Establish Equicontinuity through Derivatives

[ ] Calculate Derivatives: Determine the derivatives for each function (f_n) in the sequence generated by the Gram-Schmidt process. Analyze the first few to identify any regular pattern or structure.
[ ] Develop Closed-form Formula: If a regular pattern or predictable sequence in the derivatives is evident, derive a closed-form expression for these derivatives or their bounds.
[ ] Derive Delta for Equicontinuity: Use the closed-form formula to explicitly calculate or estimate a (\delta) that ensures (|f_n(x) - f_n(y)| < \epsilon) whenever (|x - y| < \delta) for all (n).
[ ] Proof Construction: Construct a proof that clearly demonstrates the equicontinuity of the sequence based on the calculated derivatives and derived (\delta), adhering to mathematical principles and definitions.
[ ] Documentation and Review: Document the steps, calculations, and final proof. Review the documentation to ensure it is clear, logical, and adheres to mathematical standards without any superfluous content.

crowlogic / arb4j