Analytical equation engine — narrative

Verified counts, measured tool outputs and the full workflow: analytical-engine.html; the catalog itself is MODELS.md.

What it is

150 deterministic scientific functions — one per row of the catalog — spanning 26 domains from boundary-layer meteorology to orbital mechanics. Each function is an implementation of a published equation, carries its source citation in the catalog, ships a worked steps[] derivation with every result, and is covered by math-verification unit tests (the 1,653-test suite that gates this engine exercises the equations directly, no mocks). None of them is a machine-learning approximation: a tool returns what its cited paper returns.

How a tool runs

A user's question or panel request enters through contextEngine.computeWithContext, which first enriches inputs from live feeds (terrain elevation, weather, ocean state, seismic catalog) so the same tool called twice at different places computes different, real numbers. The 7-stage workflow in toolWorkflows.ts then wraps validation, preprocessing, computation, QC, uncertainty and interpretation around the equation call. Two contracts govern the whole surface: a tool must never throw (unexpected input paths return honest NaN with an explanation), and no value is fabricated (missing catalog data yields NaN and a warning, not a plausible constant).

How to read a result

Every result includes: the equation as evaluated, the parameter substitution, unit, a QC verdict against the source's valid range, and an uncertainty statement (method: analytical propagation, empirical RMSE, or qualitative). Treat "qualitative" honestly — some tools (e.g. disaster-risk indices) are defined in their sources without error models; the uncertainty block says so instead of inventing one.

The parts

Parts I–VII run from Earth-system core (atmosphere, hydrology, seismology, remote sensing, soils) through biosphere and chemistry, ocean and coastal mechanics, geomorphology and cryosphere, climate dynamics, space environment, and finally engineering/risk/assimilation. The per-domain tool counts in the site table are measured from the catalog structure, not copied from prose.