kakutani-dichotomy

Paper I of "Statistical Pharmacology via Kakutani Dichotomy": the marginal drug Kakutani index (DKI) and the alpha_c = 1/2 criticality theorem for high-dimensional protein conformational ensembles. Paper (LaTeX/PDF), reproducible Python code, data and figures. DOI 10.5281/zenodo.23005921

Kakutani–KMS theory of ligand-induced conformational phase transitions: integrating article of the Statistical Pharmacology via Kakutani Dichotomy series (Papers I–VII), with LaTeX source, PDF and verification script.

Paper VI of Statistical Pharmacology via Kakutani Dichotomy: Wasserstein separation W_1(phi_+, phi_-) of broken phases under a Rieffel cone seminorm, certified to [0.229028, 0.229032]; the single-step scan barrier 5/12; discrete infinity-Laplacian cone geodesics; and a 2.77x FEP variance reduction for cooperative alchemical paths.

Paper IX of the Kakutani Dichotomy series: Notch-sparing gamma-secretase modulators for Alzheimer's disease, Schur-complement confinement of the Presenilin-1 catalytic block, infinity-Laplacian cone geodesics of processive tripeptide trimming, a dual-biomarker branching law, and allosteric rescue of familial PSEN1 alleles.

Paper V of Statistical Pharmacology via Kakutani Dichotomy: the chemical obstruction group Xi_beta^drug(S) = (Z/2Z)^{A_beta}, Borel-Cantelli tail order parameters, parity-cocycle invariance, and the relative-entropy staircase |A_beta| ln 2. Code, data, figure, LaTeX source and PDF.

Statistical Pharmacology via Kakutani Dichotomy X: Blocking amyloid nucleation of intrinsically disordered tau and Abeta42 monomers via tail-exponent stabilization, asymmetric baseline cubic corrections, and finite-mode crossover.

Paper II of "Statistical Pharmacology via Kakutani Dichotomy": the correlated Kakutani index (CKI), the 99.95% covariance dominance theorem (Szego rate in closed form) and spectral fingerprints of cryptic allostery. Paper (LaTeX/PDF), reproducible Python code, data and figures. DOI 10.5281/zenodo.23012217

Paper VII of Statistical Pharmacology via Kakutani Dichotomy: kakutani_pharma, a Python pipeline for Kakutani indices of MD conformational ensembles. Ledoit-Wolf regularized CKI with an exact three-way decomposition, split-trajectory null subtraction, within-half block bootstrap, and pocket-centred shell-scaling exponents. Validated on a synthetic

Paper III of "Statistical Pharmacology via Kakutani Dichotomy": spectral Kakutani-Feldman-Hajek criticality of correlated conformational modes (mode amplitude perturbation vs iso-spectral Givens rotation), the doubling tail-increment estimator that removes the finite-size bias at alpha_c = 1/2, and the geodesic parity theorem on the SPD cone. Paper

Paper VIII of Statistical Pharmacology via Kakutani Dichotomy: validation on real PDB ensembles (ubiquitin NMR, adenylate kinase), Isserlis bound and influence-function block selection, bootstrap coverage calibration. Code, data, paper.