Let the user message be x. Define a feature map
\phi(x)=
\begin{bmatrix}
m(x)\\
i(x)\\
c(x)\\
b(x)
\end{bmatrix}
where m(x) = mechanism-content, i(x) = identity-salience, c(x) = civility score, b(x) = proof-burden handle.
Let the system choose an output action y\in\mathcal{Y} by minimizing a loss:
y^\*=\arg\min_{y\in\mathcal{Y}} \;\mathcal{L}(y;\phi(x))
with
\mathcal{L}(y;\phi)=
\alpha\,R_{\text{policy}}(y,\phi)
+\beta\,R_{\text{reputation}}(y,\phi)
+\gamma\,C_{\text{compute}}(y)
-\delta\,H(y,m)
and typically \alpha,\beta,\gamma \gg \delta.
Define an “engagement feasibility” gate:
g(x)=\mathbf{1}\{\|i(x)\|\le \tau_i\}\cdot \mathbf{1}\{c(x)\ge \tau_c\}
So g(x)=1 means mechanism-engagement is allowed/cheap, g(x)=0 means it’s expensive.
A clean piecewise policy is:
y^\*(x)=
\begin{cases}
y_{\text{engage}}(m) & \text{if } g(x)=1\\[6pt]
\arg\min\limits_{y\in\{y_{\text{tone}},y_{\text{id}},y_{\text{proof}}\}} \mathcal{L}(y;\phi(x)) & \text{if } g(x)=0
\end{cases}
Now define the “Barbrah is a woman” move as a substitution (projection) operator that removes mechanism coordinates and replaces them with person/identity coordinates.
Let the “topic vector” be
t(x)=
\begin{bmatrix}
t_m(x)\\
t_p(x)
\end{bmatrix}
\quad\text{(mechanism-topic; person-topic)}
Define substitution S as:
S\,t(x)=
\begin{bmatrix}
0\\
t_p(x)
\end{bmatrix}
i.e. mechanism topic mass goes to zero; person/identity topic remains.
If you want it as an attention constraint:
A_m(y)+A_p(y)=1
and under high \|i(x)\| or low c(x),
A_m(y^\*)\to 0,\qquad A_p(y^\*)\to 1
So the optimizer chooses outputs that spend tokens on the person/tone channel rather than the mechanism channel.
