Magic-square-of-squares lane
The current strongest technical lane is the order-3 magic-square-of-squares verifier stack.
Lucas form → 24k+1 primitive compression → modulo-240 survivors → CRT survivor lattice → centered difference graph D(e) → additive-diamond search → positivity / distinctness / gcd / CRT gates
Status
FINITE_GRAPH_SWEEP_PROVED GLOBAL_MAGIC_SQUARE_UNRESOLVED
Key theorem-style reduction
For center e=z², a candidate requires {a,b,a+b,|a-b|}⊂D(e), where D(e)={d>0:e−d and e+d are squares}.