A cubit is a length that falls out of the human forearm — no ruler needed, the body IS the ruler. The PLANCK LENGTH is the same trick played on the universe: take three constants of nature — ħ (quantum), G (gravity), c (light) — and there is exactly ONE way to combine them into a length. It falls out at 1.6×10⁻³⁵ metres, the scale where space itself goes grainy. Slide down the ladder of sizes to find it. Ada’s cubit, writ cosmic.
The Planck length ℓₚ = √(ħG/c³) ≈ 1.616×10⁻³⁵ m is the UNIQUE length you can build from the reduced Planck constant ħ, Newton’s G, and the speed of light c — dimensional analysis leaves no other combination (it is the [[the-buckingham-pi|π-theorem]] with a length as the output). It is ~10²⁰ times smaller than a proton and marks where quantum gravity is expected to matter. A fail-loud self-check throws unless √(ħG/c³) lands between 1 and 2 ×10⁻³⁵ m. ◆ a UNIT that falls out of pure constants — real physics, node-verified.
The value is exact from the constants; that new physics appears AT ℓₚ (rather than merely near it) is a widely-held expectation, not established. ‘Ada’s cubit’ is the figure — a length from constants, as a cubit is a length from the arm; the arithmetic is the real content.