diff --git a/spec/API_specification/dataframe_api/column_object.py b/spec/API_specification/dataframe_api/column_object.py
index 5db4caea..9ae7de4a 100644
--- a/spec/API_specification/dataframe_api/column_object.py
+++ b/spec/API_specification/dataframe_api/column_object.py
@@ -5,9 +5,14 @@
 if TYPE_CHECKING:
     from typing_extensions import Self
 
-    from dataframe_api.dataframe_object import DataFrame
-
-    from .typing import DType, Namespace, NullType, Scalar
+    from .typing import (
+        AnyScalar,
+        DataFrame,
+        DType,
+        Namespace,
+        NullType,
+        Scalar,
+    )
 
 
 __all__ = ["Column"]
@@ -224,7 +229,7 @@ def sorted_indices(
         """
         ...
 
-    def __eq__(self, other: Self | Scalar) -> Self:  # type: ignore[override]
+    def __eq__(self, other: Self | AnyScalar) -> Self:  # type: ignore[override]
         """Compare for equality.
 
         Nulls should follow Kleene Logic.
@@ -247,7 +252,7 @@ def __eq__(self, other: Self | Scalar) -> Self:  # type: ignore[override]
         """
         ...
 
-    def __ne__(self, other: Self | Scalar) -> Self:  # type: ignore[override]
+    def __ne__(self, other: Self | AnyScalar) -> Self:  # type: ignore[override]
         """Compare for non-equality.
 
         Nulls should follow Kleene Logic.
@@ -270,7 +275,7 @@ def __ne__(self, other: Self | Scalar) -> Self:  # type: ignore[override]
         """
         ...
 
-    def __ge__(self, other: Self | Scalar) -> Self:
+    def __ge__(self, other: Self | AnyScalar) -> Self:
         """Compare for "greater than or equal to" `other`.
 
         Parameters
@@ -291,7 +296,7 @@ def __ge__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __gt__(self, other: Self | Scalar) -> Self:
+    def __gt__(self, other: Self | AnyScalar) -> Self:
         """Compare for "greater than" `other`.
 
         Parameters
@@ -312,7 +317,7 @@ def __gt__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __le__(self, other: Self | Scalar) -> Self:
+    def __le__(self, other: Self | AnyScalar) -> Self:
         """Compare for "less than or equal to" `other`.
 
         Parameters
@@ -333,7 +338,7 @@ def __le__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __lt__(self, other: Self | Scalar) -> Self:
+    def __lt__(self, other: Self | AnyScalar) -> Self:
         """Compare for "less than" `other`.
 
         Parameters
@@ -354,7 +359,7 @@ def __lt__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __and__(self, other: Self | bool) -> Self:
+    def __and__(self, other: Self | bool | Scalar) -> Self:
         """Apply logical 'and' to `other` Column (or scalar) and this Column.
 
         Nulls should follow Kleene Logic.
@@ -380,7 +385,7 @@ def __and__(self, other: Self | bool) -> Self:
         """
         ...
 
-    def __or__(self, other: Self | bool) -> Self:
+    def __or__(self, other: Self | bool | Scalar) -> Self:
         """Apply logical 'or' to `other` Column (or scalar) and this column.
 
         Nulls should follow Kleene Logic.
@@ -406,7 +411,7 @@ def __or__(self, other: Self | bool) -> Self:
         """
         ...
 
-    def __add__(self, other: Self | Scalar) -> Self:
+    def __add__(self, other: Self | AnyScalar) -> Self:
         """Add `other` column or scalar to this column.
 
         Parameters
@@ -427,7 +432,7 @@ def __add__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __sub__(self, other: Self | Scalar) -> Self:
+    def __sub__(self, other: Self | AnyScalar) -> Self:
         """Subtract `other` column or scalar from this column.
 
         Parameters
@@ -448,7 +453,7 @@ def __sub__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __mul__(self, other: Self | Scalar) -> Self:
+    def __mul__(self, other: Self | AnyScalar) -> Self:
         """Multiply `other` column or scalar with this column.
 
         Parameters
@@ -469,7 +474,7 @@ def __mul__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __truediv__(self, other: Self | Scalar) -> Self:
+    def __truediv__(self, other: Self | AnyScalar) -> Self:
         """Divide this column by `other` column or scalar. True division, returns floats.
 
         Parameters
@@ -490,7 +495,7 @@ def __truediv__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __floordiv__(self, other: Self | Scalar) -> Self:
+    def __floordiv__(self, other: Self | AnyScalar) -> Self:
         """Floor-divide `other` column or scalar to this column.
 
         Parameters
@@ -511,7 +516,7 @@ def __floordiv__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __pow__(self, other: Self | Scalar) -> Self:
+    def __pow__(self, other: Self | AnyScalar) -> Self:
         """Raise this column to the power of `other`.
 
         Integer dtype to the power of non-negative integer dtype is integer dtype.
@@ -536,7 +541,7 @@ def __pow__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __mod__(self, other: Self | Scalar) -> Self:
+    def __mod__(self, other: Self | AnyScalar) -> Self:
         """Return modulus of this column by `other` (`%` operator).
 
         Parameters
@@ -557,7 +562,7 @@ def __mod__(self, other: Self | Scalar) -> Self:
         """
         ...
 
-    def __divmod__(self, other: Self | Scalar) -> tuple[Column, Column]:
+    def __divmod__(self, other: Self | AnyScalar) -> tuple[Column, Column]:
         """Return quotient and remainder of integer division. See `divmod` builtin.
 
         Parameters
@@ -578,16 +583,16 @@ def __divmod__(self, other: Self | Scalar) -> tuple[Column, Column]:
         """
         ...
 
-    def __radd__(self, other: Self | Scalar) -> Self:
+    def __radd__(self, other: Self | AnyScalar) -> Self:
         ...
 
-    def __rsub__(self, other: Self | Scalar) -> Self:
+    def __rsub__(self, other: Self | AnyScalar) -> Self:
         ...
 
-    def __rmul__(self, other: Self | Scalar) -> Self:
+    def __rmul__(self, other: Self | AnyScalar) -> Self:
         ...
 
-    def __rtruediv__(self, other: Self | Scalar) -> Self:
+    def __rtruediv__(self, other: Self | AnyScalar) -> Self:
         ...
 
     def __rand__(self, other: Self | bool) -> Self:
@@ -596,13 +601,13 @@ def __rand__(self, other: Self | bool) -> Self:
     def __ror__(self, other: Self | bool) -> Self:
         ...
 
-    def __rfloordiv__(self, other: Self | Scalar) -> Self:
+    def __rfloordiv__(self, other: Self | AnyScalar) -> Self:
         ...
 
-    def __rpow__(self, other: Self | Scalar) -> Self:
+    def __rpow__(self, other: Self | AnyScalar) -> Self:
         ...
 
-    def __rmod__(self, other: Self | Scalar) -> Self:
+    def __rmod__(self, other: Self | AnyScalar) -> Self:
         ...
 
     def __invert__(self) -> Self:
@@ -615,7 +620,7 @@ def __invert__(self) -> Self:
         """
         ...
 
-    def any(self, *, skip_nulls: bool = True) -> bool | NullType:
+    def any(self, *, skip_nulls: bool | Scalar = True) -> Scalar:
         """Reduction returns a bool.
 
         Raises
@@ -625,7 +630,7 @@ def any(self, *, skip_nulls: bool = True) -> bool | NullType:
         """
         ...
 
-    def all(self, *, skip_nulls: bool = True) -> bool | NullType:
+    def all(self, *, skip_nulls: bool | Scalar = True) -> Scalar:
         """Reduction returns a bool.
 
         Raises
@@ -635,7 +640,7 @@ def all(self, *, skip_nulls: bool = True) -> bool | NullType:
         """
         ...
 
-    def min(self, *, skip_nulls: bool = True) -> Scalar | NullType:
+    def min(self, *, skip_nulls: bool | Scalar = True) -> Scalar:
         """Reduction returns a scalar.
 
         Any data type that supports comparisons
@@ -643,7 +648,7 @@ def min(self, *, skip_nulls: bool = True) -> Scalar | NullType:
         """
         ...
 
-    def max(self, *, skip_nulls: bool = True) -> Scalar | NullType:
+    def max(self, *, skip_nulls: bool | Scalar = True) -> Scalar:
         """Reduction returns a scalar.
 
         Any data type that supports comparisons
@@ -651,7 +656,7 @@ def max(self, *, skip_nulls: bool = True) -> Scalar | NullType:
         """
         ...
 
-    def sum(self, *, skip_nulls: bool = True) -> Scalar | NullType:
+    def sum(self, *, skip_nulls: bool | Scalar = True) -> Scalar:
         """Reduction returns a scalar.
 
         Must be supported for numerical and
@@ -660,7 +665,7 @@ def sum(self, *, skip_nulls: bool = True) -> Scalar | NullType:
         """
         ...
 
-    def prod(self, *, skip_nulls: bool = True) -> Scalar | NullType:
+    def prod(self, *, skip_nulls: bool | Scalar = True) -> Scalar:
         """Reduction returns a scalar.
 
         Must be supported for numerical data types.
@@ -668,7 +673,7 @@ def prod(self, *, skip_nulls: bool = True) -> Scalar | NullType:
         """
         ...
 
-    def median(self, *, skip_nulls: bool = True) -> Scalar | NullType:
+    def median(self, *, skip_nulls: bool | Scalar = True) -> Scalar:
         """Reduction returns a scalar.
 
         Must be supported for numerical and
@@ -678,7 +683,7 @@ def median(self, *, skip_nulls: bool = True) -> Scalar | NullType:
         """
         ...
 
-    def mean(self, *, skip_nulls: bool = True) -> Scalar | NullType:
+    def mean(self, *, skip_nulls: bool | Scalar = True) -> Scalar:
         """Reduction returns a scalar.
 
         Must be supported for numerical and
@@ -691,9 +696,9 @@ def mean(self, *, skip_nulls: bool = True) -> Scalar | NullType:
     def std(
         self,
         *,
-        correction: int | float = 1,
-        skip_nulls: bool = True,
-    ) -> Scalar | NullType:
+        correction: float = 1,
+        skip_nulls: bool | Scalar = True,
+    ) -> Scalar:
         """Reduction returns a scalar.
 
         Must be supported for numerical and
@@ -724,9 +729,9 @@ def std(
     def var(
         self,
         *,
-        correction: int | float = 1,
-        skip_nulls: bool = True,
-    ) -> Scalar | NullType:
+        correction: float | Scalar = 1,
+        skip_nulls: bool | Scalar = True,
+    ) -> Scalar:
         """Reduction returns a scalar.
 
         Must be supported for numerical and
@@ -835,7 +840,7 @@ def is_in(self, values: Self) -> Self:
         """
         ...
 
-    def unique_indices(self, *, skip_nulls: bool = True) -> Self:
+    def unique_indices(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Return indices corresponding to unique values in Column.
 
         Returns
@@ -855,7 +860,7 @@ def unique_indices(self, *, skip_nulls: bool = True) -> Self:
         """
         ...
 
-    def fill_nan(self, value: float | NullType, /) -> Self:
+    def fill_nan(self, value: float | NullType | Scalar, /) -> Self:
         """Fill floating point ``nan`` values with the given fill value.
 
         Parameters
@@ -868,7 +873,7 @@ def fill_nan(self, value: float | NullType, /) -> Self:
         """
         ...
 
-    def fill_null(self, value: Scalar, /) -> Self:
+    def fill_null(self, value: AnyScalar, /) -> Self:
         """Fill null values with the given fill value.
 
         Parameters
@@ -914,7 +919,7 @@ def to_array(self) -> Any:
         """
         ...
 
-    def rename(self, name: str) -> Self:
+    def rename(self, name: str | Scalar) -> Self:
         """Rename column.
 
         Parameters
@@ -929,17 +934,17 @@ def rename(self, name: str) -> Self:
         """
         ...
 
-    def shift(self, offset: int) -> Self:
+    def shift(self, offset: int | Scalar) -> Self:
         """Shift values by `offset` positions, filling missing values with `null`.
 
         For example, if the original column contains values `[1, 4, 2]`, then:
 
         - `.shift(1)` will return `[null, 1, 4]`,
         - `.shift(-1)` will return `[4, 2, null]`,
-    
+
         Parameters
         ----------
-        offset
+        offset : int
             How many positions to shift by.
         """
         ...
@@ -1020,7 +1025,7 @@ def iso_weekday(self) -> Self:
         """
         ...
 
-    def unix_timestamp(self, *, time_unit: Literal["s", "ms", "us"] = "s") -> Self:
+    def unix_timestamp(self, *, time_unit: str | Scalar = "s") -> Self:
         """Return number of seconds / milliseconds / microseconds since the Unix epoch.
 
         The Unix epoch is 00:00:00 UTC on 1 January 1970.
@@ -1039,3 +1044,16 @@ def unix_timestamp(self, *, time_unit: Literal["s", "ms", "us"] = "s") -> Self:
             discarded.
         """
         ...
+
+    def persist(self) -> Self:
+        """Hint that computation prior to this point should not be repeated.
+
+        This is intended as a hint, rather than as a directive. Implementations
+        which do not separate lazy vs eager execution may ignore this method and
+        treat it as a no-op.
+
+        .. note::
+            This method may trigger execution. If necessary, it should be called
+            at most once per dataframe, and as late as possible in the pipeline.
+        """
+        ...
diff --git a/spec/API_specification/dataframe_api/dataframe_object.py b/spec/API_specification/dataframe_api/dataframe_object.py
index 462fc911..4bd431ea 100644
--- a/spec/API_specification/dataframe_api/dataframe_object.py
+++ b/spec/API_specification/dataframe_api/dataframe_object.py
@@ -9,7 +9,14 @@
 
     from .column_object import Column
     from .groupby_object import GroupBy
-    from .typing import DType, Namespace, NullType, Scalar, SupportsDataFrameAPI
+    from .typing import (
+        AnyScalar,
+        DType,
+        Namespace,
+        NullType,
+        Scalar,
+        SupportsDataFrameAPI,
+    )
 
 
 __all__ = ["DataFrame"]
@@ -345,7 +352,7 @@ def sorted_indices(
         """
         ...
 
-    def __eq__(self, other: Scalar) -> Self:  # type: ignore[override]
+    def __eq__(self, other: AnyScalar) -> Self:  # type: ignore[override]
         """Compare for equality.
 
         Nulls should follow Kleene Logic.
@@ -362,7 +369,7 @@ def __eq__(self, other: Scalar) -> Self:  # type: ignore[override]
         """
         ...
 
-    def __ne__(self, other: Scalar) -> Self:  # type: ignore[override]
+    def __ne__(self, other: AnyScalar) -> Self:  # type: ignore[override]
         """Compare for non-equality.
 
         Nulls should follow Kleene Logic.
@@ -379,7 +386,7 @@ def __ne__(self, other: Scalar) -> Self:  # type: ignore[override]
         """
         ...
 
-    def __ge__(self, other: Scalar) -> Self:
+    def __ge__(self, other: AnyScalar) -> Self:
         """Compare for "greater than or equal to" `other`.
 
         Parameters
@@ -394,7 +401,7 @@ def __ge__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __gt__(self, other: Scalar) -> Self:
+    def __gt__(self, other: AnyScalar) -> Self:
         """Compare for "greater than" `other`.
 
         Parameters
@@ -409,7 +416,7 @@ def __gt__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __le__(self, other: Scalar) -> Self:
+    def __le__(self, other: AnyScalar) -> Self:
         """Compare for "less than or equal to" `other`.
 
         Parameters
@@ -424,7 +431,7 @@ def __le__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __lt__(self, other: Scalar) -> Self:
+    def __lt__(self, other: AnyScalar) -> Self:
         """Compare for "less than" `other`.
 
         Parameters
@@ -479,7 +486,7 @@ def __or__(self, other: bool) -> Self:  # noqa: FBT001
         """
         ...
 
-    def __add__(self, other: Scalar) -> Self:
+    def __add__(self, other: AnyScalar) -> Self:
         """Add `other` scalar to this dataframe.
 
         Parameters
@@ -494,7 +501,7 @@ def __add__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __sub__(self, other: Scalar) -> Self:
+    def __sub__(self, other: AnyScalar) -> Self:
         """Subtract `other` scalar from this dataframe.
 
         Parameters
@@ -509,7 +516,7 @@ def __sub__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __mul__(self, other: Scalar) -> Self:
+    def __mul__(self, other: AnyScalar) -> Self:
         """Multiply  `other` scalar with this dataframe.
 
         Parameters
@@ -524,7 +531,7 @@ def __mul__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __truediv__(self, other: Scalar) -> Self:
+    def __truediv__(self, other: AnyScalar) -> Self:
         """Divide  this dataframe by `other` scalar. True division, returns floats.
 
         Parameters
@@ -539,7 +546,7 @@ def __truediv__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __floordiv__(self, other: Scalar) -> Self:
+    def __floordiv__(self, other: AnyScalar) -> Self:
         """Floor-divide (returns integers) this dataframe by `other` scalar.
 
         Parameters
@@ -554,7 +561,7 @@ def __floordiv__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __pow__(self, other: Scalar) -> Self:
+    def __pow__(self, other: AnyScalar) -> Self:
         """Raise this dataframe to the power of `other`.
 
         Integer dtype to the power of non-negative integer dtype is integer dtype.
@@ -573,7 +580,7 @@ def __pow__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __mod__(self, other: Scalar) -> Self:
+    def __mod__(self, other: AnyScalar) -> Self:
         """Return modulus of this dataframe by `other` (`%` operator).
 
         Parameters
@@ -588,7 +595,7 @@ def __mod__(self, other: Scalar) -> Self:
         """
         ...
 
-    def __divmod__(self, other: Scalar) -> tuple[DataFrame, DataFrame]:
+    def __divmod__(self, other: AnyScalar) -> tuple[DataFrame, DataFrame]:
         """Return quotient and remainder of integer division. See `divmod` builtin.
 
         Parameters
@@ -603,31 +610,31 @@ def __divmod__(self, other: Scalar) -> tuple[DataFrame, DataFrame]:
         """
         ...
 
-    def __radd__(self, other: Scalar) -> Self:
+    def __radd__(self, other: AnyScalar) -> Self:
         ...
 
-    def __rsub__(self, other: Scalar) -> Self:
+    def __rsub__(self, other: AnyScalar) -> Self:
         ...
 
-    def __rmul__(self, other: Scalar) -> Self:
+    def __rmul__(self, other: AnyScalar) -> Self:
         ...
 
-    def __rtruediv__(self, other: Scalar) -> Self:
+    def __rtruediv__(self, other: AnyScalar) -> Self:
         ...
 
-    def __rand__(self, other: Scalar) -> Self:
+    def __rand__(self, other: AnyScalar) -> Self:
         ...
 
-    def __ror__(self, other: Scalar) -> Self:
+    def __ror__(self, other: AnyScalar) -> Self:
         ...
 
-    def __rfloordiv__(self, other: Scalar) -> Self:
+    def __rfloordiv__(self, other: AnyScalar) -> Self:
         ...
 
-    def __rpow__(self, other: Scalar) -> Self:
+    def __rpow__(self, other: AnyScalar) -> Self:
         ...
 
-    def __rmod__(self, other: Scalar) -> Self:
+    def __rmod__(self, other: AnyScalar) -> Self:
         ...
 
     def __invert__(self) -> Self:
@@ -651,7 +658,7 @@ def __iter__(self) -> NoReturn:
         """
         raise NotImplementedError("'__iter__' is intentionally not implemented.")
 
-    def any(self, *, skip_nulls: bool = True) -> Self:
+    def any(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Reduction returns a 1-row DataFrame.
 
         Raises
@@ -661,7 +668,7 @@ def any(self, *, skip_nulls: bool = True) -> Self:
         """
         ...
 
-    def all(self, *, skip_nulls: bool = True) -> Self:
+    def all(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Reduction returns a 1-row DataFrame.
 
         Raises
@@ -671,7 +678,7 @@ def all(self, *, skip_nulls: bool = True) -> Self:
         """
         ...
 
-    def any_rowwise(self, *, skip_nulls: bool = True) -> Column:
+    def any_rowwise(self, *, skip_nulls: bool | Scalar = True) -> Column:
         """Reduction returns a Column.
 
         Differs from ``DataFrame.any`` and that the reduction happens
@@ -684,7 +691,7 @@ def any_rowwise(self, *, skip_nulls: bool = True) -> Column:
         """
         ...
 
-    def all_rowwise(self, *, skip_nulls: bool = True) -> Column:
+    def all_rowwise(self, *, skip_nulls: bool | Scalar = True) -> Column:
         """Reduction returns a Column.
 
         Differs from ``DataFrame.all`` and that the reduction happens
@@ -697,31 +704,36 @@ def all_rowwise(self, *, skip_nulls: bool = True) -> Column:
         """
         ...
 
-    def min(self, *, skip_nulls: bool = True) -> Self:
+    def min(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Reduction returns a 1-row DataFrame."""
         ...
 
-    def max(self, *, skip_nulls: bool = True) -> Self:
+    def max(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Reduction returns a 1-row DataFrame."""
         ...
 
-    def sum(self, *, skip_nulls: bool = True) -> Self:
+    def sum(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Reduction returns a 1-row DataFrame."""
         ...
 
-    def prod(self, *, skip_nulls: bool = True) -> Self:
+    def prod(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Reduction returns a 1-row DataFrame."""
         ...
 
-    def median(self, *, skip_nulls: bool = True) -> Self:
+    def median(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Reduction returns a 1-row DataFrame."""
         ...
 
-    def mean(self, *, skip_nulls: bool = True) -> Self:
+    def mean(self, *, skip_nulls: bool | Scalar = True) -> Self:
         """Reduction returns a 1-row DataFrame."""
         ...
 
-    def std(self, *, correction: int | float = 1, skip_nulls: bool = True) -> Self:
+    def std(
+        self,
+        *,
+        correction: float | Scalar = 1,
+        skip_nulls: bool | Scalar = True,
+    ) -> Self:
         """Reduction returns a 1-row DataFrame.
 
         Parameters
@@ -735,7 +747,12 @@ def std(self, *, correction: int | float = 1, skip_nulls: bool = True) -> Self:
         """
         ...
 
-    def var(self, *, correction: int | float = 1, skip_nulls: bool = True) -> Self:
+    def var(
+        self,
+        *,
+        correction: float | Scalar = 1,
+        skip_nulls: bool | Scalar = True,
+    ) -> Self:
         """Reduction returns a 1-row DataFrame.
 
         Parameters
@@ -787,7 +804,7 @@ def is_nan(self) -> Self:
         """
         ...
 
-    def unique_indices(self, *keys: str, skip_nulls: bool = True) -> Column:
+    def unique_indices(self, *keys: str, skip_nulls: bool | Scalar = True) -> Column:
         """Return indices corresponding to unique values across selected columns.
 
         Parameters
@@ -813,7 +830,7 @@ def unique_indices(self, *keys: str, skip_nulls: bool = True) -> Column:
         """
         ...
 
-    def fill_nan(self, value: float | NullType, /) -> Self:
+    def fill_nan(self, value: float | NullType | Scalar, /) -> Self:
         """Fill ``nan`` values with the given fill value.
 
         The fill operation will apply to all columns with a floating-point
@@ -831,7 +848,7 @@ def fill_nan(self, value: float | NullType, /) -> Self:
 
     def fill_null(
         self,
-        value: Scalar,
+        value: AnyScalar,
         /,
         *,
         column_names: list[str] | None = None,
diff --git a/spec/API_specification/dataframe_api/groupby_object.py b/spec/API_specification/dataframe_api/groupby_object.py
index adecb8aa..8b26eff3 100644
--- a/spec/API_specification/dataframe_api/groupby_object.py
+++ b/spec/API_specification/dataframe_api/groupby_object.py
@@ -4,6 +4,7 @@
 
 if TYPE_CHECKING:
     from .dataframe_object import DataFrame
+    from .typing import Scalar
 
 
 __all__ = [
@@ -22,34 +23,44 @@ class GroupBy(Protocol):
 
     """
 
-    def any(self, *, skip_nulls: bool = True) -> DataFrame:
+    def any(self, *, skip_nulls: bool | Scalar = True) -> DataFrame:
         ...
 
-    def all(self, *, skip_nulls: bool = True) -> DataFrame:
+    def all(self, *, skip_nulls: bool | Scalar = True) -> DataFrame:
         ...
 
-    def min(self, *, skip_nulls: bool = True) -> DataFrame:
+    def min(self, *, skip_nulls: bool | Scalar = True) -> DataFrame:
         ...
 
-    def max(self, *, skip_nulls: bool = True) -> DataFrame:
+    def max(self, *, skip_nulls: bool | Scalar = True) -> DataFrame:
         ...
 
-    def sum(self, *, skip_nulls: bool = True) -> DataFrame:
+    def sum(self, *, skip_nulls: bool | Scalar = True) -> DataFrame:
         ...
 
-    def prod(self, *, skip_nulls: bool = True) -> DataFrame:
+    def prod(self, *, skip_nulls: bool | Scalar = True) -> DataFrame:
         ...
 
-    def median(self, *, skip_nulls: bool = True) -> DataFrame:
+    def median(self, *, skip_nulls: bool | Scalar = True) -> DataFrame:
         ...
 
-    def mean(self, *, skip_nulls: bool = True) -> DataFrame:
+    def mean(self, *, skip_nulls: bool | Scalar = True) -> DataFrame:
         ...
 
-    def std(self, *, correction: int | float = 1, skip_nulls: bool = True) -> DataFrame:
+    def std(
+        self,
+        *,
+        correction: float | Scalar = 1,
+        skip_nulls: bool | Scalar = True,
+    ) -> DataFrame:
         ...
 
-    def var(self, *, correction: int | float = 1, skip_nulls: bool = True) -> DataFrame:
+    def var(
+        self,
+        *,
+        correction: float | Scalar = 1,
+        skip_nulls: bool | Scalar = True,
+    ) -> DataFrame:
         ...
 
     def size(self) -> DataFrame:
@@ -74,7 +85,7 @@ def aggregate(self, *aggregation: Aggregation) -> DataFrame:
 
 
 class Aggregation(Protocol):
-    def rename(self, name: str) -> Aggregation:
+    def rename(self, name: str | Scalar) -> Aggregation:
         """Assign given name to output of aggregation.
 
         If not called, the column's name will be used as the output name.
@@ -82,35 +93,35 @@ def rename(self, name: str) -> Aggregation:
         ...
 
     @classmethod
-    def any(cls, column: str, *, skip_nulls: bool = True) -> Aggregation:
+    def any(cls, column: str, *, skip_nulls: bool | Scalar = True) -> Aggregation:
         ...
 
     @classmethod
-    def all(cls, column: str, *, skip_nulls: bool = True) -> Aggregation:
+    def all(cls, column: str, *, skip_nulls: bool | Scalar = True) -> Aggregation:
         ...
 
     @classmethod
-    def min(cls, column: str, *, skip_nulls: bool = True) -> Aggregation:
+    def min(cls, column: str, *, skip_nulls: bool | Scalar = True) -> Aggregation:
         ...
 
     @classmethod
-    def max(cls, column: str, *, skip_nulls: bool = True) -> Aggregation:
+    def max(cls, column: str, *, skip_nulls: bool | Scalar = True) -> Aggregation:
         ...
 
     @classmethod
-    def sum(cls, column: str, *, skip_nulls: bool = True) -> Aggregation:
+    def sum(cls, column: str, *, skip_nulls: bool | Scalar = True) -> Aggregation:
         ...
 
     @classmethod
-    def prod(cls, column: str, *, skip_nulls: bool = True) -> Aggregation:
+    def prod(cls, column: str, *, skip_nulls: bool | Scalar = True) -> Aggregation:
         ...
 
     @classmethod
-    def median(cls, column: str, *, skip_nulls: bool = True) -> Aggregation:
+    def median(cls, column: str, *, skip_nulls: bool | Scalar = True) -> Aggregation:
         ...
 
     @classmethod
-    def mean(cls, column: str, *, skip_nulls: bool = True) -> Aggregation:
+    def mean(cls, column: str, *, skip_nulls: bool | Scalar = True) -> Aggregation:
         ...
 
     @classmethod
@@ -118,8 +129,8 @@ def std(
         cls,
         column: str,
         *,
-        correction: int | float = 1,
-        skip_nulls: bool = True,
+        correction: float | Scalar = 1,
+        skip_nulls: bool | Scalar = True,
     ) -> Aggregation:
         ...
 
@@ -128,8 +139,8 @@ def var(
         cls,
         column: str,
         *,
-        correction: int | float = 1,
-        skip_nulls: bool = True,
+        correction: float | Scalar = 1,
+        skip_nulls: bool | Scalar = True,
     ) -> Aggregation:
         ...
 
diff --git a/spec/API_specification/dataframe_api/scalar_object.py b/spec/API_specification/dataframe_api/scalar_object.py
new file mode 100644
index 00000000..078cf2a4
--- /dev/null
+++ b/spec/API_specification/dataframe_api/scalar_object.py
@@ -0,0 +1,120 @@
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Protocol
+
+if TYPE_CHECKING:
+    from typing_extensions import Self
+
+    from dataframe_api.typing import AnyScalar, DType
+
+__all__ = ["Scalar"]
+
+
+class Scalar(Protocol):
+    """Scalar object.
+
+    Not meant to be instantiated directly, but rather created via
+    `:meth:Column.get_value` or one of the column reductions such
+    as `:meth:`Column.sum`.
+
+    Note that, just like how `:class:Column`s can hold null values,
+    a `Scalar` can also be backed by a null value. Given that `Scalar`s
+    aren't instantiated directly, but rather derived from existing
+    `Column`s, `Scalar.dtype` is determined by the parent `Column`.
+    For example, if `column` is `Column` of dtype `Int64`, then
+    `column.get_value(0)` will return a `Scalar` of dtype `Int64`
+    (even if it is backed by a null value).
+    """
+
+    def __lt__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __le__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __eq__(self, other: AnyScalar) -> Scalar:  # type: ignore[override]
+        ...
+
+    def __ne__(self, other: AnyScalar) -> Scalar:  # type: ignore[override]
+        ...
+
+    def __gt__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __ge__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __add__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __radd__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __sub__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __rsub__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __mul__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __rmul__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __mod__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    # Signatures of "__rmod__" of "Scalar" and "__mod__" of "str | int | float | Scalar"
+    # are unsafely overlapping
+    def __rmod__(self, other: AnyScalar) -> Scalar:  # type: ignore[misc]
+        ...
+
+    def __pow__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __rpow__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __floordiv__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __rfloordiv__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __truediv__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __rtruediv__(self, other: AnyScalar) -> Scalar:
+        ...
+
+    def __neg__(self) -> Scalar:
+        ...
+
+    def __abs__(self) -> Scalar:
+        ...
+
+    def __bool__(self) -> bool:
+        """Note that this return a Python scalar.
+
+        Depending on the implementation, this may raise or trigger computation.
+        """
+        ...
+
+    @property
+    def dtype(self) -> DType:
+        """Return data type of scalar."""
+        ...
+
+    def persist(self) -> Self:
+        """Hint that computation prior to this point should not be repeated.
+
+        This is intended as a hint, rather than as a directive. Implementations
+        which do not separate lazy vs eager execution may ignore this method and
+        treat it as a no-op.
+
+        .. note::
+            This may trigger computation and so should be used with care.
+            See `execution_model` page for more details.
+        """
+        ...
diff --git a/spec/API_specification/dataframe_api/typing.py b/spec/API_specification/dataframe_api/typing.py
index e344e111..574c9480 100644
--- a/spec/API_specification/dataframe_api/typing.py
+++ b/spec/API_specification/dataframe_api/typing.py
@@ -14,13 +14,12 @@
 from dataframe_api.groupby_object import Aggregation as AggregationT
 from dataframe_api.groupby_object import GroupBy
 
+from .scalar_object import Scalar
+
 if TYPE_CHECKING:
     from collections.abc import Sequence
 
 
-# Type alias: Mypy needs Any, but for readability we need to make clear this
-# is a Python scalar (i.e., an instance of `bool`, `int`, `float`, `str`, etc.)
-Scalar = Any
 # null is a special object which represents a missing value.
 # It is not valid as a type.
 
@@ -131,7 +130,6 @@ def date(self, year: int, month: int, day: int) -> Scalar:
         ...
 
 
-NullType = Namespace.NullType
 DType = Union[
     Namespace.Bool,
     Namespace.Float64,
@@ -169,15 +167,20 @@ def __column_consortium_standard__(
         ...
 
 
+PythonScalar = Union[str, int, float, bool]
+AnyScalar = Union[PythonScalar, Scalar]
+NullType = Namespace.NullType
+
+
 __all__ = [
     "Column",
     "DataFrame",
     "DType",
     "GroupBy",
     "Namespace",
-    "NullType",
+    "AnyScalar",
     "Scalar",
+    "NullType",
     "SupportsColumnAPI",
     "SupportsDataFrameAPI",
-    "Scalar",
 ]
diff --git a/spec/API_specification/examples/05_scalars_example.py b/spec/API_specification/examples/05_scalars_example.py
new file mode 100644
index 00000000..acf001a8
--- /dev/null
+++ b/spec/API_specification/examples/05_scalars_example.py
@@ -0,0 +1,34 @@
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+if TYPE_CHECKING:
+    from dataframe_api.column_object import Column
+    from dataframe_api.dataframe_object import DataFrame
+    from dataframe_api.scalar_object import Scalar
+    from dataframe_api.typing import SupportsDataFrameAPI
+
+
+def main(df_raw: SupportsDataFrameAPI) -> SupportsDataFrameAPI:
+    df = df_raw.__dataframe_consortium_standard__(api_version="2023-11.beta")
+
+    # `DataFrame.fill_null` accepts `AnyScalar` objections.
+    # This means we can fill nulls using a Standard Scalar object...
+    df = df.fill_null(df.col("a").mean())
+
+    # ... but also Python scalars:
+    df = df.fill_null(3)
+    df = df.fill_null("3")
+
+    # Scalars can be used in arithmetic expressions with other scalars, columns,
+    # or DataFrames
+    value: Scalar = df.col("a").mean()
+    col: Column = df.col("a")
+    _res1: Column = value - col
+    _res2: Scalar = value - 3
+    _res3: Scalar = 3 - value
+    _res4: Column = df.col("a") - 3
+    _res5: DataFrame = df - value
+    _res6: DataFrame = value - df
+
+    return df.dataframe
diff --git a/spec/API_specification/pyproject.toml b/spec/API_specification/pyproject.toml
index 8b88d455..31c5f2ad 100644
--- a/spec/API_specification/pyproject.toml
+++ b/spec/API_specification/pyproject.toml
@@ -47,5 +47,4 @@ ignore = [
     "N999", # invalid-module-name
     "PD901", # pandas-df-variable-name
     "PLR0913",   # too-many-arguments
-    "PYI041",  # redundant-numeric-union
 ]
diff --git a/spec/conf.py b/spec/conf.py
index cc6e3270..a89cfee5 100644
--- a/spec/conf.py
+++ b/spec/conf.py
@@ -82,10 +82,11 @@
     ('py:class', 'enum.Enum'),
     ('py:class', 'ellipsis'),
     ('py:class', 'Scalar'),
+    ('py:class', 'AnyScalar'),
+    ('py:class', 'NullType'),
     ('py:class', 'Bool'),
     ('py:class', 'optional'),
     ('py:class', 'Aggregation'),
-    ('py:class', 'NullType'),
     ('py:class', 'Namespace'),
     ('py:class', 'SupportsDataFrameAPI'),
     ('py:class', 'Self'),
diff --git a/spec/design_topics/python_builtin_types.md b/spec/design_topics/python_builtin_types.md
index c85812eb..ee0c3541 100644
--- a/spec/design_topics/python_builtin_types.md
+++ b/spec/design_topics/python_builtin_types.md
@@ -6,9 +6,9 @@ it is also potentially problematic when trying to write performant dataframe
 library code or supporting devices other than CPU.
 
 This standard specifies the use of Python types in quite a few places, and uses
-them as type annotations. As a concrete example, consider the `mean` method and
-the `float` it is documented to return, in combination with the `__gt__` method
-(i.e., the `>` operator) on the dataframe:
+them as type annotations. As a concrete example, consider the `mean` method,
+the `bool | Scalar` argument it takes, and the `Scalar` it is documented to return,
+in combination with the `__gt__` method (i.e., the `>` operator) on the dataframe:
 
 ```python
 class DataFrame:
@@ -18,24 +18,51 @@ class DataFrame:
         ...
 
 class Column:
-    def mean(self, skip_nulls: bool = True) -> float | NullType:
+    def mean(self, skip_nulls: bool | Scalar = True) -> Scalar:
         ...
 
-larger = df2 > df1.col('foo').mean()
+larger = df2 > df1.col('foo', skip_nulls = True).mean()
 ```
 
-For a GPU dataframe library, it is desirable for all data to reside on the GPU,
-and not incur a performance penalty from synchronizing instances of Python
-builtin types to CPU. In the above example, the `.mean()` call returns a
-`float`. It is likely beneficial though to implement this as a library-specific
-scalar object which duck types with `float`. This means that it should (a) have
-the same semantics as a builtin `float` when used within a library, and (b)
-support usage as a `float` outside of the library (i.e., implement
-`__float__`). Duck typing is usually not perfect, for example `isinstance`
-usage on the float-like duck type will behave differently. Such explicit "type
-of object" checks don't have to be supported.
-
-The following design rule applies everywhere builtin Python types are used
-within this API standard: _where a Python builtin type is specified, an
-implementation may always replace it by an equivalent library-specific type
-that duck types with the Python builtin type._
+Let's go through these arguments:
+- `skip_nulls: bool | Scalar`. This means we can either pass a Python `bool`, or
+  a `Scalar` object backed by a boolean;
+- the return value of `.mean()` is a `Scalar`
+- the argument `other` of `__gt__` is typed as `AnyScalar`, meaning that we can
+  compare a `DataFrame` with a Python scalar (e.g. `df > 3`) or with a `Scalar`
+  (e.g. `df > df.col('a').mean()`)
+- the return value of `__gt__` is a `Scalar`
+
+Returning values as `Scalar` allows scalars to reside on different devices (e.g. GPU),
+or to stay lazy (if a library allows it).
+
+## Example
+
+For example, if a library implements `FancyFloat` and `FancyBool` scalars,
+then the following should all be supported:
+```python
+df: DataFrame
+column_1: Column = df.col('a')
+column_2: Column = df.col('b')
+
+scalar: FancyFloat = column_1.std()
+result_1: Column = column_2 - column_1.std()
+result_2: FancyBool = column_2.std() > column_1.std()
+```
+
+Note that the scalars above are library-specific ones - they may be used to keep
+data on GPU, or to keep data lazy.
+
+The following, however, may raise, dependening on the
+implementation:
+```python
+df: DataFrame
+column = df.col('a')
+
+if column.std() > 0:  # this line may raise!
+    print('std is positive')
+```
+This is because `if column.std() > 0` will call `(column.std() > 0).__bool__()`,
+which is required by Python to produce a Python scalar.
+Therefore, a purely lazy dataframe library may choose to raise here, whereas as
+one which allows for eager execution may return a Python bool.