Logic-Driven Physics: The Genetic Code as Universal Geometric Algebra

This manuscript (Paper 4 of the First Calculus project) applies the right-side foundations of First-Classness (FC) and ontological gender to particle physics. It advances a single, concrete hypothesis: the four-letter genetic code (A, U, G, C), interpreted as a four-element geometric algebra, provides the generic algebraic substrate for both biological organisms (biorgs) and physical systems (monorgs). Under FC, no constituent may be privileged; the resulting constraint fixes a minimal four-type dyadic structure with spacetime semantics. The paper identifies the four RNA bases with four generic dyad types and corresponding physical roles: A as a timelike dyad (j = mF) carrying electromagnetic charge; G as a spacelike dyad (i = FM) carrying weak hypercharge / weak interaction; U as a lightlike dyad (ε = fF) carrying gravitational charge; and C as a singular dyad (η = mM) carrying colour charge / whole (strong interaction at the quark level). These dyads are treated as “quarklets”: quarks, leptons, and bosons are constructed from triads of quarklets (codons). The manuscript gives explicit, calculable rules for generic spin and multiple kinds of generic charge derived purely from codon geometry, and compares the resulting particle assignments against the Standard Model via programmed database calculations. A critical correction relative to the original 2015 draft is implemented: A and G were previously swapped in the base–field correspondence; the present version assigns electromagnetic charge to A and weak hypercharge to G. The structural geometry of the four-letter code and codon space is preserved; only the base-to-field mapping is corrected.