Dual Singularities

by Dan Katz and Francis Heaney

This is a Siamese Twins puzzle (one clue from each pair fits into one of the two grids) except in certain squares (circled in the solution grids below), both the across and down entries switch grids as they pass the circle, so that each grid contains the first portion of one word and the second portion of the other, overlapping by the circled letter.

The letters in the squares where entries switch grids spell out the phrase "ODD SQUARES" (and they certainly are, aren't they?) Reading the letters in the squares corresponding to odd square numbers (1, 9, 25, 49, and 81) spells FRIDA in the first grid and KAHLO in the second.