All limits.

A scoped, source-linked candidate record for largest bacterial cell diameter.

A scoped, source-linked candidate record for smallest flowering plant genome.

A scoped, source-linked candidate record for longest known animal lifespan.

A scoped, source-linked candidate record for human cortical neuron count.

A scoped, source-linked candidate record for mammalian gestation length.

A scoped, source-linked candidate record for maximum mammalian diving depth.

A scoped, source-linked candidate record for hummingbird wingbeat frequency.

A scoped, source-linked candidate record for tardigrade desiccation survival.

A scoped, source-linked candidate record for largest known viral genome.

A scoped, source-linked candidate record for maximum bacterial growth rate model.

A scoped, source-linked candidate record for carbon-nanotube tensile strength.

A scoped, source-linked candidate record for graphene thermal conductivity.

A scoped, source-linked candidate record for mgb₂ superconducting transition.

A scoped, source-linked candidate record for ybco ambient-pressure transition.

A scoped, source-linked candidate record for ultralow-density silica aerogel.

A scoped, source-linked candidate record for metallic-glass strength.

A scoped, source-linked candidate record for diamond thermal conductivity.

A scoped, source-linked candidate record for perovskite solar-cell efficiency.

A scoped, source-linked candidate record for ultrahard nanocrystalline diamond.

A scoped, source-linked candidate record for metallic-glass elastic limit.

A scoped, source-linked candidate record for carbon-fiber specific strength.

A scoped, source-linked candidate record for kevlar tensile strength.

A scoped, source-linked candidate record for bulk graphene fracture strength.

A scoped, source-linked candidate record for single-wall nanotube thermal conductivity.

A scoped, source-linked candidate record for bulk copper thermal conductivity.

A scoped, source-linked candidate record for silicon carbide hardness.

A scoped, source-linked candidate record for zirconia fracture toughness.

A scoped, source-linked candidate record for nitinol recoverable strain.

A scoped, source-linked candidate record for bulk metallic-glass fracture toughness.

A scoped, source-linked candidate record for high-entropy alloy strength.

A scoped, source-linked candidate record for aluminum-lithium alloy density.

A scoped, source-linked candidate record for aerographite density.

A scoped, source-linked candidate record for silica glass optical transmission.

A scoped, source-linked candidate record for superelastic niti strain.

A scoped, source-linked candidate record for bulk superconducting iron pnictide transition.

A scoped, source-linked candidate record for hydrogen storage in metal-organic frameworks.

A scoped, source-linked candidate record for perovskite led external quantum efficiency.

A scoped, source-linked candidate record for bulk nanocrystalline copper strength.

A scoped, source-linked candidate record for thermoelectric figure of merit frontier.

A scoped, source-linked candidate record for amorphous carbon hardness.

Exact self-attention naively materializes a score matrix that grows quadratically with sequence length, which is what limits how long a context transformer models can practically handle. IO-aware kernels like FlashAttention avoid materializing that full matrix, trading a fixed compute cost for dramatically less memory traffic.

The entropy — and so the total information content — of any physical system is capped by its energy and physical size: S ≤ 2π k_B E R/(ℏ c) for a system with energy E confined within radius R, setting an absolute upper limit on how much information can fit in a bounded region of space.

The speed of light in vacuum is one of the few physical constants whose value is exact by definition rather than measurement — the 1983 SI redefinition of the metre fixed it precisely, making it the ultimate speed limit for information and matter in relativity.

Photosynthesis converts sunlight into chemical energy, but real-world efficiency falls far short of the theoretical maximum due to biochemical and physical losses. This record cites the observed efficiency ceiling for C3 plants — the majority of crop species — under a specific modeled canopy scenario.

No heat engine operating between two temperature reservoirs can convert heat to work more efficiently than a reversible one: the Carnot limit η ≤ 1 − T_c/T_h, where T_h and T_c are the hot and cold reservoir temperatures.

Before neutron stars were even confirmed to exist, Chandrasekhar showed that white dwarf stars have a maximum possible mass — beyond it, electron degeneracy pressure can no longer support the star against gravitational collapse. His original 1931 calculation used an idealized, composition-independent model.

Training a fixed compute budget into an ever-larger model isn't always the best use of that compute — the Chinchilla study found that model size and training-token count should scale together, not model size alone, to reach the best loss for a given budget.

Covering the plane with congruent circles and leaving no gaps forces the circles to overlap. The thinnest such covering — the arrangement with the least overlap, achieved by centering circles on a hexagonal lattice — has density 2π/√27 ≈ 1.209, meaning the circles' total area exceeds the plane's area by about 21%.

DNA can in principle store far more information per gram than any other known medium. This tracks two genuinely different figures that should never be conflated: the theoretical raw nucleotide encoding limit, and the density actually demonstrated by real error-corrected schemes like DNA Fountain — which are orders of magnitude apart.

The sphere packing problem asks what fraction of space can be filled by non-overlapping equal spheres. In eight dimensions, the extraordinarily symmetric E8 lattice achieves the provably optimal arrangement — a landmark 2016 result.