Go The Entropic Way For Math

Normal sudoku rules apply. Cells on a purple entropic line must alternate between low (123), medium (456) and high (789), any group of 3 connected cells on the line MUST contain one of each entropy. Digits in a dotted cage sum to the total given in the top left corner of the cage without repeat. Digits on a grey line must read the same forwards as backwards. Cells separated by a black dot has one digit double the other (1:2 ratio). Cells separated by a white dot are consecutive. Cells separated by a V sum to 5. No negative constraints.