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, and 48 once reflections are included — the full octahedral group Oh. Strata canonicalizes under the 24 proper rotations; reflections are deliberately excluded, so what we take is the chirality-safe half of the group. Equivalent orientations collapse to one representative instead of one apiece. That's not a heuristic — it's the exact rotational symmetry of the grid itself, so it's reuse Strata is entitled to, not reuse it hopes for.
Backend selection by measurement
Strata bakes both paths under measurement during certification and records which finished faster — GPU or CPU. Later bakes read that stored result rather than re-racing. There's no hand-set threshold guessing which modules "should" prefer which backend: the measurement decides, though it is the measurement from the certifying run, not the current one. Re-certify and the routing moves with it.
Measured speedup
S is simply the ratio of the two measured times above — not a projection, a reading. With symmetry skipping enabled the fleet aggregate at the 32-cube tier is 5.8× — total CPU wall divided by total GPU wall, over 99 modules. Per module the spread is much wider and it runs both ways: from 1.0×, meaning no benefit at all, up to 26×, with about a third of modules under 5×. Measured separately, without symmetry skipping the GPU path was slower than the CPU reference at a coarser tier. Those are two runs rather than one controlled comparison — the CPU baseline differed between them — so we take symmetry as the reason the GPU path pays without publishing an on/off multiplier we did not measure. We state the range and its floor because a range without its floor only shows you the flattering end.
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 has passed certification at a given resolution, that result 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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