Geometrization of Observer Consensus: \\ Conflict Metrics, Information Geometry, and Boundary Time Structure

In the timeless block universe perspective, the universe is modeled as a topological structure consisting of a causal partial order, while any concrete observer can only access a finite region and carries a predictive model about the global causal network. Descriptions by different observers of the same causal region generate conflicts at multiple levels: directed cycles appear when locally gluing partial orders, time scale functions are inconsistent, generalized entropy arrows and modular flow directions are inconsistent, and there is Z_2 sector mismatch in the Null--Modular double cover. This paper constructs a unified ``consensus geometry space'' embedding observers' statistical models, causal sets, time scales, and boundary states into a product manifold with a Riemannian metric, and defines a total potential energy function encoding the above conflict metrics as geometric potential. Under the synergy of linear and nonlinear information geometry, causal set geometry, and quantum state space geometry, we prove: under well-posedness assumptions such as completeness and strong convexity, the gradient flow of this potential gives a natural ``consensus dynamics'' making all conflict metrics monotonically decrease and converge to a ``consensus manifold.'' On the consensus manifold, local partial orders can be consistently glued into a global causal partial order, unified mother scale functions differ only by affine rescaling, generalized entropy arrows and modular flow directions agree in overlapping regions, and all observers inhabit the same Z_2 topological sector. Finally, we couple this geometrization framework with boundary time geometry, unified time scales, and Null--Modular double covers, proposing applications and engineering implementation pathways in multi-observer quantum field theory, holographic information, and multi-agent systems.