A Philosophical Explanation of Mathematical Effectiveness: The Key-Value-Information-Model Interface Analysis from the Computational Observer Perspective

The "unreasonable effectiveness" of mathematics in physics is a central problem in the philosophy of science. This paper introduces a working hypothesis: if the universe structurally resembles a computational system, and observers are situated within it, then the relation between mathematics and physics can be reformulated as an interface problem between observer and underlying reality. On this basis, the paper proposes the Key-Value-Information-Model framework, distinguishing natural rules from algorithmic rules, and explaining mathematical effectiveness in terms of information cross-validation and model correction. The framework provides a conceptually clear account of how observers access reality through mathematics.