recognition /
Modal /
Modal.ModalGeometry /
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formal statement (Lean)
131 def modal_period : ℕ := 8
proof body
Definition body.
132
133 /-- **MODAL NYQUIST LIMIT**: The finest modal resolution is one tick.
134
135 Possibilities that differ by less than one tick are "modally equivalent."
136 This is analogous to the Nyquist sampling theorem:
137 - Maximum modal frequency = 1/(2τ₀)
138 - Modal bandwidth = 4 ticks per octave -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (17)
Lean names referenced from this declaration's body.
octave
in IndisputableMonolith.Aesthetics.MusicalScale
decl_use
octave
in IndisputableMonolith.Constants
decl_use
tick
in IndisputableMonolith.Constants
decl_use
tick
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
one
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
one
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
octave
in IndisputableMonolith.Foundation.UniversalForcing.Strict.Music
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
octave
in IndisputableMonolith.Masses.CoherenceExponent
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
octave
in IndisputableMonolith.MusicTheory.HarmonicModes
decl_use
that
in IndisputableMonolith.NumberTheory.PhiLadderLattice
decl_use
one
in IndisputableMonolith.QFT.SpinStatistics
decl_use
one
in IndisputableMonolith.RecogSpec.Core
decl_use
bandwidth
in IndisputableMonolith.Unification.RecognitionBandwidth
decl_use