name: synth-residual-recovery
description: The synth fidelity report's `model_residual_correlations` section — captured vs recovered residual correlation per applied pair, why it is not `pairwise`, its bounded worst-first listing, and why step-target endpoints stay unmeasured.
type: guide
kind: design
applies_to: inspect, predict, manifest
covers: [synth from-profile, fidelity report, residual_correlations, recovery]
requires: [capability:synth]
Synth residual-correlation recovery
omitempty — a report for a profile captured without --residual-correlations is byte-identical — and, like every section, scores ONLY relationships generation actually applied (synth-fidelity-report).
Residual-correlation recovery (model_residual_correlations)
The models question (synth-model-recovery) asked BETWEEN fields: per applied residual correlation, captured rho beside recovered. Deliberately not folded into pairwise, and the two section names are the load-bearing distinction — pairwise scores Spec.Correlations (value-scale, realized by the copula), this scores Spec.ResidualCorrelations (residual-scale, realized by the residual correlator). Different numbers over the same two fields, and resolveConflicts excludes a modelled field from Spec.Correlations precisely so the two arms fire on DISJOINT field sets.
The recovered side uses the refit’s residuals, not residuals against the captured coefficients — those fold every coefficient gap models already reports into a correlation and state one finding twice. Scale is latent for the reason the coefficients are: generation correlates the zs. The model refits produce the residuals as a by-product, so both sections ride one decode of the synthetic partition.
Bounded because quadratic: compared / flagged / mean_delta / max_delta cover EVERY pair; pairs lists only the worst maxResidualRecoveryPairs (20) by absolute delta with omitted counting the rest, so an unlisted pair recovered at least as well as the last listed. flagged fires on ResidualRecoveryTolerance (0.10) ALONE — a correlation is unit-free and its SE is under 0.02 over thousands of rows, so a noise-scaled band would collapse onto the floor. Unmeasured pairs ride a separate list carrying captured_rho and no recovered slot (insufficient_overlap / no_variance, plus a recovery-only no_model_fit).
A STAIRCASE endpoint lands in no_model_fit, deliberately. A coefficient can be calibrated because OLS is linear in its response; a correlation cannot — the factor relating two score residuals’ correlation to the correlation of the residuals that drove the draws depends on the PAIR’s joint distribution rather than either marginal, and no projection removes it. On a survey cohort of staircase targets that leaves compared at 1, the rest counted under no_model_fit — counted, never silent. Quote the participant count with the figure: the total is C(applied models, 2), so the same finding reads as a different fraction on a cohort with a different applied-model count. Closing it needs a polychoric-style bivariate calibration or an ordered-probit refit; internal/processing/regression has neither (binomial+probit is a reserved, unimplemented link).