theorem proved tactic proof

`alpha_over_pi_small`

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

formal statement (Lean)

 134theorem alpha_over_pi_small : alpha / Real.pi < (11/16 : ℝ) := by

proof body

Tactic-mode proof.

 135  -- From omega_lambda_positive: 11/16 - (alpha/pi) > 0
 136  have h1 : 11/16 - (alpha / Real.pi) > 0 := omega_lambda_positive
 137  linarith
 138
 139/-! ## C-010: The Smallness Problem Resolution -/
 140
 141/-- **THEOREM C-010.7**: The "natural" value of Λ is NOT M_Planck^4.
 142
 143    In RS, the vacuum energy is set by the ledger structure, not
 144    by the Planck scale. The geometric seed 11/16 is the natural scale. -/

depends on (17)

Lean names referenced from this declaration's body.

of in IndisputableMonolith.Astrophysics.NucleosynthesisTiers decl_use
alpha in IndisputableMonolith.Constants.Alpha decl_use
scale in IndisputableMonolith.Cosmology.LargeScaleStructureFromRS decl_use
of in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization decl_use
is in IndisputableMonolith.Foundation.OptionAEmpiricalProgram decl_use
of in IndisputableMonolith.Foundation.PhiForcingDerived decl_use
is in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi decl_use
of in IndisputableMonolith.Foundation.SpectralEmergence decl_use
is in IndisputableMonolith.GameTheory.MechanismDesignFromSigma decl_use
of in IndisputableMonolith.Information.PhysicsComplexityStructure decl_use
Resolution in IndisputableMonolith.Mathematics.BirchTateStructure decl_use
is in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom decl_use
Resolution in IndisputableMonolith.Physics.QuarkCoordinateReconciliation decl_use
value in IndisputableMonolith.QFT.SpinStatistics decl_use
Resolution in IndisputableMonolith.Quantum.Firewall decl_use
omega_lambda_positive in IndisputableMonolith.Unification.RegistryPredictionsProved decl_use
vacuum in IndisputableMonolith.Unification.YangMillsMassGap decl_use