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A Local Resolution of the Problem of Time has recently been given, alongsidereformulation as A Local Theory of Background Independence. The classical partof this can be viewed as requiring just Lie's Mathematics, albeit entrenched insubsequent topological and differential-geometric developments and extended tocontemporary Physics' state spaces. We now widen this approach by mildrecategorization to one based on Nambu's generalization of Lie's Mathematics,as follows. i) In this approach, the Lie derivative still suffices to encodeRelationalism. 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 aclass of Nambu algebraic structures of generators or of first-classconstraints. iii) Nambu observables are defined by Nambu bracketszero-commutation with generators or with first-class constraints; we use theNambu analogue of the Jacobi identity to simplify this discussion relative to aprevious treatment. These Nambu brackets relations can moreover be recast asexplicit PDEs to be solved using the Flow Method. Nambu observables themselvesform Nambu algebras. Lattices of Nambu constraint or generator algebraicsubstructures furthermore induce dual lattices of Nambu observablessubalgebras. iv) Deformation of Nambu algebraic structures encounteringRigidity gives a means of Constructing more structure from less. v)Reallocation of Intermediary-Object Invariance gives the general Nambualgebraic structure's analogue of posing Refoliation Invariance for GR. We alsodraw some motivation from M-Theory's use of Nambu Mathematics along the linesof Bagger, Lambert and Gustavsson, finding some qualitative distinctionsbetween this, GR and Supergravity as regards how Background Independence isrealized.

Nambu variant of Local Resolution of Problem of Time and Background Independence