Circular Completion and Full-Branch Positivity in the Modulo-840 Residual Erdős–Straus Star

This note proves the fixed-shell divisor calculus, the two-target normalized shell form, the reduction of the hard prime support to the six square classes modulo 840, the cyclic circular completion of those six classes, the A₈³ snowflake realization, and the preservation of target positivity under circular completion. The positivity statement is kept in the full split-zero edge branch; the circular snowflake is a complete endpoint support lift, not a replacement for the support-positive coefficient. Every theorem stated below is proved explicitly.