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In the rapidly evolving field of computational and data-driven materials engineering, the interplay between algorithmic processes and established scientific paradigms shapes the reliability of predictive outcomes. Traditional scientific consensus emerges from iterative experimental validation, peer review, and cumulative evidence, fostering a shared understanding of material behaviors and properties. In contrast, algorithmic consensus arises from the aggregation of computational models, often leveraging machine learning architectures to distill patterns from vast datasets. This manuscript explores the tensions and synergies between these two forms of consensus in materials prediction, highlighting how data-driven approaches can either reinforce or challenge longstanding scientific interpretations. A conceptual gap persists in integrating these consensus mechanisms, where algorithmic outputs may diverge from empirical benchmarks due to representation biases or uncertainty propagation. To address this, we introduce the Consensus Integration Lattice (CIL), a novel framework that structures the alignment of algorithmic and scientific consensus through layered computational workflows, feedback mechanisms, and epistemic risk assessments. By conceptualizing discovery pipelines that couple high-throughput simulations with multimodal data integration, CIL facilitates more robust materials predictions. Implications extend to autonomous discovery systems, inverse design strategies, and uncertainty quantification, potentially enhancing the efficiency of materials informatics ecosystems. This work underscores the need for infrastructure-level analyses to bridge computational agility with scientific rigor, paving the way for hybrid paradigms in materials engineering.