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Evidence, Validation, and Nonperturbative Status

Comparing nonperturbative calculations requires more than comparing quoted numbers. This chapter asks whether methods compute the same observable, take compatible limits, and fail for different reasons. It then separates a useful cross-check from the mathematical construction or spectral theorem needed for a stronger conclusion.

Enter this chapter

Section titled “Enter this chapter”

Begin with Claim Status Across Nonperturbative Methods to separate each scientific proposition from the method that produced it.

Helpful background. Review What Does Nonperturbative Mean? for the meaning of nonperturbative control.

Topics

Section titled “Topics”
  1. Claim Status Across Nonperturbative Methods — Distinguishes exact identities, controlled approximations, and numerical conclusions.
  2. Translating Observables Across Analytic and Regulated Methods — Aligns operators, states, schemes, boundaries, and limits.
  3. Correlated Evidence, Independence, and Triangulation — Tests shared assumptions before treating agreement as independent support.
  4. Rigorous Status, Construction, and Open Problems — Separates regulated existence, continuum construction, and spectral conclusions.

How the ideas fit together

Section titled “How the ideas fit together”

Two estimates of a mass may share scale setting, input ensembles, or a spectral ansatz. Their agreement then tests fewer independent assumptions than two unrelated calculations. In statistical language, a common error does not shrink simply because the number of estimates grows; correlations must enter the combination. A separate issue remains even after numerical agreement: a finite-regulator spectrum does not establish existence and a positive gap in the continuum, infinite-volume theory. The strength of the conclusion follows from the limits actually controlled. Lyons, Gibaut, and Clifford 1988, pp. 110–117.

Where to go next

Section titled “Where to go next”

Continue to Lattice Observables and Continuum Inference to turn regulated measurements into continuum observables with separated uncertainties.

References

Section titled “References”
  • Lyons, Louis, Duncan Gibaut, and Peter Clifford. “How to Combine Correlated Estimates of a Single Physical Quantity.” Nuclear Instruments and Methods in Physics Research Section A 270, no. 1 (1988): 110–117. DOI.