pith. machine review for the scientific record. sign in
def definition def or abbrev

symmetryGroupPreferenceCert

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

 311def symmetryGroupPreferenceCert : SymmetryGroupPreferenceCert where
 312  orbit_pos := orbitCount_pos

proof body

Definition body.

 313  orbit_p6m_eq_max := orbitCount_p6m
 314  ratio_le_one := symmetryRatio_le_one
 315  J_nonneg := wallpaperJ_nonneg
 316  J_p6m_zero := wallpaperJ_p6m_eq_zero
 317  J_p1_pos := wallpaperJ_p1_pos
 318  J_mono := wallpaperJ_mono_in_orbits
 319  preference_p6m_max := preference_p6m_max
 320
 321/-! ## §6. One-statement summary -/
 322
 323/-- **SYMMETRY GROUP PREFERENCE ONE-STATEMENT.** Three structural
 324facts assembled into one theorem:
 325
 326(1) `p6m` (orbit count 12) sits at J-cost zero.
 327(2) `p1` (orbit count 1) sits at J-cost strictly positive.
 328(3) For any pair, the group with more orbits has lower J-cost.
 329
 330This forces the universal preference ordering:
 331maximum-symmetry groups are universally preferred to lower-symmetry
 332groups under the J-cost-derived preference functional. -/

depends on (18)

Lean names referenced from this declaration's body.