Parametric families · proof map

Magic squares you can do more than look at.

The interactive atlas connects every generator to its square-valued mask, formulas, complete LaTeX proof, and an honest formalization status.

Open the laboratory ↗How the proofs work

23 + 234/9 and 5/9 orbits

5/9square-valued mask

5shared lemmas

ABCDGexact certificate

A17689

B27889

C11449

D12769

E19009

F25249

G26569

H10129

J20329

E19 009x−1 320y7 560

✓ proof-core

Proof-backed catalog

From formula to square, without a gap

All families →

Red–red

ABEHJ

The red progressions AEJ and BEH; this family contains known 6/9 and 7/9 enhancements.

↗02

Red–blue

ABCDH

The arithmetic-progression triple CDH, compatible with an x²+2y² norm on ABDH.

↗03

Yellow–brown

ABCDG

The yellow support BCDG and the weighted brown conic ABCG.

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Research principle

“If a symbolic proof does not exist yet, that is a gap—not a result.”

The interface displays computations; proof-core is responsible for claims. Attractive examples never substitute for identities, and every construction exposes its status.