res_bottom
plain-language theorem explainer
The bottom quark residue on the phi-ladder is fixed at the rational value -2. Researchers deriving quark masses from the Recognition framework cite this constant to anchor the third-generation structural mass calculation. It is supplied by direct assignment matching the ideal topological position in the quarter-ladder hypothesis.
Claim. The bottom quark residue satisfies $R_b = -2$.
background
In the Recognition Science framework, masses follow the formula yardstick times phi to the power of (rung minus 8 plus gap), with the phi-ladder providing discrete topological positions. The Quarter-Ladder Hypothesis places quarks at quarter-integer rungs sharing the lepton structural base but offset from integer positions; the module states the bottom at R equals -2.00 equals -8/4. Upstream results in the parent module define residues via successive subtraction of generation steps from res_top, with residues_match_steps confirming the bottom equals -2.
proof idea
One-line definition that directly assigns the rational constant -8/4 to res_bottom.
why it matters
This definition supplies the residue input to bottom_mass_match, which verifies the predicted mass near 4147 MeV lies within 1 percent of the observed 4180 MeV. It implements the bottom position in the T12 Quarter-Ladder Hypothesis, enabling the residue chain for charm and lighter quarks. The placement connects to the eight-tick octave and phi-ladder scaling used throughout the mass derivations.
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