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theorem proved term proof

omega_lambda_lt_one

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formal statement (Lean)

  58theorem omega_lambda_lt_one : omega_lambda < 1 := by

proof body

Term-mode proof.

  59  unfold omega_lambda
  60  have h_alpha := alphaLock_pos
  61  have h_pi := Real.pi_pos
  62  linarith [show (0 : ℝ) < alphaLock / Real.pi from div_pos h_alpha h_pi]
  63
  64/-! ## Cosmological Constant Problem Resolution -/
  65
  66/-- **D-003 Resolution**: The cosmological constant is NOT the vacuum energy
  67    of QFT. It is the fraction of vacuum modes in the ledger.
  68
  69    The "10^120 discrepancy" dissolves because:
  70    1. QFT vacuum energy is a misidentification (not a physical observable)
  71    2. The actual Ω_Λ comes from ledger mode counting: 11/16 − α/π
  72    3. This is a NUMBER, not an energy density requiring renormalization
  73
  74    There is no fine-tuning because there is no parameter to tune. -/

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