HermSplit

The same cone over several blocks, which is what an inequality feasible set needs

4/4 passed in 33ms

Test	What it does	Result
test_one_block	On the trace-one problem herm_split over one block returns the same dual, status and point as herm_cone, and it is the least eigenvalue.	✅ pass
test_sign_block	A matrix block with a sign block minimises Tr(rho W) over SUBNORMALISED states at $min(0,{\lambda }_{min}(W))$, the shape Kanitschar Eq. (21)'s trace window takes.	✅ pass
test_split_duality	Three diagonal blocks make a linear programme whose certified value stays below the closed-form optimum 3, a loose tolerance returning less than a tight one.	✅ pass
test_split_refusals	Malformed split problems are refused by name: a side-zero block, planes not matching the declared sides, terms not five per nonzero, an entry naming a missing block, and a start outside the cone.	✅ pass