Q_tilde_down

In the Z-map topological derivation, a recognition boundary of charge $Q$ couples to the $F = 2D$ faces of the 3-cube. Ledger entries must be integers (T8: $\delta$-units $\simeq \mathbb{Z}$), so charges are integerized by the face count. At $D = 3$ one has $F = 6$, the minimal positive even integer that sends every SM charge ${-1, 2/3, -1/3}$ into $\mathbb{Z}$.

The resulting integerized charges are written $\tilde{Q} = F Q$. For the down quark, $Q = -1/3$, hence $\tilde{Q}{\mathrm{down}} = 6 \times (-1/3) = -2$. The same scale produces $\tilde{Q}{\mathrm{lepton}} = -6$ and $\tilde{Q}_{\mathrm{up}} = 4$. These three integers are the only inputs to the even polynomial $Z(\tilde{Q}) = a\tilde{Q}^2 + b\tilde{Q}^4$ of Stage 2.

Pure definition: the constant is the integer literal $-2$, annotated as $6 \times (-1/3)$. No lemma is applied and no tactic runs.

Every concrete Z-evaluation in this module substitutes this constant. Downstream theorems bare_Z_values, full_Z_values, canonical_separates, and canonical_ordered reduce $Z_{\mathrm{down}}$ by unfolding $\tilde{Q}_{\mathrm{down}} = -2$, yielding the bare anchor 20 and the color-offset anchor 24. Those anchors in turn force the unique coefficients $(a,b) = (1,1)$ and the color offset $c = 4$ (coefficients_forced_from_quark_bare_anchors, full_anchor_tuple_forces_coefficients_and_offset).

Within the Recognition framework the definition sits at Stage 1 of the topological Z-map: face-count integerization forced by T8 and $D = 3$. It is the down-sector input that makes family separation and the ordered hierarchy hold for the canonical polynomial.