A constraint-based selection principle for the Standard Model gauge group: a substrate with derived dynamics, a no-go theorem, and the measure problem

Key Points

• This work aims to establish a discrete substrate model as a framework for understanding gauge group dynamics through derived theorems.
• Development of a discrete substrate model with observable and unobservable elements.
• Proof of dynamical rules including monotone total, oscillation sector, and annihilation upon equalization.
• Simulation to validate the identities between residue and annihilation.
• Proved an unobservable, strictly monotone total indicating an arrow-of-time residue.
• Demonstrated an observable ±1 walk representing an oscillation sector.
• Validated the residue–annihilation identity in simulation.