Magic Squaresproof atlas
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General proof chapter

Brown lemma: a weighted conic

The brown support ABCG satisfies a separate weighted relation; the ABCDG family combines it with a yellow norm relation.

012A+2B=C+3G2A+2B=C+3G
02A=a2,B=b2,C=c2,G=g2A=a^2,\quad B=b^2,\quad C=c^2,\quad G=g^2
032a2+2b2−c2−3g2=02a^2+2b^2-c^2-3g^2=0
The polynomial parametrization of this conic and its compatibility with B+C=D+G are certified by yellow_brown_abcdg_square_mask.