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theorem proved term proof

stable_existence_requires_discrete

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formal statement (Lean)

 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)

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