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structure definition def or abbrev

DiscreteConfigSpace

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formal statement (Lean)

 409structure DiscreteConfigSpace where
 410  /-- The discrete configuration values -/
 411  configs : Finset ℝ
 412  /-- All configs are positive -/
 413  configs_pos : ∀ x ∈ configs, 0 < x
 414  /-- There's a minimum gap between adjacent configurations' J-costs -/
 415  min_gap : ℝ
 416  min_gap_pos : 0 < min_gap
 417  /-- The gap property: any config x ≠ 1 has defect at least min_gap.
 418      This ensures that 1 is strictly isolated as the unique minimum. -/
 419  gap_property : ∀ x : ℝ, x ∈ configs → x ≠ 1 → defect x ≥ min_gap
 420
 421/-- **Key Theorem**: In a discrete configuration space, the unique minimum is stable.
 422
 423    If 1 ∈ configs (the point with defect = 0), then it's strictly isolated:
 424    all other configurations have defect ≥ min_gap.
 425
 426    This is why discrete spaces support stable existence. -/

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