We propose an augmented precedence principle that integrates an algorithmic information prior to favor simpler, low-entropy patterns in the evolution of causal sets. Applied to the sequential growth dynamics of causal set theory, this Occamistic bias naturally selects manifold-like configurations that approximate smooth spacetimes, thereby addressing the entropy dominance problem. On these emergent manifolds, the statistical accumulation of repeated quantum events gives rise to effective quantum dynamics from which the Schroedinger equation is derived. This perspective shows promise of potential extension to chromodynamics; and moreover, by interpreting the spacetime metric as a quantum operator and deriving gravitational dynamics from the minimization of quantum relative entropy between the intrinsic metric and a matter-induced metric, one can establish a connection with entropic theories of gravity. The Occamistic Precedence framework is extended to a relational, Universal Cognition perspective in which the decentralized cosmic ledger "remembers" its past through local interactions, enabling observer-dependent transitions between quantum (Schroedinger-like) and classical (Bellman-like) cognitive regimes providing physical underpinning to mental processes in biological and engineered systems, and potentially also providing a new way of looking at "extraordinary" mental processes such as altered states of consciousness and psi phenomena. Overall, our work suggests that gravity, quantum mechanics, and anomalous cognitive effects may emerge from an underlying, history-dependent process governed by fundamental information-theoretic principles.