  This paper offers suggested improvements to the causal sets program in
discrete gravity, which treats spacetime geometry as an emergent manifestation
of causal structure at the fundamental scale. This viewpoint, which I refer to
as the causal metric hypothesis, is summarized by Rafael Sorkin's phrase,
"order plus number equals geometry." Proposed improvements include recognition
of a generally nontransitive causal relation more fundamental than the causal
order, an improved local picture of causal structure, development and use of
relation space methods, and a new background-independent version of the
histories approach to quantum theory. Besides causal set theory, \`a la
Bombelli, Lee, Meyer, and Sorkin, this effort draws on Isham's topos-theoretic
framework for physics, Sorkin's quantum measure theory, Finkelstein's causal
nets, and Grothendieck's structural principles. This approach circumvents
undesirable structural features in causal set theory, such as the permeability
of maximal antichains, studied by Major, Rideout, and Surya, and the
configuration space pathology arising from the asymptotic enumeration of
Kleitman and Rothschild. The paper culminates in the theory of co-relative
histories and kinematic schemes, combining the causal metric hypothesis, the
histories approach to quantum theory, and Grothendieck's relative viewpoint.
This leads to the derivation of causal Schr\"odinger-type equations as
dynamical laws for discrete quantum spacetime.
