cascadeMass
plain-language theorem explainer
cascadeMass encodes the Recognition Science mass formula for fermion generations as m_n = m_0 * phi^(-α n). Theorists working on the Standard Model hierarchy puzzle would reference this when explaining exponential mass suppression via the golden ratio. It is implemented as a direct one-line algebraic definition.
Claim. $m_n = m_0 φ^{-α n}$ where $m_0$ is the base mass for the lightest generation, $α$ is the cascade exponent, and $n$ indexes the generation.
background
The Physics.MassHierarchy module derives the Standard Model fermion mass hierarchy from Recognition Science's φ-structure. The module document states that each generation differs by factors involving powers of φ ≈ 1.618, producing ratios up to 10^5 between the top quark and electron. The definition supplies the explicit formula m_n = m_0 × φ^(-α n) for n = 1,2,3 corresponding to the three generations.
proof idea
The definition is a direct algebraic expression that multiplies the base mass m0 by phi raised to the power of minus alpha times n.
why it matters
This definition underpins the cascade_decreases theorem, which establishes that masses strictly decrease with generation index. It fills the SM-006 target of deriving the fermion mass hierarchy from first principles, as outlined in the module's reference to a PRL paper on the topic. It connects to the framework's T6 phi fixed point and T7 eight-tick octave that sets three generations.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.