Added the Single-seed paper to docs and _autocitation and removed two…

… pyright: ignore comments

diffrax/_autocitation.py

@@ -10,6 +10,7 @@
 
 from ._adjoint import BacksolveAdjoint, DirectAdjoint, RecursiveCheckpointAdjoint
 from ._brownian import AbstractBrownianPath, VirtualBrownianTree
+from ._custom_types import BrownianIncrement
 from ._heuristics import is_cde, is_sde
 from ._integrate import diffeqsolve
 from ._misc import adjoint_rms_seminorm
@@ -347,7 +348,7 @@ def _virtual_brownian_tree(terms):
     is_vbt = lambda x: isinstance(x, VirtualBrownianTree)
     leaves = jtu.tree_leaves(terms, is_leaf=is_vbt)
     if any(is_vbt(leaf) for leaf in leaves):
-        vbt_ref, _ = _parse_reference_multi(VirtualBrownianTree)
+        vbt_ref, _, _ = _parse_reference_multi(VirtualBrownianTree)
         return (
             r"""
 % You are simulating Brownian motion using a virtual Brownian tree, which was introduced
@@ -359,17 +360,34 @@ def _virtual_brownian_tree(terms):
 
 @citation_rules.append
 def _space_time_levy_area(terms):
-    has_levy_area = lambda x: isinstance(x, AbstractBrownianPath) and x.levy_area != ""
+    has_levy_area = (
+        lambda x: isinstance(x, AbstractBrownianPath)
+        and x.levy_area != BrownianIncrement
+    )
     leaves = jtu.tree_leaves(terms, is_leaf=has_levy_area)
     if any(has_levy_area(leaf) for leaf in leaves):
-        _, levy_area_ref = _parse_reference_multi(VirtualBrownianTree)
-        return (
-            r"""
-% You are simulating Brownian motion using space-time Levy area, the formulae for which
-% were developed in:
+        return r"""
+% You are simulating Brownian motion using Levy area, the formulae for which
+% are due to:
+@misc{jelinčič2024singleseed,
+  title={Single-seed generation of Brownian paths and integrals
+  for adaptive and high order SDE solvers},
+  author={Andraž Jelinčič and James Foster and Patrick Kidger},
+  year={2024},
+  eprint={2405.06464},
+  archivePrefix={arXiv},
+  primaryClass={math.NA}
+}
+
+% and Theorem 6.1.6 of
+@phdthesis{foster2020a,
+  publisher = {University of Oxford},
+  school = {University of Oxford},
+  title = {Numerical approximations for stochastic differential equations},
+  author = {Foster, James M.},
+  year = {2020}
+}
 """
-            + levy_area_ref
-        )
 
 
 @citation_rules.append

diffrax/_brownian/tree.py

@@ -213,11 +213,21 @@ class VirtualBrownianTree(AbstractBrownianPath):
         ```
 
         The implementation here is an improvement on the above, in that it additionally
-        simulates space-time and space-time-time Levy areas. This is due to the paper
+        simulates space-time and space-time-time Levy areas, and exactly matches the
+        distribution of the Brownian motion and its Levy areas at all query times.
+        This is due to the paper
 
-        "Single-seed generation of Brownian paths and integrals
-        for adaptive and high order SDE solvers"
-        TODO: add the paper bitex
+        ```bibtex
+        @misc{jelinčič2024singleseed,
+          title={Single-seed generation of Brownian paths and integrals
+          for adaptive and high order SDE solvers},
+          author={Andraž Jelinčič and James Foster and Patrick Kidger},
+          year={2024},
+          eprint={2405.06464},
+          archivePrefix={arXiv},
+          primaryClass={math.NA}
+        }
+        ```
 
         and Theorem 6.1.6 of
 
@@ -230,9 +240,6 @@ class VirtualBrownianTree(AbstractBrownianPath):
           year = {2020}
         }
         ```
-
-        In addition, the implementation here is a further improvement on these by using
-        an interpolation method which ensures the conditional 2nd moments are correct.
     """
 
     t0: RealScalarLike

test/helpers.py

@@ -159,7 +159,7 @@ def _batch_sde_solve(
         shape=struct,
         tol=bm_tol,
         key=key,
-        levy_area=concrete_la,  # pyright: ignore
+        levy_area=concrete_la,
     )
     terms = get_terms(bm)
     if controller is None: