function plotSpectralDistributionCumulants(results, varargin)
%% plotSpectralCumulants
% Author:       Karthik
% Date:         2025-10-02
% Version:      1.0
%
% Description:
%   Plot first four cumulants of recentered spectral curves vs scan parameter.
%
% Inputs:
%   results_struct - struct returned by plotSpectralCurvesRecentered
%                    (fields: curves, x_values, scan_parameter_values)
%
% Notes:
%   Computes cumulants across repetitions at selected theta values
%   and plots them in 4 tiled subplots.

    % --- Parse name-value pairs ---
    p = inputParser;
    addParameter(p, 'Title', 'Spectral Cumulants', @(x) ischar(x) || isstring(x));
    addParameter(p, 'XLabel', 'Scan Parameter', @(x) ischar(x) || isstring(x));
    addParameter(p, 'FontName', 'Arial', @ischar);
    addParameter(p, 'FontSize', 14, @isnumeric);
    addParameter(p, 'FigNum', [], @(x) isempty(x) || (isnumeric(x) && isscalar(x)));
    addParameter(p, 'SkipSaveFigures', false, @islogical);
    addParameter(p, 'SaveFileName', 'SpectralCumulants.fig', @ischar);
    addParameter(p, 'SaveDirectory', pwd, @ischar);
    addParameter(p, 'MaxOrder', 4, @isnumeric);
    parse(p, varargin{:});
    opts = p.Results;

    % --- Setup ---
    N_params     = numel(results.curves);
    xvals        = results.scan_reference_values;
    thetaVals    = results.x_values * pi;

    % --- Select specific theta indices (like in g2 case) ---
    desiredTheta = [pi/12 pi/6 pi/3];
    [~, thIdx]   = arrayfun(@(t) min(abs(thetaVals - t)), desiredTheta);
    thetaLabels  = {'\pi/12','\pi/6','\pi/3'};

    % --- Compute cumulants: [theta × scan × cumulantOrder] ---
    kappa = zeros(numel(thIdx), N_params, opts.MaxOrder);
    for i = 1:N_params
        for t = 1:numel(thIdx)
            reps_values = results.curves{i}(:, thIdx(t));
            kappa(t,i,:) = Calculator.computeCumulants(reps_values, opts.MaxOrder);
        end
    end

    % --- Colormap ---
    fullCmap = Colormaps.coolwarm(256);
    Ntheta   = numel(thIdx);
    blueSide = fullCmap(1:100,:);          % avoid white
    redSide  = fullCmap(157:end,:);
    trimmedCmap = [blueSide; redSide];
    indices = round(linspace(1,size(trimmedCmap,1),Ntheta));
    cmap = trimmedCmap(indices,:);

    % --- Create figure ---
    if isempty(opts.FigNum), fig = figure; else, fig = figure(opts.FigNum); end
    clf(fig);
    set(fig,'Color','w','Position',[100 100 950 750]);
    t = tiledlayout(2,2,'TileSpacing','Compact','Padding','Compact');
    title(t, opts.Title, 'FontName', opts.FontName, 'FontSize', opts.FontSize+4);

    cumulLabels = {'\kappa_1','\kappa_2','\kappa_3','\kappa_4'};
    cumulTitles = {'Mean','Variance','Skewness','Binder Cumulant'};

    for k = 1:opts.MaxOrder
        ax = nexttile; hold(ax,'on');
        for idx = 1:numel(thIdx)
            plot(ax, xvals, squeeze(kappa(idx,:,k)), '-o', ...
                'Color', cmap(idx,:), 'LineWidth', 2, 'MarkerSize', 8, 'MarkerFaceColor', cmap(idx,:));
        end
        ylabel(ax, cumulLabels{k}, 'FontName', opts.FontName, 'FontSize', opts.FontSize);
        xlabel(ax, opts.XLabel, 'FontName', opts.FontName, 'FontSize', opts.FontSize);
        title(ax, cumulTitles{k}, 'FontName', opts.FontName, 'FontSize', opts.FontSize+2);
        grid(ax,'on'); set(ax,'FontName',opts.FontName,'FontSize',opts.FontSize);

        % --- Legend ---
        legend(ax, thetaLabels, 'Location', 'best', 'FontSize', opts.FontSize-2);
    end

    % --- Save figure ---
    if ~opts.SkipSaveFigures
        if ~exist(opts.SaveDirectory,'dir'), mkdir(opts.SaveDirectory); end
        savefig(fig, fullfile(opts.SaveDirectory, opts.SaveFileName));
    end
end