  A Local Resolution of the Problem of Time has recently been given, alongside
reformulation as A Local Theory of Background Independence. The classical part
of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in
subsequent topological and differential-geometric developments and extended to
contemporary Physics' state spaces. We now widen this approach by mild
recategorization to one based on Nambu's generalization of Lie's Mathematics,
as follows. i) In this approach, the Lie derivative still suffices to encode
Relationalism. ii) Closure is now assessed using the Nambu bracket - with $n$
slots rather than 2, so the first nontrivially Lie case has 3 slots - and a
`Nambu Algorithm' analogue of the Dirac and Lie Algorithms. This produces a
class of Nambu algebraic structures of generators or of first-class
constraints. iii) Nambu observables are defined by Nambu brackets
zero-commutation with generators or with first-class constraints; we use the
Nambu analogue of the Jacobi identity to simplify this discussion relative to a
previous treatment. These Nambu brackets relations can moreover be recast as
explicit PDEs to be solved using the Flow Method. Nambu observables themselves
form Nambu algebras. Lattices of Nambu constraint or generator algebraic
substructures furthermore induce dual lattices of Nambu observables
subalgebras. iv) Deformation of Nambu algebraic structures encountering
Rigidity gives a means of Constructing more structure from less. v)
Reallocation of Intermediary-Object Invariance gives the general Nambu
algebraic structure's analogue of posing Refoliation Invariance for GR. We also
draw some motivation from M-Theory's use of Nambu Mathematics along the lines
of Bagger, Lambert and Gustavsson, finding some qualitative distinctions
between this, GR and Supergravity as regards how Background Independence is
realized.
