docs(v2.0.0-alpha.4): enrich v2.0 notebooks with FR sandwich + real-world examples

Each of the eight v2.0 companion notebooks (10_bsde through
17_generative_calibration) now follows the mandatory pedagogical
sandwich structure:

  PRE markdown : theorem / model / pivot equation / what the cell verifies
  CODE cell    : labelled prints + at least one matplotlib figure
  POST markdown: expected result, graph reading, conclusion

Each notebook carries at least one concrete real-world example
(heat plate, inverted pendulum, opinion polarization, collective
decision, OU drift under Cauchy noise, mixture vs gaussian MMD, etc.)

Generator script: scripts/enrich_v2_notebooks.py
Doc plots refreshed via scripts/inject_doc_plots.py.

docs/source/algorithms/agent_based.rst

@@ -44,6 +44,8 @@ Generic interacting-agent simulator (`consensus_dynamics`) — linear bounded-co
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__agent_based/block_03_fig_01.png
    :align: center
@@ -70,6 +72,8 @@ Generic interacting-agent simulator (`consensus_dynamics`) — linear bounded-co
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__agent_based/block_04_fig_01.png
    :align: center

docs/source/algorithms/bsde.rst

@@ -52,6 +52,8 @@ With $a(t) \equiv -\rho$, $b = c = 0$ and $Y_T = 1$ the analytic deterministic s
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__bsde/block_03_fig_01.png
    :align: center
@@ -90,6 +92,8 @@ Crank–Nicolson is second-order in `Δt`.
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__bsde/block_05_fig_01.png
    :align: center

docs/source/algorithms/generative_calibration_hooks.rst

@@ -36,6 +36,8 @@ Maximum-Mean-Discrepancy distance with Gaussian kernel (`mmd_gaussian`).  Self-d
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__generative_calibration_hooks/block_03_fig_01.png
    :align: center
@@ -63,6 +65,8 @@ Bandwidth dependence
 
 
 
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 .. image:: ../_static/auto/algorithms__generative_calibration_hooks/block_04_fig_01.png
    :align: center

docs/source/algorithms/mckean_vlasov.rst

@@ -45,6 +45,8 @@ Interacting-particle Euler scheme for $dX_t = θ(\bar X_t - X_t) dt + σ dW_t$ (
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__mckean_vlasov/block_03_fig_01.png
    :align: center
@@ -68,6 +70,8 @@ Interacting-particle Euler scheme for $dX_t = θ(\bar X_t - X_t) dt + σ dW_t$ (
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__mckean_vlasov/block_04_fig_01.png
    :align: center

docs/source/algorithms/pde.rst

@@ -51,6 +51,8 @@ $\partial_t m = \tfrac12 \partial_{xx} m$ with Gaussian initial density should r
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__pde/block_03_fig_01.png
    :align: center
@@ -92,6 +94,8 @@ $-\Delta u = 2\pi^2 \sin(\pi x)\sin(\pi y)$ on the unit square with zero Dirichl
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__pde/block_05_fig_01.png
    :align: center
@@ -128,6 +132,8 @@ Heat-only relaxation ($H = 0$, σ² > 0) preserves a constant value, while a qua
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__pde/block_07_fig_01.png
    :align: center

docs/source/algorithms/quadratic_impact_control.rst

@@ -45,6 +45,8 @@ $h'(t) = h(t)^2/γ - φ$ with $h(T) = A$.  When $γ = φ = A = 1$ the right-hand
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__quadratic_impact_control/block_03_fig_01.png
    :align: center
@@ -74,6 +76,8 @@ Vary $A$, fix $γ = 1$, $φ = 0.25$, $T = 1$.
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__quadratic_impact_control/block_04_fig_01.png
    :align: center

docs/source/algorithms/robust_drift.rst

@@ -47,6 +47,8 @@ Synthetic stationary process with 5 % outliers
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__robust_drift/block_03_fig_01.png
    :align: center
@@ -85,6 +87,8 @@ Synthetic stationary process with 5 % outliers
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__robust_drift/block_05_fig_01.png
    :align: center

docs/source/algorithms/stochastic_control.rst

@@ -46,6 +46,8 @@ Two modes; only mode 1 pays a unit reward.  Free switching should give `V_0(0) =
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__stochastic_control/block_03_fig_01.png
    :align: center
@@ -85,6 +87,8 @@ Closed-form Riccati for $a=q=0$, $b=r=s_T=1$, $T=1$ is $P(t) = 1/(1 + (T - t))$,
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__stochastic_control/block_05_fig_01.png
    :align: center
@@ -117,6 +121,8 @@ Affine premium $δ_±(λ) = α_± + κ_± λ$.  First-order condition: $\lambda^
 
 
 
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 .. AUTO-PLOT-BEGIN
 .. image:: ../_static/auto/algorithms__stochastic_control/block_06_fig_01.png
    :align: center