theorem
proved
term proof
optimal_at_minimum_is_holographic
show as:
view Lean formalization →
formal statement (Lean)
138theorem optimal_at_minimum_is_holographic {V : Type*}
139 {adj : V → V → Prop}
140 (hconn : ∀ u v : V, Relation.ReflTransGen adj u v)
141 {field : V → ℝ} (hpos : ∀ v, 0 < field v)
142 (at_min : ∀ v w, adj v w → Jcost (field v / field w) = 0) :
143 ∀ v w : V, field v = field w :=
proof body
Term-mode proof.
144 GraphRigidity.ratio_rigidity hconn hpos at_min
145
146/-! ## Part 7: Master Certificate -/
147
148/-- **LOCAL CACHE FORCING CERTIFICATE**:
149 1. J(φ^d) strictly increasing (cost grows with distance)
150 2. J(φ^0) = 0 (collocated access is free)
151 3. d > 0 ⟹ J(φ^0) < J(φ^d) (collocation beats remote)
152 4. r² = r + 1, r > 0 ⟹ r = φ (Fibonacci forces φ) -/