Astronomy

Propagate near-Earth and GNSS-region orbits with a semi-analytical averaged-element model in the Brouwer–Lyddane / PB05 tradition: orbit-averaged secular drift of the mean elements under the EGM96 zonal field J2–J6 (numerical Gauss-equation averaging — the Delaunay-normalisation analogue with the closed-form J2 rates as a built-in cross-check), first-order J2 short-period mean↔osculating reconstruction, long-period J3 frozen-orbit analysis (e = −J3·sin i/(2·J2·p), ω = 90°), double-averaged luni-solar quadrupole secular effects on an elliptical inclined perturber orbit (the Celletti/Kozai–Lidov term with the 39.23° critical mutual inclination), tesseral ground-track resonance checks (1:1, 2:1, 3:2, 5:2 and small-rational commensurabilities with Earth rotation), sun-synchronous inclination solving, and an in-report RK4 numerical-propagation cross-validation of the averaged model.

Media

Detect kick, snare, and hi-hat hits in a drum track or full mix, then layer or replace them with your own samples (or built-in synthesized ones).

Format Conversion

Encode a complete Web Push send: RFC 8291 aes128gcm payload encryption, RFC 8292 VAPID ES256 JWT, RFC 8030 headers, APNs/FCM cross-walk and decrypt round-trip verification.

Games

Validate GC-codes (base-31 with offset, or hex era), place caches on the 81-cell D/T Fizzy grid, chain multi-stage bearing projections into WGS84 waypoints, and cross-check puzzle finals against checker coordinates.

Development

Convert an N-bit value to binary, Gray, one-hot and thermometer codes with a counting truth table, Hamming-distance chart and Verilog/VHDL encoder stubs.

Development

Drop any game save file — Minecraft NBT, Unreal Engine GVAS, Palworld containers, JSON/XML/INI/Lua text saves, SQLite profiles — and get the detected format, engine versions, key progress fields and a bounded structural tree.

Data Processing

Paste one or two columns of numbers and get the complete descriptive suite — mean/median/mode, sample and population variance, type-7 quartiles and percentiles, MAD, adjusted skewness and kurtosis, Tukey outliers — plus covariance, Pearson r, tie-corrected Spearman rho and least-squares regression for two columns.

Finance

Side-by-side monthly rent-vs-buy simulation: mortgage amortization, property tax, insurance, HOA and maintenance against rent plus renter insurance; the renter invests the down payment and monthly savings at an opportunity-cost rate. Outputs break-even year on net sale proceeds, per-year differential NPV, SALT-cap-aware after-tax cash flows, a differential IRR, and a ±20% tornado sensitivity chart.

Text Processing

Two-way Excel 365 dynamic-array workbench: expand LET/LAMBDA/MAP/SCAN/REDUCE/BYROW/BYCOL/MAKEARRAY formulas into an AST with step-traced evaluation (LET bindings, lambda first calls, intermediate matrices, optional A1-anchored sample data), and translate plain-English intents like "7-day rolling average" or "running total" into working LAMBDA/MAP/SCAN formulas.

Health

Interpret Jamar / Camry / EH101 grip readings against age/sex population norms (Massy-Westropp 2011: z-score, percentile, % of norm), sarcopenia weakness cutoffs (EWGSOP2, AWGS, Fried), the 10% asymmetry rule; compute rate of force development from force-time curves (0–50…0–250 ms windows, peak RFD, impulse, time-to-peak per Maffiuletti 2016); and repeated-trial fatigue index.

Development

Statically analyze a pytest conftest.py chain: render the fixture dependency graph across all five scopes (function/class/module/package/session), detect deeper-conftest overrides, ScopeMismatch edges, and cross-test state pollution — mock.patch().start() without .stop(), monkeypatch leaking from broad-scope fixtures, and with mock.patch held open across yield.

Geography

Encode lat/lng into Uber H3 hexagons (res 0-15) and Google S2 Hilbert cells (level 1-30) with index, id, token, quadkey, areas, k-ring neighbors, compaction, parent ladders and round-trip drift.