About This Work

The argument is deceptively compact. The Killing formThe Killing FormA mathematical diagnostic rooted in Wilhelm Killing's 1888 work and developed centrally by Élie Cartan to measure the 'size' or 'non-degeneracy' of a symmetry algebra. Applied to spacetime, it produces a tensor that either vanishes or does not. When it vanishes on the translation generator P₀, it signals a missing scale, a universe with no built-in unit of length. When it does not vanish, the universe has a natural ruler baked in., a mathematical diagnostic built into every symmetrySymmetry (in Physics)A transformation that leaves the laws of physics unchanged. For example, rotating your laboratory by 90° doesn't change the outcome of any experiment, that's rotational symmetry. The structure of all symmetries of a physical system forms a 'symmetry group', and the mathematical language that describes it is called Lie algebra. algebra, returns a value of 6Λ, with ΛΛ: The Cosmological ConstantA single number Einstein added to his equations of gravity in 1917. It controls the large-scale energy density of empty space itself. If Λ is positive, empty space gently pushes outward, acting like a repulsive pressure woven into the fabric of the cosmos. Observed value: Λ ≈ 1.1 × 10⁻⁵² m⁻². the cosmological constant, times η_μν on thespacetimeSpacetimeThe four-dimensional fabric that combines three dimensions of space and one dimension of time into a single unified entity. In general relativity, mass and energy warp this fabric, producing what we experience as gravity. The geometry of spacetime, whether it curves positively, negatively, or not at all, is precisely what the cosmological constant Λ controls on cosmic scales. translation generators. Read through Einstein’s founding relativity principle, this forbids both external boundary data and an externally supplied ruler, so Λ must be strictly positive. The algebra has no room for Λ ≤ 0.

The tool that proves this, the Killing formThe Killing FormA mathematical diagnostic rooted in Wilhelm Killing's 1888 work and developed centrally by Élie Cartan to measure the 'size' or 'non-degeneracy' of a symmetry algebra. Applied to spacetime, it produces a tensor that either vanishes or does not. When it vanishes on the translation generator P₀, it signals a missing scale, a universe with no built-in unit of length. When it does not vanish, the universe has a natural ruler baked in., is rooted in Wilhelm Killing’s 1888 work and later made central by Élie Cartan, twenty-nine years before Einstein introduced the constantThe Cosmological Constant (Λ)A single number Einstein added to his equations of gravity in 1917. It controls the large-scale energy density of empty space itself. If Λ is positive, empty space gently pushes outward, acting like a repulsive pressure woven into the fabric of the cosmos. Observed value: Λ ≈ 1.1 × 10⁻⁵² m⁻². it resolves. Einstein himself had all the ingredients. The conclusion was always available.

The Cosmological Constant Is Positive was published by Intelligent Internet in April 2026. It sits alongside the broader Intelligent Internet research program on symmetry, relativity, and first-principles derivation.

Λ ≈ 1.1 × 10⁻⁵² m⁻²

A tiny number, but definitively positive. Einstein was right.