Pith. sign in

Why is space three-dimensional?

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. Your answer will appear below.
confidence: high in recognition cached
  1. Linking requires D = 3 (Alexander duality)

The theorem linking_requires_D3 proves that non-trivial circle linking exists only for D = 3, via the equivalence SphereAdmitsCircleLinking D ↔ D = 3 established by alexander_duality_circle_linking from reduced cohomology of S¹.

  1. 8-tick = 2^D forces D = 3

The theorem eight_tick_forces_D3 derives D = 3 from the identity eight_tick = 2^D together with the auxiliary result eight_tick = 2^3.

  1. Cl_3 spinor structure

D = 3 yields Cl_3 ≅ M₂(ℂ) with 2-component spinors (Spin(3) ≅ SU(2)), as shown by spinor_dim_D3 = 2 and the HasRSSpinorStructure predicate specialized to D = 3.

  1. Cited Lean anchors

The derivation rests on the theorems listed in the cited_theorems array below.

cited recognition theorems

outside recognition

Aspects Recognition does not yet address:

  • dimension_forced theorem definition (mentioned only in docstring)

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.