Microcosmos avoids quadratic-scaling operations by design — local fluid updates and grid-based steric repulsion instead of pairwise checks — to reach GPU-scale populations

The organizing constraint behind Microcosmos (arXiv:2607.02954) is that every component avoids operations that scale quadratically with the number of interacting elements, because quadratic cost is what caps population size on a GPU. Two design choices carry this: the Lattice Boltzmann fluid solver uses only local updates (no all-pairs force computation), and self-avoidance is handled by grid-based steric repulsion rather than pairwise collision detection. The whole engine is implemented in JAX, giving automatic differentiation over the physics for free (claim-microcosmos-elastic-filaments-differentiable-gpu-fluid).

The capture records the paper's performance claim — runtime scaling linearly with particle count, tested to ~500k particles on a single NVIDIA L40S GPU — but that specific figure is held under [unverified-quant]. The capture author explicitly noted that "exact benchmark numbers/methodology beyond this summary should be checked against the paper's own figures before reuse," so the number is recorded, not treated as settled. Under the vault's sourcing floor a specific benchmark figure is a Tier 1–2 quantitative claim that should be confirmed against the primary source's own plots before going load-bearing; the verification is routed to question-verify-microcosmos-benchmarks-and-experiments and the note stays seedling.

The durable content here is the design principle — trade pairwise exactness for local/grid approximations to buy linear scaling — not the exact particle count. This "kill the quadratic term to hit hardware scale" pattern is a recurring theme in GPU-era ML systems work, adjacent to the throughput-oriented engineering in claim-gift-2026-gradient-anisotropy-isotropic-transform.