standard proteinogenic amino acids (Ala, Arg, Asn, Asp, Cys, Gln, Glu, Gly, His, Ile, Leu, Lys, Met, Phe, Pro, Ser, Thr, Trp, Tyr, Val) + stop signal; all L-handed (except achiral glycine); selenocysteine and pyrrolysine are recoded extensions, not new alphabet members.
Measurable range: Side-chain mass 1 Da (Gly H) → 186 Da (Trp indole); hydrophobicity (Kyte-Doolittle) -4.5 (Arg) to +4.5 (Ile); pKa of ionizable side chains spans pH 3.6 (Asp/Glu) to pH 12.5 (Arg).
Observation method: Mass spectrometry (LC-MS/MS); Edman degradation; amino-acid analysis (post-hydrolysis HPLC); X-ray crystallography of L-vs-D enantiomers; circular dichroism.
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel
- K_χ pseudoscalar fixes a single sign across the life sector
- all 19 chiral proteinogenic amino acids are L (S-configuration at α-carbon)
- amino acid as chirality-locked output of 𝒢
Manuscript reference: manuscript-sources/book-06/part04/ch27-genetic-code.tex
Lean Coverage
Status: Planned