The Mathematics
The math it stands on.
Strata isn't fast because we tuned it to be fast — it's fast because the geometry of a cube gives up work for free, and we built the pipeline to take that work instead of redoing it.
Cubic voxel scaling
A module voxelized on an n-cube grid has n³ cells — the cost of resolution is cubic, not linear. That's why Strata certifies at three fixed tiers instead of an arbitrary resolution: n = 16 gives 4,096 cells, n = 32 gives 32,768, and n = 64 gives 262,144. Each step up is an 8× jump in work, so knowing exactly where you sit on that curve — and not silently drifting past it — is the first thing correctness depends on.
Octahedral canonicalization
A cube has 24 rotational symmetries, doubled to 48 once reflections are included — the full octahedral group Oh. Any voxel pattern and its 48 orientations are, structurally, the same problem solved 48 times. Strata canonicalizes each pattern under this group before certifying it, so equivalent orientations collapse to one representative instead of one apiece. That's not a heuristic — it's the exact symmetry of the grid itself, so it's reuse Strata is entitled to, not reuse it hopes for.
Backend selection by measurement
For every module, Strata bakes both paths under measurement and keeps whichever finished faster — GPU or CPU. There's no hand-set threshold guessing which modules "should" prefer which backend; the module tells the pipeline directly, per bake, on the hardware actually running it. When the workload shape changes, the routing changes with it, automatically.
Measured speedup
S is simply the ratio of the two measured times above — not a projection, a reading. Across the current fleet that ratio lands roughly in the 4–7× range on average, with individual modules doing better when their geometry favors the GPU path. We report it as a measured range because it is one: it moves as hardware and the module library change, and we'd rather show you the honest spread than a single number that stops being true.
Amdahl's law
Here f is the fraction of a bake that actually parallelizes; p is how many parallel units you throw at it. Amdahl's law says the sequential remainder — the (1 − f) that can't be split — caps your speedup no matter how much parallel hardware you add. We hold ourselves to this on purpose: it's the honest reason we quote a measured range instead of a bigger number, and the reason future work targets f itself, not just p.
Idempotent certification
Once a module is proven correct at a given resolution, that proof is cached — checking it again is a lookup, not a recompute. So the cost of growing the library is a sum over only the assets that are actually new, never a sum over everything that's already been certified. That's what keeps a large module library affordable: it grows additively with what you add, not multiplicatively with what you already have.
What this is
None of this is a promise about a number you haven't seen yet. It's the arithmetic of a cube, a symmetry group, and a cache — worked out plainly so the speed and the correctness are both things you can check, not things you have to take our word for. Strata ships a module when it's certified, and the math above is exactly what "certified" is standing on.
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