pySHT-native method catalog

This catalog records research methods added beyond the SHT 0.1.9 migration surface. They do not appear in the R crosswalk. “Public” means the callable, formula ledger, boundary contract, and advertised calibration evidence have passed the current release gate; a blocked method has no public callable.

Foundational cohort

Method	Python function	Primary source	Status
Chen–Qin dense mean test	mean.cq_2samp	Chen–Qin (2010)	Public
Li fixed-small-sample mean tests	mean.li_1samp, li_2samp, li_ksamp	Li (2023)	Public
CZZ covariance identity and sphericity	covariance.czz_identity_1samp, czz_sphericity_1samp	Chen–Zhang–Zhong (2010)	Public
DISCO/energy distribution equality	equaldist.energy_ksamp	Rizzo–Székely (2010)	Public
Distance-covariance independence	independence.distance_covariance	Székely–Rizzo–Bakirov (2007)	Public
Rayleigh circular uniformity	circular.rayleigh	Rayleigh statistic; simulation-calibrated	Public
Watson circular uniformity	circular.watson	Watson (1961)	Public

Omnibus, kernel, and mutual-dependence cohort

Method	Python function	Primary source	Status
Maximum mean discrepancy	equaldist.mmd_2samp	Gretton et al. (2012)	Public
HSIC pairwise independence	independence.hsic	Gretton et al. (2008)	Public
dHSIC mutual independence	independence.dhsic	Pfister et al. (2018)	Public
Distance multivariance	independence.distance_multivariance	Böttcher et al. (2019)	Public
Henze–Zirkler multivariate normality	normality.henze_zirkler	Henze–Zirkler (1990)	Public
Energy multivariate normality	normality.energy	Székely–Rizzo (2005)	Public
Modified Hermans–Rasson circular uniformity	circular.hermans_rasson	Hermans–Rasson (1985)	Public
Mardia–Watson–Wheeler circular equality	circular.mardia_watson_wheeler_ksamp	Mardia (1972)	Public

Structured-domain cohort

Method	Python function	Primary source	Status
EHY rectangular uniformity	uniformity.ehy	Ebner–Henze–Yukich (2018)	Public
EHY simplex uniformity	simplex.ehy_uniformity	Ebner–Henze–Yukich (2018)	Public
Alpha-energy compositional equality	simplex.alpha_energy_ksamp	Sevinç–Tsagris (2026)	Public

Advanced candidates held behind gates

Method	Planned function	Reason it is not public
Ball Divergence	equaldist.ball_divergence_2samp	Floating-distance equality cannot yet preserve every exact closed-ball symmetry without merging a representably unequal near-tie
Xue–Yao multiplier mean test	mean.xy_2samp	The planned 999-draw calibration was too conservative in its audited regime
Yu–Li–Xue covariance combination	covariance.ylx_2samp	Joint component independence and a 20,000-dataset size gate remain incomplete
Jiang–Wen–Jiang–Wang–Zhang covariance test	covariance.jwjwz_2samp	Finite estimator and calibration have not been reconciled with a literal oracle
Yu–Li–Xue–Li joint test	mean_covariance.ylxl_2samp	The default Fisher/power-enhancement branch has not completed its equation and calibration gates

These blocked names are documentation metadata, not imports. pySHT does not publish placeholders or substitute another statistic under the planned name.