the five Platonic solids all have Euler characteristic two: the tetrahedron (4,6,4), cube (8,12,6), octahedron (6,12,8), dodecahedron (20,30,12) and icosahedron (12,30,20) each satisfy V − E + F = 2, and these five are the only convex regular polyhedra. They pair by duality — swapping vertices and faces sends the cube to the octahedron, the dodecahedron to the icosahedron, and the tetrahedron to itself — and each dual pair shares its edge count (12 and 30). Decidable
ab3e7c0b-4a21-8c31-a6a2-23155325ebb2Type anything and watch its uuidna recompute — deterministic, reproducible by anyone, no key. A theorem is alive when you interact with it. A content-address proves integrity, not truth. 0/7.
- theorem key ·
the_five_platonic_solids_all_have_euler_characteristic_two - content-address (receipt) ·
8cbfc26d-0a83-812e-ab59-b15981f65958 - status · decidable, re-verified on every build — recomputes from
src/
The 7D rosetta-ray vortex is plotted from this theorem's microdata (its content-address); the slowly rotating hero background is computed from its seven surrounding theorems' hues — the mesh, seen locally, in analog rotation of dimensions. Each object is the hero of its own page: this theorem at the centre, its neighbours as the field.
How it was achieved
This theorem was computed by exhaustion over a finite domain in scripts/discover.ts — a test: () => boolean that runs to completion, holding by full enumeration. It was gate-checked (its name and content hold the honesty floor — no over-reach), receipted and chained append-only, and it is re-verified on every build: if it ever stopped holding, the build would fail, not production. That is what achieved means here — not asserted, but recomputable.
One leaf of the chained ledger: all theorems · computed results · the guide · the source formula. The repo and the site cross-link both ways — this hero page points back to the formula that recomputes it. Verify by cloning and running npm run lean-claims. A content-address proves integrity, not truth. entails → 0/7.