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theorem proved term proof

totalWeight_pos

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formal statement (Lean)

  91theorem totalWeight_pos : 0 < totalWeight := by

proof body

Term-mode proof.

  92  unfold totalWeight
  93  obtain ⟨h0, h1, h2, h3, h4⟩ := tier_weights_pos
  94  linarith
  95
  96/-- Total weight summed over tiers equals `1 + 1/φ + 1/φ² + 1/φ³ + 1/φ⁴`,
  97which by the φ²=φ+1 identity simplifies to `(φ⁵ + φ⁴ + φ³ + φ² + φ)/φ⁵`,
  98and since `φ⁵ = 5φ + 3` and `φ + 1 + φ⁻¹ + φ⁻² = (φ⁴+φ³+φ²+φ)/φ³`,
  99the closed-form value is `(2φ⁵ - 1)/φ⁴`. We just need `> 0` for the
 100master cert; the empirical Dunbar number is read off directly. -/

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