quarter_step
plain-language theorem explainer
quarter_step supplies the multiplicative step phi to the power one-fourth for positioning quarks on the quarter-ladder. Phenomenological fits in the hypothesis layer for heavy quark masses would cite this constant to achieve sub-two-percent agreement with observed values. The declaration is a direct noncomputable real-number definition with no reduction steps.
Claim. The quarter-ladder step size is defined as $phi^{1/4}$ where $phi$ is the golden-ratio fixed point satisfying the Recognition Composition Law.
background
The Recognition Science mass formula places particles on the phi-ladder via yardstick times phi to the power of (rung minus eight plus gap(Z)). The core model restricts rungs to integers for parameter-free derivations from geometry, as seen in the rung definitions for leptons, up quarks, and down quarks. The quarter-ladder convention, documented in this module, relaxes that restriction to quarter-integer residues for quarks only, embedding each integer k as k/4 on the real line per the quarter embedding in Support.RungFractions.
proof idea
One-line definition that directly evaluates the real power phi raised to one-fourth.
why it matters
This definition populates the exploratory quarter-ladder layer that the module separates from the canonical integer-rung core. It supplies the base increment used by downstream quark-mass calculations in Physics.QuarkMasses and Hierarchy to reach the listed fractional residues (5.75 for top, -2 for bottom, etc.). The module explicitly assigns this construction to the hypothesis layer rather than the parameter-free core, preserving the integer-rung derivations for the main Recognition chain.
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