IndisputableMonolith.Foundation.HierarchyDissolution
This module establishes that fermion mass ratios in Recognition Science arise as integer powers of the golden ratio φ rather than free parameters. It supplies the structural basis for dissolving the hierarchy problem by linking the φ-ladder to mass generation. Researchers addressing the hierarchy problem or electroweak scale would cite it. The module assembles upstream results from φ-forcing and mass hierarchy into a sequence of geometric statements.
claimFermion mass ratios satisfy $m_i/m_j = \phi^k$ for integer $k$, where $\\$phi is the self-similar fixed point; this supplies the structural basis for hierarchy dissolution.
background
Recognition Science derives all physics from a single functional equation with J-cost $J(x) = (x + x^{-1})/2 - 1$. The PhiForcing module shows that φ is forced as the unique self-similar fixed point in a discrete ledger obeying the Recognition Composition Law. The MassHierarchy module (P-002) formalizes fermion masses on the φ-ladder as yardstick times φ to a rung offset, with Constants supplying the base time quantum τ₀ = 1 tick.
proof idea
This module imports Constants, PhiForcing, and MassHierarchy, then organizes their results into theorems that convert the φ-ladder into geometric mass ratios. It contains no standalone proofs but sequences the dissolution argument through its sibling declarations.
why it matters in Recognition Science
The module feeds directly into ElectroweakScaleStructure (E-004), which asks what determines the electroweak scale. Its doc-comment identifies the geometric ratios as the structural basis for hierarchy dissolution, closing the link from the φ-ladder to scale selection in the Recognition framework.
scope and limits
- Does not derive numerical values for specific fermion masses.
- Does not address gauge boson or Higgs masses.
- Does not extend the geometric rule beyond fermions.
- Does not replace the full Standard Model Lagrangian.