  The Lie claw digraph controls Background Independence and thus the Problem of
Time and indeed the Fundamental Nature of Physical Law. This has been
established in the realms of Flat and Differential Geometry with varying
amounts of extra mathematical structure. This Lie claw digraph has Generator
Closure at its centre (Lie brackets), Relationalism at its root (implemented by
Lie derivatives), and, as its leaves, Assignment of Observables (zero
commutants under Lie brackets) and Constructability from Less Structure Assumed
(working if generator Deformation leads to Lie brackets algebraic Rigidity).
This centre is enabled by automorphisms and powered by the Generalized Lie
Algorithm extension of the Dirac Algorithm (itself sufficing for the canonical
subcase, for which generators are constraints). The Problem of Time's facet
ordering problem is resolved.
