Symmetry Obstruction and Gauge Fixing in the S3 Field Calm Sector

This note isolates the remaining microscopic bottleneck for closing the weak-field Newtonian limit in a single-field (S^{3}) ontology. It proves that if the calm variable is taken as a global internal phase generated by an exact symmetry, the minimized twist defect energy is phase-independent and the linear source coupling vanishes ((a=0)). It then formulates a gauge-fixed alternative: an anchored calm field with (\tau(\infty)=0) and a symmetry-invariant three-run interaction-energy subtraction whose centered slope defines (a) in a fixed topological sector. The result provides a precise, falsifiable criterion for when the identity (G=a^{2}c^{4}/(4\pi K_{0})) can become a parameter-free prediction within the (S^{3}) field framework.