Falsification Tree and Scope

01What must be fixed first

An interpretable exclusion fixes theory/version, domain, allowed parameter region, calibration data, observable, selection rules, uncertainties and correlations, likelihood or statistic, rejection region and power. If an amplitude can be tuned arbitrarily to zero, a null result constrains parameters rather than excluding the whole family.

02How a null result constrains a model

Suppose a fixed model predicts a nonzero $\Delta O=X$. If the fully calibrated data are compatible with zero while the confidence interval excludes $X$, and shared backgrounds and selection effects have been checked, the model–apparatus mapping is excluded at the declared confidence level. “Precision smaller than X” is insufficient: correlated noise, degeneracy, multiple testing and power matter.

A nonzero signal does not automatically support ASD. Its sign, phase, shape and amplitude must match ASD while ordinary systematics and comparison models are evaluated. Unclosed systematic covariance leaves significance unclosed too.

03Failures at different levels

“Reassess dependent uses” is more accurate than “reject everything.” Mathematical identities and physical identification conditions must be recorded separately.

04Publish positive, null and failed results

Positive results report identifiability and alternative-model comparisons; null results report excluded parameter regions; equivalent models report non-discrimination. Unclosed models report missing equations. Record all in the Research Ledger, rather than changing the target after the result while retaining its original prediction label.