|
PLR as Involutions on 24 Triads
|
EP01
|
|
|
D₁₂ Acts Simply Transitively
|
EP01
|
|
|
Tonnetz Torus Identification
|
EP01
|
|
|
Tymoczko Orbifold Quotient
|
EP01
|
|
|
Wave Equation Derivation
|
EP02
|
|
|
D'Alembert General Solution
|
EP02
|
|
|
Normal Modes and Harmonic Series
|
EP02
|
|
|
Fourier Series Completeness
|
EP02
|
|
|
Energy Conservation by Orthogonality
|
EP02
|
|
|
Cut Vertex via DFS Back-Edges (Tarjan)
|
EP03
|
|
|
Whitney's Theorem (k-connectivity)
|
EP03
|
|
|
Menger's Theorem
|
EP03
|
|
|
Simple Transitivity of Polyphony Graph
|
EP03
|
|
|
Klein V₄ as Row Symmetry Group
|
EP04
|
|
|
Orbit-Stabilizer Theorem
|
EP04
|
|
|
Burnside's Lemma (Chord Counting)
|
EP04
|
|
|
All-Interval Row Constraint (sum mod 12)
|
EP04
|
|
|
Turán's Theorem
|
EP05
|
|
|
Mantel's Theorem (r=2 case)
|
EP05
|
|
|
Orbit-Stabilizer Theorem
|
EP05
|
|
|
Perfect Graph Theorem (Lovász 1972)
|
EP06
|
|
|
Interval Graphs are Perfect
|
EP06
|
|
|
Greedy Coloring on Interval Graphs
|
EP06
|
|
|
Brooks' Theorem
|
EP06
|
|
|
Shannon Entropy Maximum (Jensen's Inequality)
|
EP07
|
|
|
Source Coding Theorem
|
EP07
|
|
|
Entropy Rate of Markov Chains
|
EP07
|
|
|
Pitch Helix Projection (Shepard 1964/1982)
|
EP08
|
|
|
Tritone Paradox (Deutsch 1986)
|
EP08
|
|
|
Quotient Topology of Chroma Circle
|
EP08
|
|
|
Nonlinear Frequency Generation
|
EP09
|
|
|
Combination Tone Formula mf₁ ± nf₂
|
EP09
|
|
|
Cubic Difference Tone Dominance
|
EP09
|
|
|
Distance Preservation Under Reflection
|
EP10
|
|
|
D₁₂ as Symmetry Group of the Chromatic Scale
|
EP10
|
|
|
Negative Harmony Reflection Formula
|
EP10
|
|
|
Irrationality of log₂3 and log₂5
|
EP11
|
|
|
Syntonic Comma as an Obstruction
|
EP11
|
|
|
Continued Fraction Approximation of log₂(3/2)
|
EP11
|
|
|
7 Generates ℤ₁₂ (gcd Condition)
|
EP12
|
|
|
Subgroup Lattice of ℤ₁₂
|
EP12
|
|
|
Circle of Fifths as Quotient of the Spiral
|
EP12
|
|
|
LCM Periodicity of Polyrhythm
|
EP13
|
|
|
Rhythm-Pitch Duality (~20 Hz threshold)
|
EP13
|
|
|
Helmholtz Consonance = 1/LCM
|
EP13
|
|
|
Discrete Hodge Theorem (ker L_k ≅ H^k)
|
EP14
|
|
|
Hodge Decomposition (exact ⊕ coexact ⊕ harmonic)
|
EP14
|
|
|
Poincaré Duality (cell count bijection)
|
EP14
|
|
|
Boundary-squared = 0
|
EP14
|
|
|
Orchestra Spectral Attenuation (−9 dB/octave)
|
EP15
|
|
|
Singer's Formant Clustering (Sundberg 1974)
|
EP15
|
|
|
Fletcher-Munson Perceptual Weighting
|
EP15
|
|
|
Sabine Reverberation Formula
|
EP15
|
|
|
Total Penetration Index (49 dB)
|
EP15
|
|