Why I’m building a "Sovereign" Physics Math Layer

I like fixedpoint math. I'd be interested to see how you're going to handle stuff like sqrt or vector normalisation. Do you use multiple fixedpoint scales? Dynamic scales or multiple types? Also, what exactly is the point of the accumulated rounding error tracking? Is it for debugging purposes?

In my experience, it makes most sense to have a unique number type per problem domain, and then convert between those, instead of trying to have a universal type. That lets the programmer choose the scale, size, and precision appropriately. Also, divisions on integers are expensive, so it is best to find workarounds.

Not sure what you mean by truth hierarchy and provenance report.

For sqrt and normalize, I'm using a lookup table with linear interpolation, then one or two Newton-Raphson refinement steps. It's slower than hardware float, but the result is bit-identical across platforms, which is the whole point.

On scales — yes, I use multiple fixed-point types per domain rather than one universal type. Each has a baked-in scale chosen for its range/precision tradeoff. I'm not trying to make one type rule them all.

The error tracking isn't for debugging exactly — it's metrological. When you chain unit conversions (say, feet → meters → newtons), rounding accumulates. The ± margin tells you how much of your result is "real" vs. drift. Useful if you're feeding outputs into scientific tooling or logging results you need to defend later.

The Truth Hierarchy is just a documented chain of where each constant or conversion factor came from — NIST, BIPM, ISO 80000, etc. The Provenance Report is a signed attestation that no value was eyeballed or approximated without disclosure. Overkill for most games, but that's kind of the pitch.

Do you have a background in cryptography, perhaps? It sounds like what a cryptographer would come up with.