Cross-Regime Inference and Evidence Synthesis

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Cross-regime inference is where apparently complementary gravity tests can become either genuinely powerful or quietly incoherent. A sound synthesis maps one theory into each observable, represents shared inputs once, models environment and selection, and preserves null, positive, conflicting, and uninformative results. It never assumes that identical coefficient names imply identical physics or that different instruments imply independent evidence.

Helpful background. Weak Metric Perturbations and Gauge Freedom supplies weak-field gravity and its parameter conventions. Probability and Inference for Gravity supplies probability and statistical inference. The Tests of Gravity overview supplies the volume-wide regime map. Gravitational-Wave Astronomy supplies gravitational-wave data analysis and inference.

Enter this chapter

For experiments $j=1,\ldots,J$ , a coherent synthesis has the form

p(\{d_j\}\mid\alpha) =\int d\lambda\,\pi(\lambda\mid\alpha) \prod_j\int d\eta_j\, p\!\left(d_j\mid F_j(\alpha,\lambda),\eta_j\right) \pi(\eta_j\mid\lambda),

with additional selection normalization whenever the observed sample depends on theory or population parameters. The common theory parameters are $\alpha$ ; the maps $F_j$ encode regime, scale, environment, source structure, and conventions; $\lambda$ represents shared inputs; and $\eta_j$ holds local nuisance quantities.

This expression is a guide, not a demand that every public result can be exactly recombined. When likelihoods, priors, selections, or covariance are unavailable, the synthesis must remain conditional or approximate. Precision does not compensate for missing statistical meaning.

Current evidential statements use the cutoff 2026-08-19. Later releases should trigger a documented reassessment rather than be mixed into the fixed comparison silently.

Route through the synthesis

Mapping Theory Parameters Across Regimes constructs experiment-specific maps from one action, branch, and boundary state to weak-field, compact-body, wave, and cosmological coordinates.
Correlated Systematics and Shared Inputs exposes covariance from standards, ephemerides, catalogs, simulations, cosmology, calibration, and reused priors.
Screening and Environmental Selection treats effective charges and screening states as solved, uncertain quantities fixed before gravity residuals are inspected.
Hierarchical Multi-Experiment Likelihoods separates universal theory parameters, population variation, local nuisance variables, and selection-normalized catalog inference.
Tensions, Outliers, and Look-Elsewhere Effects calibrates exploratory discrepancies and defines what independent replication must accomplish.
Criteria for Cross-Regime Evidence Synthesis gives cumulative gates from operational measurement through held-back predictive comparison.

The order is deliberate. A hierarchy built before the theory maps are defined combines the wrong quantities more efficiently. A tension statistic computed before shared covariance is represented measures bookkeeping as well as physics. A global conclusion stated before replication and prediction overreaches the evidence.

Four ways a combination can fail

Failure	Symptom	Repair
Universal-coefficient assumption	Unrelated framework parameters are overlaid on one axis	Map common theory parameters through each regime
False independence	Error shrinks implausibly as analyses sharing inputs are multiplied	Introduce shared latent variables and block covariance
Outcome-dependent environment or event selection	Effect strengthens under a threshold chosen after viewing residuals	Freeze selection and calibrate it with injections or simulations
Posterior multiplication	Priors and duplicated data are counted repeatedly	Recover likelihood factors and use one hierarchy

A fifth failure is rhetorical: treating every consistent result as confirmation. A test with little power is uninformative, and an alternative that screens itself in a regime is not constrained there. Expected sensitivity, validity, and theory prediction determine the evidential sign.

Complementarity has a precise meaning

Experiments are complementary when their theory-map Jacobians probe different parameter directions, their nuisance responses differ, and their validity domains overlap the theory point being tested. Different scales alone do not guarantee complementarity. Two precise experiments can constrain the same projection, while one modestly precise environmental test can break a theory degeneracy.

Independence is also graded. Independent detector noise does not remove a shared source catalog or calibration standard. A cross-check that uses a different instrument but the same simulation and prior is valuable, yet not fully independent. The synthesis should name what changed and what remained shared.

The most persuasive deviation would have a correlated signature: a parameter-dependent effect in one regime, a predicted absence or screened response in another, and a third held-back observable reproduced without retuning. Conversely, broad null evidence is strongest when the same theory point would have produced detectable effects in several independently calibrated regimes.

Review the chapter

A laboratory experiment, a pulsar analysis, and a galaxy survey publish posteriors for coefficients called $\beta$ . Design a minimal decision tree for determining whether the three products can be combined.

Solution

First identify each coefficient’s operational definition, convention, validity domain, likelihood, prior, dataset, and selection. Next choose one theory and derive the three mappings from common parameters, including laboratory boundaries, compact-body sensitivities, and galactic environment. If no such map exists, the coefficients must remain separate. If it does, identify shared standards, ephemerides, catalogs, simulations, and prior information, then build one likelihood or hierarchy with those inputs represented once. Finally test selection and posterior-reweighting support with simulations and leave-one-regime-out prediction. Only a stable result after these steps is a cross-regime constraint.