Copula

Return the calibrated 2-parameter t-copula fits for peg_type.

The parametric successor to λ_L: per DENSE pair (n_joint_tail >= 50) a t-copula fit recovering correlation ρ and tail-fatness ν, with the fitted log-likelihood as an honest goodness-of-fit. Reads the latest run's frozen pair_copula rows (written by the slow-cycle calibration pass), FITTED pairs first then by ρ desc, wrapped in the same provenance envelope as /pairwise (calibration_window / qualified_entity_count / formula_version from the latest calibration run) plus the §6 copula disclaimer. Pairs below the dense-core floor carry fit_status='not_fitted' / support_tier='insufficient_support' with ρ/ν null — reported, never fit; a met-the-floor-but-untrustworthy fit carries fit_status='fit_failed'. fit_source discloses WHICH substrate produced an attempted fit — 'continuous' (the real joint-tail series, ν meaningful) or 'binary_fallback' (count-derived indicators, ν only coarsely identified); null when no fit was attempted. Pre-calibration (no run / no rows) returns an empty set with a null envelope.

STEP 2 (estimator pinned + stability gate): provisional is now a PER-ROW, earned status. A row is promoted (provisional=false, estimator_version= 'copula_t_v1', attested under the 'pair_copula_v1' domain) only when its ν passed the bootstrap stability gate (stability_gate_passed — the fit sample met the synthetic-harness-validated floor AND the bootstrap ν CI is narrow enough that ν is identified for THIS pair). Rows that fail stay provisional/v0 and are never attested. The envelope's top-level provisional is true iff ANY returned row is provisional (mixed states are honest: some pairs trusted, some not) — and true on an empty set (nothing has earned trust yet).

CERTIFICATION (migration 287): rows are served from pair_copula_certified and carry certification_defect / is_certified. Four historical rows passed the stability gate while ν was pinned at the estimator bound with a collapsed CI — a non-identification signature, not a stable fit. They are flagged rather than dropped (a dropped row is invisible; a flagged row is a disclosure), and is_certified is the promoted-AND-sound subset. stability_gate_reason names why a fit was refused promotion.