  The flavor puzzle of the Standard Model quark sector is formulated in a
non-perturbative way, using basis invariants that are independent of the choice
of quark field basis. To achieve this, we first derive the algebraic ring of 10
CP even (primary) and 1 CP odd (secondary) basis invariants, using the Hilbert
series and plethystic logarithm. An orthogonal basis in the ring of basis
invariants is explicitly constructed, using hermitian projection operators
derived via birdtrack diagrams. The thereby constructed invariants have well
defined CP transformation behavior and give the most direct access to the
flavor symmetric alignments of basis covariants. We firstly "measure" the
orthogonal basis invariants from experimental data and characterize their
location in the available parameter space. The experimentally observed
orthogonal basis invariants take very close to maximal values and are highly
correlated. Explaining the location of the invariants at close to maximal
points, including the associated miniscule and highly correlated deviations,
corresponds to solving the flavor puzzle in the invariant language. Once
properly normalized, the orthogonal basis invariants are close to scale (RGE)
invariant, hence, provide exquisite targets for fits of both, low- and
high-scale (bottom-up and top-down) flavor models. Our result provides an
entirely new angle on the flavor puzzle, and opens up ample opportunities for
its ultimate exploration.
