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Constants /
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formal statement (Lean)
192 def octavePhase (t : ℕ) : Fin 8 := ⟨t % 8, Nat.mod_lt t (by norm_num)⟩
proof body
Definition body.
193
194 /-! ## Gap-45 Synchronization
195
196 The gap-45 rung (φ⁴⁵) provides critical phase synchronization:
197 - lcm(8, 45) = 360 synchronizes the octave and gap cycles
198 - This forces D = 3 as the unique dimension with this property
199 -/
200
201 /-- The gap-45 rung: φ⁴⁵. -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (20)
Lean names referenced from this declaration's body.
octave
in IndisputableMonolith.Aesthetics.MusicalScale
decl_use
rung
in IndisputableMonolith.Compat.Constants
decl_use
octave
in IndisputableMonolith.Constants
decl_use
octavePhase
in IndisputableMonolith.Cost.Ndim.Octave
decl_use
rung
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
phase
in IndisputableMonolith.Foundation.EightTick
decl_use
forces
in IndisputableMonolith.Foundation.MagnitudeOfMismatch
decl_use
as
in IndisputableMonolith.Foundation.SimplicialLedger.ContinuumBridge
decl_use
octave
in IndisputableMonolith.Foundation.UniversalForcing.Strict.Music
decl_use
gap
in IndisputableMonolith.Gap45.Derivation
decl_use
gap
in IndisputableMonolith.Masses.AnchorPolicy
decl_use
rung
in IndisputableMonolith.Masses.AnchorPolicy
decl_use
octave
in IndisputableMonolith.Masses.CoherenceExponent
decl_use
gap
in IndisputableMonolith.Masses.RSBridge.Anchor
decl_use
rung
in IndisputableMonolith.Masses.RSBridge.Anchor
decl_use
octave
in IndisputableMonolith.MusicTheory.HarmonicModes
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
phase
in IndisputableMonolith.NumberTheory.RiemannHypothesis.Wedge
decl_use
gap
in IndisputableMonolith.RSBridge.Anchor
decl_use
rung
in IndisputableMonolith.RSBridge.Anchor
decl_use