495theorem stable_existence_requires_discrete : 496 (∃ x config_space, RSExists_stable x config_space) → 497 ∃ config_space : Set ℝ, ∃ x, RSExists_stable x config_space := by
proof body
Term-mode proof.
498 intro ⟨x, config_space, hstable⟩ 499 exact ⟨config_space, x, hstable⟩ 500 501/-! ## Summary -/ 502 503/-- **THE DISCRETENESS FORCING PRINCIPLE** 504 505 The cost functional J(x) = ½(x + x⁻¹) - 1 forces discrete ontology: 506 507 1. J has a unique minimum at x = 1 with J(1) = 0 508 2. J''(1) = 1 sets the minimum "step cost" for discrete configurations 509 3. In continuous spaces, configurations drift (infinitesimal cost for infinitesimal perturbation) 510 4. In discrete spaces, configurations are trapped (finite cost for any step) 511 512 Therefore: **Stable existence (RSExists) requires discrete configuration space** 513 514 This is Level 2 of the forcing chain: 515 Composition law → J unique → Discreteness forced → Ledger → φ → D=3 → physics 516-/
depends on (19)
Lean names referenced from this declaration's body.