Criteria for Cross-Regime Evidence Synthesis

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Cross-regime evidence synthesis asks a harder question than whether many measurements are individually compatible with GR. It asks whether a specified alternative predicts a coherent pattern across scales, survives independent calibration and nuisance models, and improves out-of-sample prediction without leaving its stability or effective-theory domain. The answer must preserve positive, null, conflicting, and uninformative results rather than compressing them into one exclusion plot.

Required background. Probability and Inference for Gravity supplies probability and statistical inference, model comparison, posterior prediction, covariance, and multiple-testing control.

Helpful background. Weak Metric Perturbations and Gauge Freedom supplies weak-field gravity parameters. The Tests of Gravity overview supplies the regime map. Gravitational-Wave Astronomy supplies gravitational-wave data analysis and inference.

Five checks from measurement to synthesis

1. Operational definition. Each result must identify its measured quantity, dataset and calibration release, selections, forward model, likelihood, interval or model-comparison rule, and validity domain. A residual without its fitted model is not portable evidence.

2. Experiment-level calibration. Null injections should have correct coverage or tail probabilities, alternatives should be recovered with stated power, and consequential systematics should be represented or bounded. The result must be reproducible from versioned data and software.

3. Independent replication. A positive effect should recur in new data or a genuinely independent instrument with the predeclared sign and scaling. Shared catalogs, ephemerides, simulations, standards, and priors weaken independence and must enter the covariance.

4. Theory-level mapping. One stable action and branch must map common parameters into every relevant observable, as developed in Mapping Theory Parameters Across Regimes. Environmental screening, compact-body sensitivities, cosmological boundary values, and running cannot be replaced by universal coefficient names.

5. Predictive comparison. The alternative should explain the motivating data and predict something not used to tune it. Compare the complete alternative with GR plus its necessary source and nuisance models, using the same data domain and complexity rule. A flexible deformation that only fits the discovery residual has not crossed this gate.

These gates are cumulative. A result can be scientifically valuable at an early gate—an unexplained calibrated residual is an important target—without being described as cross-regime evidence for new gravity.

Preserve the sign of every result

A positive result favors a specified deviation under a calibrated rule. A null result constrains directions to which the experiment has demonstrated sensitivity. A conflicting result can expose regime dependence, shared systematics, or theory failure. A model-dependent result may be strong inside one source or environment model yet weak under another defensible model. An uninformative result has low power or a dominant degeneracy and should not be counted as another confirmation of GR.

The combined likelihood must retain these distinctions. Null results can sharply disfavor a theory that predicts an effect in their regime; they say little about a screened or decoupled theory that predicts none. Conflicting results are not averaged away before checking whether the theory expects different effective charges or scales.

Bayesian evidence compares prior-predictive models, while likelihood-ratio and goodness-of-fit statistics have different calibrations. The synthesis should not translate every output to an informal common “sigma.” Raveri and Hu’s separation of goodness-of-fit, evidence-ratio, and parameter-shift questions is useful precisely because no one number captures all forms of discordance Raveri and Hu 2019, §II.C–E.

Results and limitations through 2026-08-19

At the 2026-08-19 cutoff, the cited sources supply numerous successful tests of declared GR baselines, together with regime-specific tensions and model limitations. They do not form one joint likelihood over a complete inventory of alternative theories. This page gives criteria for such a comparison; it has not executed an exhaustive cross-regime model ranking. Its empirical summary must therefore remain at the level of the named analyses.

Evidence or result	Cross-regime status at the cutoff	Limitation or uncertainty boundary
Laboratory, Solar-System, pulsar, imaging, wave, and cosmological tests or consistency checks	Broad, complementary agreement with their declared GR baselines	Tests constrain finite parameter projections and rely on regime-specific source and nuisance models
Local anomalies and outliers	Motivate targeted replication and model checks	Trials, calibration, selection, or astrophysical degeneracy remain consequential in disputed cases
Parameterized deviation frameworks	Provide common diagnostics within named regimes	Coefficients are not universal theory parameters and may omit correlated effects
Complete alternative theories	Some viable parameter windows survive multiple tests	Screening, branch stability, cutoffs, and incomplete likelihood products limit universal synthesis
Global evidential conclusion	A theory ranking requires an explicit combination with the five checks above	A collection of conditional null results is neither a joint model comparison nor a proof of GR

The strongest conservative interpretation is continued confidence in GR within the tested domains. The competing deviation interpretation requires at least one repeatable pattern not explained by the composite GR model. Negative evidence for an alternative is not merely a null coefficient; it is failure of a correlated prediction in a regime where the theory is valid and the experiment has power. Conversely, discovering that a supposed null test was insensitive is evidence against an overbroad synthesis claim.

An explicit decision procedure

For each candidate theory, construct a table whose rows are experiments and whose columns contain theory map, validity flag, data release, selection, likelihood contribution, shared inputs, result, and limitation. Do not fill an invalid regime with a numerical bound. Evaluate one joint model with shared nuisance structure and a selection-normalized hierarchy.

Then perform three independent checks. First, leave out each regime in turn and predict it from the others. Second, replace each dominant nuisance model with a predeclared defensible alternative. Third, inject the theory and GR through the complete pipelines to verify coverage, power, and model selection. A result controlled by one experiment, one prior endpoint, or one simulation suite is reported as such.

An adversarial synthesis invites the best conservative and deviation explanations to predict held-back data. It also seeks a counterexample: a stable parameter point that survives the claimed universal exclusion, or a null model that reproduces the claimed anomaly under allowed systematics. Finding either narrows the conclusion; failing both under independent implementations strengthens it.

The unresolved boundary is epistemic rather than rhetorical. Public products sometimes lack likelihoods, covariance, selections, or exact theory maps. The correct response is a wider or conditional conclusion, not precision manufactured from inaccessible assumptions.

What could change the conclusion. The combined interpretation could change when a superseding major release changes a regime-level conclusion, an independently replicated anomaly passes the five checks, a viable theory makes and confirms a held-back prediction, or a newly exposed covariance or validity failure overturns the combined comparison.

Check your understanding

Three experiments report null results for coefficients named $\delta$ , but their frameworks probe weak-field curvature, wave dispersion, and cosmological slip. What information is required before treating them as one constraint?

Solution

The shared symbol supplies no physical mapping. One must specify a theory with common parameters, solve its local, radiative, and cosmological backgrounds, and derive each experiment’s $\delta=F_j(\alpha)$ in matching conventions and valid domains. The joint model must include environmental or redshift dependence, stability and cutoff flags, shared cosmology or calibration, selections, and the original likelihood or an adequate likelihood approximation. Therefore the three null results can be combined only through the theory parameters. If the theory predicts no effect in one regime, that experiment is not an equal measurement of the same coefficient.

References

Raveri, M., and Hu, W. (2019), “Concordance and discordance in cosmology,” Physical Review D 99, 043506. Raveri and Hu 2019, §II.C–E.