• 1 Program overview ▶
    • 1.1 The spine
    • 1.2 The three risk kernels
    • 1.3 Global modelling decisions
  • 2 The support layer ▶
    • 2.1 PMF calculus
    • 2.2 The geometric family and local bounds
    • 2.3 Fourier analysis on \(\mathbb {Z}/3^n\mathbb {Z}\)
  • 3 The Collatz–Syracuse dictionary and logarithmic density
  • 4 The Syracuse random variable and its valuation
  • 5 First passage, stabilization, and the main theorem ▶
    • 5.1 The main theorem
    • 5.2 First passage (§5)
  • 6 Fine-scale mixing (§6)
  • 7 The crux: character decay via renewal versus triangles (§7) ▶
    • 7.1 Setup and the phase functions
    • 7.2 The triangle structure of the black set
    • 7.3 The holding process and its finitized renewal recursion (D6)
    • 7.4 The three cases of Prop 7.8
    • 7.5 Assembly: Prop 1.17
  • Dependency graph

Tao 2019 Collatz Blueprint

TaoCollatz

  • 1 Program overview
    • 1.1 The spine
    • 1.2 The three risk kernels
    • 1.3 Global modelling decisions
  • 2 The support layer
    • 2.1 PMF calculus
    • 2.2 The geometric family and local bounds
    • 2.3 Fourier analysis on \(\mathbb {Z}/3^n\mathbb {Z}\)
  • 3 The Collatz–Syracuse dictionary and logarithmic density
  • 4 The Syracuse random variable and its valuation
  • 5 First passage, stabilization, and the main theorem
    • 5.1 The main theorem
    • 5.2 First passage (§5)
  • 6 Fine-scale mixing (§6)
  • 7 The crux: character decay via renewal versus triangles (§7)
    • 7.1 Setup and the phase functions
    • 7.2 The triangle structure of the black set
    • 7.3 The holding process and its finitized renewal recursion (D6)
    • 7.4 The three cases of Prop 7.8
    • 7.5 Assembly: Prop 1.17