Struct ResponseCurvatureFit 

pub struct ResponseCurvatureFit {
    pub dim: usize,
    pub kappa_hat: f64,
    pub kappa_r2: f64,
    pub characteristic_radius: f64,
    pub base: Array1<f64>,
    pub v_p_hat: f64,
    pub railed_at_resolution_limit: bool,
    pub sign_resolved: bool,
    pub profile_ci: KappaProfileCi,
    pub flatness: FlatnessTest,
}

Outcome of fitting curvature as an estimand on a constant-curvature response geometry: the optimised κ̂, its tangent base point, the profile-likelihood CI, and the interior-point flatness (Wilks) test of κ = 0.

Fields

dim: usize

The dimension d of the constant-curvature response manifold.

kappa_hat: f64

The REML/evidence-optimal curvature κ̂ (argmin of the profiled criterion).

Units 1/length² — κ̂ is therefore scale-dependent: rescaling the cloud y ↦ α·y rescales κ̂ ↦ κ̂/α². For a scale-free statement of how curved the cloud is, read kappa_r2 instead. When the cloud is curved BEYOND what its spread can resolve (it fills a large fraction of the sphere S^d(1/√κ̂)), the optimiser rails to the chart-resolution cap and railed_at_resolution_limit is true: κ̂ is then a lower bound on |κ|, not a point estimate.

kappa_r2: f64

The DIMENSIONLESS geometric invariant the cloud actually determines: κ̂ · r² with r = characteristic_radius. This is scale-FREE (κ̂·r² is invariant under y ↦ α·y, since κ̂ ↦ κ̂/α² and r ↦ α·r) — the honest answer to “how curved is this cloud relative to its own spread”. |κ̂·r²| ≪ 1 ⇒ nearly flat at this scale; κ̂·r² ↗ (π/2)² ⇒ the cloud fills the sphere and curvature is at the chart-resolution limit.

characteristic_radius: f64

Characteristic geodesic radius r of the cloud at κ = 0 (the doubled-gauge chart distance r = 2·max_i‖y_i − μ‖): the length scale against which κ̂ is dimensionless. Reported so the caller can convert between scale-dependent κ̂ and the scale-free κ̂·r² without re-deriving the chart gauge.

base: Array1<f64>

The intrinsic Fréchet-mean base point at κ̂ (the tangent expansion point the scalar GAMs are fitted around).

v_p_hat: f64

Profiled criterion value V_p(κ̂) (concentrated negative log-evidence).

railed_at_resolution_limit: bool

true when the κ̂ search converged ONTO the chart-resolution cap rather than an interior optimum: the data want curvature at or beyond the conjugate radius of their geodesic spread (the cloud fills the sphere). In that case κ̂ / the CI upper end are NOT a resolved point estimate but a HONEST “curvature exceeds chart-resolvable range at this scale” flag — the caller must report it as such and never as a silent κ̂ = ci_hi. The hyperbolic side cannot rail this way (κ < 0 has no conjugate radius), so a rail here always means strongly spherical relative to the spread.

sign_resolved: bool

true only when the SIGN of κ̂ is statistically resolved — i.e. the profile-likelihood CI excludes 0 (profile_ci.verdict ≠ Flat).

Why a point estimate alone is not enough (the #944/#1059 flat-floor)

Curvature is resolvable only through the dimensionless product κ·r² (see kappa_r2); the per-point Fisher information for κ scales like σ⁴. When the cloud is nearly flat at its own scale (|κ·r²| ≪ 1), the profiled criterion is so shallow that its single-cloud argmin κ̂ can land on the WRONG SIDE OF ZERO purely by Monte-Carlo fluctuation — empirically a coin-flip below |κ·r²| ≈ 0.03, reliable above ≈ 0.09 (the #944 power curve). The estimand itself is UNBIASED (the criterion averaged over clouds minimises exactly at κ⋆), so this is a resolution limit, not a bias.

The CI, in contrast, is honest in this regime: at an under-resolved operating point it reports Flat (straddles 0) rather than a confident wrong sign — it essentially never claims the wrong-signed geometry. So the SIGN-bearing summary the caller may quote is the CI verdict, not the bare κ̂. This flag exposes that contract on the point-estimate surface: when it is false, κ̂’s sign is noise — the caller must report “curvature not resolved at this scale (|κ·r²| too small)” and quote the CI / kappa_r2, never a sign-confident κ̂. It is the flat-floor twin of railed_at_resolution_limit (the spherical-cap rail); together they bracket the two ends of the resolvable κ·r² band where κ̂ is a genuine interior point estimate.

profile_ci: KappaProfileCi

Profile-likelihood CI for κ and the geometry verdict from its sign.

flatness: FlatnessTest

Interior-point χ²₁ likelihood-ratio test of flatness (κ = 0).

Trait Implementations

impl Clone for ResponseCurvatureFit

fn clone(&self) -> ResponseCurvatureFit

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ResponseCurvatureFit

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.