docs(v2.0.0-alpha.6): convert all inline $...$ to :math: role in v2 RST pages

RST does not parse dollar-math (the dollarmath MyST extension applies
only to .md files), so every inline LaTeX expression was rendered as
raw text on Read the Docs — with backslashes silently stripped by the
RST escape mechanism (e.g. \bar s shown as 'bar s', \mathbb{E} shown
as 'mathbb{E}'). The eight v2.0 algorithm pages now use the proper
:math: role for inline math (224 expressions converted), so MathJax
renders every symbol correctly.

Affected pages: bsde, pde, stochastic_control, quadratic_impact_control,
mckean_vlasov, agent_based, robust_drift, generative_calibration_hooks.

docs/source/algorithms/agent_based.rst

@@ -10,53 +10,53 @@ update rule
    \qquad \bar s^k \;=\; \frac1N \sum_{j=1}^N s^k_j,
    \qquad \xi^k_i \sim \mathcal{N}(0, \sigma^2),
 
-with $\alpha \in (0, 1]$ the *averaging weight* and $\sigma$ the noise scale.  This is the
+with :math:`\alpha \in (0, 1]` the *averaging weight* and :math:`\sigma` the noise scale.  This is the
 DeGroot–Friedkin–Johnsen baseline of opinion dynamics, and the *complete-graph* limit of the
 Hegselmann–Krause and Vicsek flocking models.
 
 Mathematical background
 -----------------------
 
-**Mean conservation.**  Averaging the update over $i$ gives
-$\bar s^{k+1} = \bar s^k + \bar\xi^k$ with $\mathbb{E}[\bar\xi^k] = 0$, so the empirical mean
+**Mean conservation.**  Averaging the update over :math:`i` gives
+:math:`\bar s^{k+1} = \bar s^k + \bar\xi^k` with :math:`\mathbb{E}[\bar\xi^k] = 0`, so the empirical mean
 is a *martingale* and is exactly preserved in expectation:
 
 .. math::
 
    \mathbb{E}[\bar s^k] \;=\; \bar s^0 \quad \text{for all } k \ge 0.
 
-In the noiseless case $\sigma = 0$ the mean is preserved *path-by-path*.
+In the noiseless case :math:`\sigma = 0` the mean is preserved *path-by-path*.
 
-**Geometric contraction of the spread.**  Define the deviation $d^k_i := s^k_i - \bar s^k$.
+**Geometric contraction of the spread.**  Define the deviation :math:`d^k_i := s^k_i - \bar s^k`.
 The update implies
 
 .. math::
 
    d^{k+1}_i \;=\; (1 - \alpha)\, d^k_i \;+\; \bigl(\xi^k_i - \bar\xi^k\bigr) ,
 
-so in the absence of noise $\| d^k \|_\infty \le (1 - \alpha)^k \| d^0 \|_\infty$ — the spread
-*contracts geometrically* with rate $1 - \alpha$.  The companion notebook plots
-$\max_i s^k_i - \min_i s^k_i$ on a log scale across $\alpha \in \{0.05, \dots, 1\}$ and
+so in the absence of noise :math:`\| d^k \|_\infty \le (1 - \alpha)^k \| d^0 \|_\infty` — the spread
+*contracts geometrically* with rate :math:`1 - \alpha`.  The companion notebook plots
+:math:`\max_i s^k_i - \min_i s^k_i` on a log scale across :math:`\alpha \in \{0.05, \dots, 1\}` and
 recovers exactly this slope.
 
 **Stationary variance with noise.**  Treating the deviation as an AR(1) process with input
-variance $\sigma^2 (1 - 1/N)$, the steady-state variance of any single agent's deviation is
+variance :math:`\sigma^2 (1 - 1/N)`, the steady-state variance of any single agent's deviation is
 
 .. math::
 
    \mathrm{Var}_\infty(d_i) \;=\; \frac{\sigma^2 (1 - 1/N)}{1 - (1 - \alpha)^2}
      \;\xrightarrow[\alpha \to 0]{}\; \frac{\sigma^2}{2\alpha}\,(1 - 1/N).
 
-**Continuous-time limit (linear Vlasov).**  Sending $\alpha = \theta\, \Delta t$,
-$\xi^k_i = \sigma \sqrt{\Delta t}\, W^i_k$ and $\Delta t \to 0$ recovers the McKean–Vlasov SDE
-$dX^i_t = \theta(\bar X_t - X^i_t)\, dt + \sigma\, dW^i_t$ of :doc:`mckean_vlasov` — the
+**Continuous-time limit (linear Vlasov).**  Sending :math:`\alpha = \theta\, \Delta t`,
+:math:`\xi^k_i = \sigma \sqrt{\Delta t}\, W^i_k` and :math:`\Delta t \to 0` recovers the McKean–Vlasov SDE
+:math:`dX^i_t = \theta(\bar X_t - X^i_t)\, dt + \sigma\, dW^i_t` of :doc:`mckean_vlasov` — the
 discrete consensus update is the prototype of mean-field interaction.
 
 **Spectral interpretation.**  On a general weighted graph the update reads
-$s^{k+1} = (I - \alpha L)\, s^k + \xi^k$, where $L$ is the normalised Laplacian.  The
-complete-graph case shipped here has $L = I - \tfrac1N \mathbf{1}\mathbf{1}^\top$ with
-eigenvalue $1$ on the orthogonal complement of $\mathbf{1}$, hence the contraction rate
-$1 - \alpha$ above.  Replacing $\mathbf{1}\mathbf{1}^\top / N$ by an arbitrary stochastic
+:math:`s^{k+1} = (I - \alpha L)\, s^k + \xi^k`, where :math:`L` is the normalised Laplacian.  The
+complete-graph case shipped here has :math:`L = I - \tfrac1N \mathbf{1}\mathbf{1}^\top` with
+eigenvalue :math:`1` on the orthogonal complement of :math:`\mathbf{1}`, hence the contraction rate
+:math:`1 - \alpha` above.  Replacing :math:`\mathbf{1}\mathbf{1}^\top / N` by an arbitrary stochastic
 matrix produces the full DeGroot model and is a one-liner extension on the Rust side.
 
 Why it matters
@@ -66,7 +66,7 @@ Why it matters
   (Bayesian persuasion, social media echo chambers, voting-system stability).
 * **Distributed estimation & federated learning.**  Average-consensus protocols for sensor
   networks, gossip algorithms, federated averaging — all reduce to the same contraction
-  argument with explicit convergence rate $1 - \alpha$.
+  argument with explicit convergence rate :math:`1 - \alpha`.
 * **Coupled-oscillator physics.**  Linear approximation of the Kuramoto / Vicsek models near
   the synchronised regime; direct comparison with the McKean–Vlasov continuous limit.