recognition /
Foundation /
Foundation.SpectralEmergence /
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formal statement (Lean)
301 theorem rung_ratio (ys : ℝ) (hys : 0 < ys) (n : ℤ) :
302 mass_rung ys (n + 1) / mass_rung ys n = phi := by
proof body
Term-mode proof.
303 rw [mass_rung_step]
304 have hmr : mass_rung ys n ≠ 0 := ne_of_gt (mass_rung_pos ys hys n)
305 rw [mul_div_cancel_right₀ phi hmr]
306
307 /-- **THEOREM**: The φ-ladder is self-similar: the ratio between
308 ANY two rungs separated by k steps is φ^k. -/
depends on (9)
Lean names referenced from this declaration's body.
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
mass_rung
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
mass_rung_pos
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
mass_rung_step
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
two
in IndisputableMonolith.QFT.SpinStatistics
decl_use
self
in IndisputableMonolith.RecogSpec.Core
decl_use