ashfordeOU Cross-cutting domain pack (router)
Route here when the task is the skill format, packaging, or delivery layer, the standard atmosphere, the engineering documentation layer, or numerical analysis.
Domain
Cross-cutting and foundational: the skill-format and delivery specification (SEP-2640) that governs how this library packages and serves skills over MCP, skill evaluation, the ISA standard atmosphere for performance work, unit conversion, the documentation discipline for engineering reports and margins, and the numerical analysis discipline (verification, regression, uncertainty propagation, integration) for engineering calculations.
Sub-skills in this pack
| Path | Skill | When to route to it |
|---|---|---|
| cross-cutting/sep2640/skill-delivery | SEP-2640 skill delivery | SKILL.md packaging, skill URIs, MCP resources, server readiness |
| cross-cutting/sep2640/skill-evaluation | Skill evaluation | SEP-2640 conformance checks, weighted quality score, acceptance verdict, coverage ratio |
| cross-cutting/sep2640/skill-authoring | Skill authoring | frontmatter template, kebab-case name rule, pre-publish conformance check, required fields |
| cross-cutting/units-atmos/isa-atmosphere | ISA atmosphere | standard atmosphere, temperature lapse, pressure altitude, density |
| cross-cutting/units-atmos/unit-conversion | Unit conversion | SI/imperial/aviation units, length, speed, temperature, pressure, density, Mach |
| cross-cutting/units-atmos/temperature-conversion | Temperature conversion | kelvin, celsius, fahrenheit, rankine, absolute zero, temperature difference |
| cross-cutting/documentation/engineering-margins | Engineering margins | margin of safety, allowable vs applied load, limit and ultimate basis, report sentence |
| cross-cutting/documentation/engineering-report | Engineering report | report anatomy, abstract length, required sections, completeness verdict |
| cross-cutting/numerics/convergence-verification | Convergence verification | Richardson extrapolation, GCI, observed order, discretization error, mesh refinement |
| cross-cutting/numerics/least-squares-regression | Least squares regression | OLS slope and intercept, residual standard deviation, R-squared, prediction |
| cross-cutting/numerics/uncertainty-propagation | Uncertainty propagation | GUM first order law, sensitivity coefficients, combined uncertainty, coverage factor |
| cross-cutting/numerics/numerical-integration | Numerical integration | trapezoid rule, Simpson rule, Gauss-Legendre quadrature, Richardson error estimate |
| cross-cutting/numerics/finite-difference-derivatives | Finite difference derivatives | forward/backward/central difference, step size, second derivative, tabulated data |
| cross-cutting/numerics/monte-carlo-sampling | Monte Carlo sampling | seeded draws, sample mean and standard deviation, percentile confidence interval, histogram |
| cross-cutting/numerics/interpolation | Table interpolation | linear interpolation, piecewise linear, natural cubic spline, table lookup, tabulated data points, extrapolation |
| cross-cutting/numerics/ode-solvers | ODE solvers | explicit Euler, Heun RK2, classical RK4, initial value problem, step size convergence, closed-form comparison |
| cross-cutting/numerics/matrix-operations | Matrix operations | Gaussian elimination with partial pivoting, linear system solve Ax=b, determinant, matrix inverse, singularity detection |
| cross-cutting/numerics/fast-fourier-transform | Fast Fourier transform | DFT definition, radix-2 Cooley-Tukey FFT, magnitude and phase spectrum, inverse FFT, Parseval energy check |
| cross-cutting/tolerancing/tolerance-stackup | Tolerance stackup | worst case, root sum square, assembly limits, nominal dimension, dominant contributor |
| cross-cutting/tolerancing/position-tolerance-calc | GD&T position tolerance | true position, tolerance zone diameter, MMC bonus tolerance, virtual condition, hole and pin |
| cross-cutting/tolerancing/fastener-position-tolerance-calc | Fastener position tolerance | fixed fastener formula, floating fastener formula, projected tolerance zone, mating hole clearance, positional tolerance budget |
| cross-cutting/numerics/eigenvalue-decomposition | Eigenvalue decomposition | eigenvalue, eigenvector, Jacobi algorithm, power iteration, deflation, Rayleigh quotient, symmetric matrix |
| cross-cutting/numerics/root-finding | Root finding | bisection, Newton-Raphson, secant method, convergence tolerance, bracketing |
| cross-cutting/units-atmos/dimensional-analysis | Dimensional analysis | Buckingham Pi theorem, dimensional homogeneity, Pi groups, Reynolds number, unit consistency |
| cross-cutting/data-sources/aeronautical-data-sources | Aeronautical data sources | data source credibility, revision status, publisher, engineering reference, citation line, authoritative source |
| cross-cutting/tolerancing/datum-reference-frames | Datum reference frames | datum reference frames, GD&T, datum precedence, primary secondary tertiary, feature control frame, material condition, MMB LMB RMB, degrees of freedom, datum simulators, ASME Y14.5 |
| cross-cutting/tolerancing/gdandt-basics | GD&T basics | GD&T, feature control frame, datum reference frame, form tolerance, orientation tolerance, MMC, LMC, RFS, bonus tolerance |
| cross-cutting/export-control/export-control-awareness | Export Control Awareness | ITAR, EAR, USML, EAR99, 600-series, defense articles, technical data, export control, deemed export, fundamental research, public domain, compliance review, sharing data with foreign collaborators. |
| cross-cutting/numerics/optimization-algorithms | Optimization algorithms | minimize, golden section search, gradient descent, Nelder-Mead, line search, unconstrained optimum |
| cross-cutting/numerics/quaternion-algebra | Quaternion algebra | quaternion product, rotate vector by quaternion, euler to quaternion, quaternion to euler, direction cosine matrix, slerp, quaternion conjugate, unit quaternion, axis angle to quaternion |
| cross-cutting/numerics/probability-distributions | Probability distributions | probability distribution fitting, weibull fit, lognormal, exponential fit, goodness of fit, kolmogorov smirnov, chi-square fit test, quantile, reliability, hazard function |
| cross-cutting/numerics/hypothesis-testing | Hypothesis testing | hypothesis testing, student t test, welch test, paired t test, ANOVA, F test for variances, chi-square test of independence, p-value, significance level |
| cross-cutting/numerics/digital-filter-design | Digital filter design | Butterworth IIR filter design, bilinear transform, prewarping, lowpass and highpass coefficients, filter magnitude response |
| cross-cutting/numerics/cross-correlation-analysis | Cross-correlation analysis | cross-correlation, autocorrelation, time delay estimation, lag, normalized correlation coefficient, channel similarity, delay between signals |
| cross-cutting/numerics/descriptive-statistics | Descriptive statistics | descriptive statistics, summary statistics, five number summary, interquartile range, coefficient of variation, outlier flagging |
| cross-cutting/numerics/fir-filter-design | FIR lowpass filter design | FIR filter, windowed-sinc, finite impulse response, linear phase, filter taps, group delay, Hamming window |
| cross-cutting/units-atmos/airspeed-conversion | Airspeed conversion | calibrated airspeed, equivalent airspeed, true airspeed, Mach airspeed, impact pressure, airspeed-indicator compressibility correction | | cross-cutting/numerics/complex-number-algebra | Complex number algebra | complex arithmetic, polar form, Euler formula, De Moivre, roots of unity, phasor math | | cross-cutting/numerics/power-spectral-density | Power spectral density | power spectral density, Welch periodogram, Hann window, spectral density estimation, equivalent noise bandwidth, random vibration survey | | cross-cutting/numerics/confidence-interval-estimation | Confidence interval estimation | confidence interval, t interval, chi square variance interval, mean difference interval, quantile inversion, small sample statistics | | cross-cutting/units-atmos/density-altitude | Density altitude | density altitude, non standard day, ISA deviation, hot day performance, density ratio, inverse ISA, performance reduction | | cross-cutting/numerics/singular-value-decomposition | Singular value decomposition | singular value decomposition, one sided Jacobi SVD, numerical rank, condition number estimation, Moore Penrose inverse | | cross-cutting/numerics/rank-based-hypothesis-testing | Rank based hypothesis testing | rank based hypothesis testing, Wilcoxon rank sum test, Mann Whitney U test, Wilcoxon signed rank test, sign test, normality free comparison, two sample rank test |
| cross-cutting/numerics/information-entropy | Information entropy | Shannon entropy, binary entropy function, information content, source coding bound, bits per symbol | | cross-cutting/numerics/runs-test | Runs test | runs test, Wald-Wolfowitz runs, sequence randomness test, runs count, expected runs, z statistic | | cross-cutting/numerics/grubbs-outlier-test | Grubbs outlier test | grubbs outlier test, G statistic, single outlier test, grubbs critical value, outlier screening verdict | | cross-cutting/numerics/multiple-linear-regression | Multiple linear regression | multiple linear regression, variance inflation factor, adjusted R squared, partial regression coefficient, regression F test, coefficient standard error, multicollinearity check | | cross-cutting/numerics/proportion-confidence-interval | Proportion confidence interval | proportion confidence interval, Wilson score interval, Clopper Pearson interval, binomial proportion, exact confidence bound, two proportion difference | | cross-cutting/numerics/fisher-exact-test | Fisher exact test | fisher exact test, two by two contingency, hypergeometric exact p, small expected count, exact independence test, odds ratio | | cross-cutting/numerics/chi-square-goodness-of-fit | Chi square goodness of fit | chi square goodness of fit, categorical model test, observed versus expected, count data model fit, goodness of fit p value | | cross-cutting/numerics/kruskal-wallis-test | Kruskal Wallis test | kruskal wallis test, H statistic, nonparametric ANOVA, rank based multi group, distribution free k sample | | cross-cutting/numerics/exact-binomial-test | Exact binomial test | exact binomial test, single proportion test, binomial tail p value, k of n significance, mid p binomial | | cross-cutting/numerics/poisson-confidence-interval | Poisson confidence interval | poisson confidence interval, count rate interval, defect rate estimation, Garwood exact interval, poisson rate CI | | cross-cutting/numerics/power-analysis | Power analysis | power analysis, sample size determination, type II error, effect size, minimum sample size, achieved power |
| cross-cutting/numerics/bandpass-bandstop-filter-design | Bandpass bandstop filter design | bandpass filter design, bandstop filter design, Butterworth bandpass, digital frequency transformation, band edge verification |
| cross-cutting/numerics/fir-bandpass-bandstop-filter-design | Fir Bandpass Bandstop Filter Design | fir-highpass-filter-design, fir-bandpass-filter-design, fir-bandstop-filter-design, spectral-inversion-method, frequency-translation-method, windowed-sinc-band-filter, linear-phase-band-filter |
Routing guidance
Skill packaging and MCP delivery questions route to the SEP-2640 skill-delivery sub-skill; evaluating a delivered skill's conformance and quality routes to the skill-evaluation sub-skill; authoring a new SKILL.md (template, kebab-case name, required fields)- Itar questions route to the export-control export-control-awareness sub-skill. routes to the skill-authoring sub-skill.
Standard atmosphere questions route to the units-atmos isa-atmosphere sub-skill; converting units between systems routes to the unit-conversion sub-skill; converting between temperature scales (kelvin, celsius, fahrenheit, rankine) routes to the temperature-conversion sub-skill.
Margin of safety and report sentence questions route to the documentation engineering-margins sub-skill; report structure and completeness questions route to the engineering-report sub-skill.
Mesh refinement, Richardson extrapolation, and discretization error questions route to the numerics convergence-verification sub-skill.
Regression fitting questions (slope, intercept, R-squared, prediction) route to the numerics least-squares-regression sub-skill.
Measurement uncertainty questions (GUM, combined and expanded uncertainty, coverage factor) route to the numerics uncertainty-propagation sub-skill.
Quadrature and integral-estimate questions (trapezoid, Simpson, Gauss-Legendre) route to the numerics numerical-integration sub-skill.
Numerical differentiation questions (forward, backward, central difference, step size, tabulated derivatives) route to the numerics finite-difference-derivatives sub-skill.
Sampling and distribution questions (seeded Monte Carlo draws, percentiles, confidence intervals, histograms) route to the numerics monte-carlo-sampling sub-skill.
Table lookup and interpolation questions (linear interpolation, piecewise linear, natural cubic spline, tabulated data points, extrapolation beyond the table ends) route to the numerics interpolation sub-skill.
Initial-value problem and differential-equation questions (explicit Euler, Heun RK2, classical RK4, step size convergence, error against a closed-form solution) route to the numerics ode-solvers sub-skill.
Dense linear system and matrix questions (Gaussian elimination with partial pivoting, Ax=b solve, determinant, matrix inverse, singular matrix detection) route to the numerics matrix-operations sub-skill.
Frequency-domain and spectral questions (discrete Fourier transform, radix-2 Cooley-Tukey FFT, magnitude and phase spectrum, inverse FFT, Parseval energy check) route to the numerics fast-fourier-transform sub-skill.
Aerospace engineering questions route to their domain pack (avionics, space-systems, systems-engineering-safety, manufacturing-quality).
Tolerance stack-up, worst case, and root sum square assembly questions route to the tolerancing tolerance-stackup sub-skill.
True position, MMC bonus tolerance, and virtual condition questions route to the tolerancing position-tolerance-calc sub-skill.
Eigenvalue and eigenvector computation, Jacobi eigenvalue algorithm, power iteration, deflation, and Rayleigh quotient questions route to the numerics eigenvalue-decomposition sub-skill.
Bisection, Newton-Raphson, secant method, and convergence tolerance questions route to the numerics root-finding sub-skill.
Dimensional analysis, Buckingham Pi theorem, Pi group formation, and dimensional homogeneity checks route to the units-atmos dimensional-analysis sub-skill.
Data source credibility, revision control, and engineering citation questions route to the data-sources aeronautical-data-sources sub-skill.
GD&T datum reference frame establishment, datum precedence, degrees of freedom constraint, and feature control frame construction route to the tolerancing datum-reference-frames sub-skill.
Geometric dimensioning and tolerancing fundamentals, feature control frames, datum reference frames, form and orientation tolerances, and MMC/LMC/RFS bonus tolerance questions route to the tolerancing gdandt-basics sub-skill.
Quaternion products, vector rotation, euler and direction-cosine conversions, and slerp algebra questions route to the numerics quaternion-algebra sub-skill.
FIR lowpass filter questions (windowed-sinc, finite impulse response taps, linear phase, group delay, Hamming window) route to the numerics fir-filter-design sub-skill.
Digital filter design questions (butterworth iir filter design, bilinear transform, prewarping, lowpass and highpass coefficients, filter magnitude response) route to the digital-filter-design sub-skill.
Cross-correlation, autocorrelation, and time-delay estimation questions route to the numerics cross-correlation-analysis sub-skill.
Sample summary and outlier questions (descriptive statistics, five number summary, interquartile range, coefficient of variation, 1.5 IQR outlier rule) route to the numerics descriptive-statistics sub-skill.
Airspeed conversion questions (calibrated airspeed, equivalent airspeed, true airspeed, Mach airspeed, impact pressure, airspeed-indicator compressibility correction) route to the units-atmos airspeed-conversion sub-skill.
Complex number algebra questions (complex arithmetic, polar form, Euler formula, De Moivre powers, roots of unity, phasor math) route to the numerics complex-number-algebra sub-skill.
Power spectral density estimation questions (Welch averaged periodogram, Hann window, equivalent noise bandwidth, random vibration survey) route to the numerics power-spectral-density sub-skill.
Confidence interval estimation questions (t interval for the mean, chi-square variance interval, pooled or Welch difference interval) route to the numerics confidence-interval-estimation sub-skill.
Density altitude questions (pressure altitude and OAT to density altitude, non-standard day, ISA deviation) route to the units-atmos density-altitude sub-skill.
Singular value decomposition questions (one-sided Jacobi SVD factors, singular values, condition number, numerical rank, Moore-Penrose pseudoinverse) route to the numerics singular-value-decomposition sub-skill.
Nonparametric hypothesis testing questions (Wilcoxon rank-sum and Mann-Whitney U, Wilcoxon signed-rank, sign test with continuity correction) route to the numerics rank-based-hypothesis-testing sub-skill.
Information content questions (Shannon entropy bits per symbol, binary entropy function, uniform entropy bound, minimum source coding bit rate) route to the numerics information-entropy sub-skill.
Install
To install only this pack, copy or symlink each leaf folder above into your host's skills directory (see README Install for per-host commands).
Numerical minimization (golden section, gradient descent, Nelder-Mead) questions route to the numerics optimization-algorithms sub-skill.
Distribution fitting questions (weibull, lognormal, exponential and normal fit, goodness of fit, quantile and reliability from the fitted parameters) route to the numerics probability-distributions sub-skill.
Significance test questions (t test, Welch, paired t, ANOVA, F variance test, chi-square independence, p-value verdicts) route to the numerics hypothesis-testing sub-skill.
Wald-Wolfowitz runs test questions (runs count, expected runs under the randomness null, z statistic verdict) route to the numerics runs-test sub-skill.
Grubbs single-outlier questions (G statistic against the critical value, reject or no-outlier verdict, rejected value screening for a normal sample) route to the numerics grubbs-outlier-test sub-skill.
Multi-predictor linear regression questions (normal-equation OLS with two or more predictors, variance inflation factor, adjusted R-squared, partial-regression t-test, overall F test) route to the numerics multiple-linear-regression sub-skill.
Binomial proportion interval questions (Wilson score interval, continuity-corrected Wilson, exact Clopper-Pearson bound, two-proportion difference interval) route to the numerics proportion-confidence-interval sub-skill.
Small-sample 2x2 contingency questions (Fisher exact test, hypergeometric tail probability, odds ratio, exact p-value when the expected count is below 5) route to the numerics fisher-exact-test sub-skill.
Categorical model-fit questions (chi-square goodness-of-fit statistic for observed versus expected counts in k categories, exact p-value from the survival function, uniform or Poisson count model checks) route to the numerics chi-square-goodness-of-fit sub-skill.
Multi-group rank comparison questions (Kruskal-Wallis H statistic with the ties correction, nonparametric k-sample significance without normality) route to the numerics kruskal-wallis-test sub-skill.
Single-proportion significance questions (exact binomial tail test of an observed k-of-n count against a hypothesized p0, mid-p variant, small-count recommendation) route to the numerics exact-binomial-test sub-skill.
Poisson rate interval questions (exact Garwood chi-square bounds for a count over an exposure, defect rate per unit, normal-approximation cross-check) route to the numerics poisson-confidence-interval sub-skill.
Test-sizing questions (minimum sample size per group from alpha, power and effect size for two-sample, one-sample and proportion comparisons, achieved power at the rounded sample size, type-II error) route to the numerics power-analysis sub-skill.
Bandpass and bandstop digital-filter questions (Butterworth IIR bandpass/bandstop by the z-domain frequency transformation, band-edge verification) route to the numerics bandpass-bandstop-filter-design sub-skill; lowpass and highpass questions stay with digital-filter-design.
FIR band and highpass filter questions (windowed-sinc FIR highpass by spectral inversion, FIR bandpass by cosine frequency translation, FIR bandstop by inversion of the translated bandpass, linear-phase band-filter tap sets) route to the numerics fir-bandpass-bandstop-filter-design sub-skill; FIR lowpass stays with fir-filter-design.
Mating fastener pattern questions (ASME Y14.5 fixed and floating fastener positional tolerance budgets, projected tolerance zone, minimum clearance hole at MMC) route to the tolerancing fastener-position-tolerance-calc sub-skill.