Constraint Closure and the ℓ1 Structure of Physical Law

This paper develops a constraint-based toy model framework in which core structural features of physical law arise from a single requirement: global consistency of local transport. A violation of consistency is formalized as a transport defect, and we show that enforcing locality, additivity, and faithfulness uniquely selects the ℓ¹ norm as the admissible defect measure. Under ℓ¹ minimization, global consistency requires exact cancellation of transport defects. This condition is shown to be equivalent to anomaly cancellation constraints in gauge theory. Solving the resulting consistency equations yields the Standard Model charge relations for a minimal fermionic generation. The framework further demonstrates that minimal cyclic transport induces a three-mode spectral structure, consistent with observed generation multiplicity, and that admissible symmetry decomposes into SU(3) × SU(2) × U(1) as the minimal structure supporting consistent transport. Continuum gravitational dynamics arise as a limiting description of discrete defect minimization via Regge-type constructions. The results do not assume continuum field equations or symmetry postulates. Instead, they show how charge constraints, gauge structure, and continuum limits emerge from a unified requirement of global consistency under ℓ¹-constrained transport.