168theorem eleven_is_passive_edges : (11 : ℕ) = cube_edges D - active_edges_per_tick := by
proof body
Term-mode proof.
169 native_decide 170 171/-! ## Part 6: Physical Interpretation 172 173**Why Solid Angle?** 174 175The 11 passive edges of the cube Q₃ each contribute to the electromagnetic 176coupling from all directions. The question is: how do we count "all directions"? 177 178**Answer**: In D=3, "all directions" means the unit 2-sphere S². 179The measure of S² is exactly 4π steradians. 180 181Each passive edge "sees" the recognition event from all 4π steradians of directions. 182The total geometric seed is therefore: 183 (passive edges) × (solid angle) / (normalization) 184= 11 × 4π × (normalized coupling per edge) 185= 4π × 11 186 187The 4π factor is not arbitrary — it is the unique rotationally invariant 188measure on directions in 3D space. 189-/ 190 191/-! ## Summary 192 193The factor 4π in the geometric seed 4π·11 is **uniquely forced** by: 194 1951. **Dimension D=3** is forced by the linking requirement (T9) 1962. **Isotropy** is required because recognition has no preferred direction 1973. **Unit normalization** means we use the unit sphere 1984. **4π = S²** is the unique surface area of the unit 2-sphere 199 200No other factor (2π, 8π, π, etc.) satisfies all three requirements. 201-/ 202 203end SolidAngleExclusivity 204end Constants 205end IndisputableMonolith
depends on (25)
Lean names referenced from this declaration's body.