m_bottom
plain-language theorem explainer
Bottom-quark mass at the RS anchor μ*, obtained by the single forward mass law on the down sector with the bottom rung and charge Z = −1/3. Ratio theorems (bottom/strange = φ^6) and the six-quark residue-coordinate theorem cite it. The body is a one-line specialization of the shared predict_mass pipeline; no PDG input enters.
Claim. The bottom-quark mass at the anchor scale $\mu^*$ is the forward prediction $m_b(\mu^*)=A_{\mathrm{down}}\,\varphi^{r_b-8+\mathrm{gap}(Z_b)}$ in the down-quark sector, with integer rung $r_b$ from generation torsion and charge-band coordinate $Z_b=-1/3$.
background
The QuarkForwardPipeline module builds one Convention-A pipeline for all six quarks: sector yardstick $A_s$ from cube counting (V,E,F,…), integer rung from generation torsion, and band correction $\mathrm{gap}(Z)=\log_\varphi(1+Z/\varphi)$. Predicted mass is $m_i(\mu^*)=A_s,\varphi^{r_i-8+\mathrm{gap}(Z_i)}$. No measured quark mass is an input; only counting-layer integers, $\varphi$ (T5/T6), and $\alpha$ appear.
Outputs are dimensionless ratios to the electron at the same anchor, so the calibration seam drops out. Bottom sits in the down sector (charge $-1/3$) with its generation rung $r_{\mathrm{down}}(\mathrm{b})$. The same predict_mass wrapper defines $m_u,m_c,m_t,m_d,m_s$ as siblings.
Upstream mass-law and Z-map modules supply the yardstick, rung table, and charge-band map; the present binding only chooses the bottom labels.
proof idea
Definition, not a proof. It instantiates the shared forward predictor on three fixed arguments: down-quark sector, the integer rung labeled bottom, and the down-sector charge $Z=-1/3$. No algebraic reduction or tactic work occurs at this site; positivity and ratio identities are proved downstream from the general predictor lemmas.
why it matters
Closes the bottom slot in the six-quark forward table. Downstream, bottom_to_strange_eq_phi6 reads off $m_b/m_s=\varphi^6$ from the rung gap $21-15=6$ after unfolding this binding and the strange sibling. m_bottom_pos inherits strict positivity from the general predictor. The unified residue theorem packages all six masses (including bottom) as residue coordinates relative to the electron, showing the quarter/residue convention is derived from the same pipeline rather than fitted.
In the RS mass formula (yardstick $\times,\varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$) this is the concrete bottom instance on the $\varphi$-ladder. It supports the module claim of genuine forward prediction with no PDG targeting.
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