gut_24_from_8_times_3
plain-language theorem explainer
The equality 24 = 8 × 3 encodes the unification of the eight-tick octave with three spatial dimensions to fix the GUT coupling scale. A researcher constructing the running-couplings summary in Recognition Science QFT would cite this when placing α_GUT between the weak and strong values. The proof is a direct reflexivity step on natural-number arithmetic.
Claim. $24 = 8 × 3$, where the factor 8 is the tick count of the octave and the factor 3 is the number of spatial dimensions.
background
The module derives running couplings from φ-ladder scaling, with each rung corresponding to an energy scale at which J-cost optimization changes. Running couplings are the scale dependence of α, α_s and α_W under the renormalization group. The local setting treats different φ-rungs as distinct energy regimes whose J-costs produce the observed running.
proof idea
The proof is a one-line term that applies reflexivity to the arithmetic identity 24 = 8 * 3.
why it matters
This supplies the gut_structure field inside runningCouplingsProofs. It closes the unification step that links the eight-tick octave (T7) and D = 3 (T8) to the GUT scale, supporting the claim α_GUT = 1/24 in RS-native units.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.