diff --git a/src/math_spec/dimensions.py b/src/math_spec/dimensions.py
index a9300c46..4b6e4541 100644
--- a/src/math_spec/dimensions.py
+++ b/src/math_spec/dimensions.py
@@ -222,7 +222,7 @@ def _dims_call(
             raise DimensionError(
                 f'{context}: {node.name}(over={over.name}) but the expression has dims {sorted(inner)}.'
             )
-        _check_named_amount(node, over.name, schema, context)
+        _check_named_amount(node, over.name, inner, schema, context)
         partition = node.kwargs.get('by')
         if partition is not None:
             assert isinstance(partition, LookupNode)
@@ -252,6 +252,20 @@ def _dims_call(
 #: rules below.
 _AMOUNTS = {'shift': ('offset', 'offset'), 'sum_back': ('within', 'width')}
 
+#: Why negating a named amount at the call site is not what the caller means.
+#: ``shift`` has a direction and keeps it in the data; a window's direction is
+#: its own name, and a width is a count, which has none.
+_NEGATED = {
+    'shift': (
+        'A named offset carries its sign in its values, so that one row pointing backwards says '
+        'so where the data is read — negate the column instead.'
+    ),
+    'sum_back': (
+        'A width counts positions and so has no direction; which way a window reaches is the '
+        "operator's own name rather than the sign of its width."
+    ),
+}
+
 #: Why a named amount that varies along the axis it walks is not the thing its
 #: operator claims to be.
 _VARIES = {
@@ -260,19 +274,24 @@ def _dims_call(
 }
 
 
-def _check_named_amount(node: FunctionCallNode, over: str, schema: Model, context: str) -> None:
-    """The two rules that hold of an ``offset=`` or ``within=`` naming a parameter.
+def _check_named_amount(node: FunctionCallNode, over: str, inner: frozenset[str], schema: Model, context: str) -> None:
+    """The rules that hold of an ``offset=`` or ``within=`` naming a parameter.
 
-    Both are about the *amount*, not about a dim set, but they live here
+    They are about the *amount* rather than about a dim set, but they live here
     because here is where the schema is in hand — a parameter's ``dtype`` and
-    its ``dims`` are read off the same declaration, and splitting the pair
-    across two passes would give one rule of a documented pair two voices.
+    its ``dims`` are read off the same declaration, and splitting a documented
+    set across two passes would give one rule of it several voices.
 
-    A literal is checked by the grammar already: it parses as a number and a
-    number carries no dims, so only a named amount can break either rule.
+    A literal breaks none of them: it parses as a number, and a number has
+    neither a dtype to declare nor dims to vary over.
     """
     kwarg, noun = _AMOUNTS[node.name]
     amount = node.kwargs[kwarg]
+    if isinstance(amount, UnaryOperatorNode) and isinstance(amount.operand, ParameterNode):
+        raise DimensionError(
+            f'{context}: {node.name}({kwarg}={amount.op}{amount.operand.name}) negates a named '
+            f'{noun}. {_NEGATED[node.name]}'
+        )
     if not isinstance(amount, ParameterNode):
         return
     declared = schema.parameters[amount.name]
@@ -290,6 +309,16 @@ def _check_named_amount(node: FunctionCallNode, over: str, schema: Model, contex
             f'carries it. A named {noun} that varies along the axis it walks is {_VARIES[node.name]} '
             f"— declare '{amount.name}' over dims '{over}' is not one of."
         )
+    partition = node.kwargs.get('by')
+    groups = frozenset(partition.into) if isinstance(partition, LookupNode) else frozenset()
+    if stray := sorted(frozenset(declared.dims) - inner - groups):
+        raise DimensionError(
+            f'{context}: {node.name}({kwarg}={amount.name}) reads its {noun} at the coordinate it '
+            f"walks, but '{amount.name}' varies over {stray}, which that coordinate does not carry "
+            f'(dims {sorted(inner)}). A dim the coordinate does not have is no coordinate at all — '
+            f"declare '{amount.name}' over dims the expression carries, or group by a lookup into "
+            f'one of {stray}, so that each group is reached by its own {noun}.'
+        )
 
 
 # ---------------------------------------------------------------------------
diff --git a/src/math_spec/typesetting/walk.py b/src/math_spec/typesetting/walk.py
index 2954b372..fd388cba 100644
--- a/src/math_spec/typesetting/walk.py
+++ b/src/math_spec/typesetting/walk.py
@@ -85,15 +85,19 @@
 
 
 def _amount(node: ArithmeticNode) -> int | str:
-    """``shift``'s ``by=``: a signed number, or the name of a parameter.
+    """``shift``'s ``offset=``: a signed number, or the name of a parameter.
 
     A negated literal parses as a unary minus over a number rather than as a
-    negative one, so reading the ``NumberNode`` alone both aborted on ``by=-1``
-    and left the forward direction of every translation operator unreachable.
-
-    A named offset comes back as its name. It is always backward — the language
-    refuses ``by=-p``, so the direction lives in the data — and it renders as
-    the parameter's own symbol rather than as a number.
+    negative one, so reading the ``NumberNode`` alone both aborted on
+    ``offset=-1`` and left the forward direction of every translation operator
+    unreachable.
+
+    A named offset comes back as its name. It is always backward, because a
+    negated one is refused at load — :func:`math_spec.dimensions.check_schema`,
+    so the direction lives in the data — and it renders as the parameter's own
+    symbol rather than as a number. The assert below is that rule's
+    precondition rather than a hope: before it was enforced, this raised a bare
+    ``AssertionError`` out of the typesetter on a model that had loaded clean.
     """
     if isinstance(node, ParameterNode):
         return node.name
@@ -241,8 +245,8 @@ def translation(self, step: _Step, group: str = '') -> str:
         the group the translation stays inside.
         """
         backward, forward = _TRANSLATIONS[step.policy]
-        # a named offset is always backward: `by=-p` is refused, so the sign is
-        # in the data and the operator cannot read it off the call
+        # a named offset is always backward: `offset=-p` is refused at load, so
+        # the sign is in the data and the operator cannot read it off the call
         operator = self.op(backward if isinstance(step.by, str) or step.by > 0 else forward)
         if step.fill:
             operator = self.format.subscript(operator, [step.fill])
diff --git a/tests/test_dimensions.py b/tests/test_dimensions.py
index 501998ff..1b32a56f 100644
--- a/tests/test_dimensions.py
+++ b/tests/test_dimensions.py
@@ -31,7 +31,11 @@
         'generator': {'values': ['wind', 'gas']},
         'bus': {'values': ['n', 's']},
     },
-    'lookups': {'gen_bus': {'over': 'generator', 'into': 'bus'}},
+    'lookups': {
+        'gen_bus': {'over': 'generator', 'into': 'bus'},
+        # over `snapshot`, so it can partition the axis the translations walk
+        'snap_bus': {'over': 'snapshot', 'into': 'bus'},
+    },
     'parameters': {
         'p_max': {'dims': ['generator']},
         'cost': {'dims': ['generator']},
@@ -40,6 +44,8 @@
         # need a parameter that obeys them and one that spans the axis walked
         'spinup': {'dims': ['generator'], 'dtype': 'int'},
         'horizon': {'dims': ['snapshot'], 'dtype': 'int'},
+        # over a dim `p` does not carry, so it is readable only through a `by=`
+        'bus_lead': {'dims': ['bus'], 'dtype': 'int'},
     },
     'variables': {'p': {'foreach': ['snapshot', 'generator'], 'bounds': {'lower': 0, 'upper': 'p_max'}}},
     'constraints': {
@@ -86,6 +92,9 @@ def test_the_base_model_typechecks():
         ("shift(p, over=snapshot, offset=1, edge='wrap')", {'snapshot', 'generator'}),
         ("shift(p, over=snapshot, offset=spinup, edge='wrap')", {'snapshot', 'generator'}),
         ('sum_back(p, over=snapshot, within=spinup)', {'snapshot', 'generator'}),
+        # the same offset a `by=` makes readable: one lag per group it maps into
+        ("shift(p, over=snapshot, offset=bus_lead, edge='wrap', by=snap_bus)", {'snapshot', 'generator'}),
+        ('sum_back(p, over=snapshot, within=bus_lead, by=snap_bus)', {'snapshot', 'generator'}),
     ],
 )
 def test_dim_inference(expr, expected):
@@ -157,6 +166,24 @@ def test_dim_inference(expr, expected):
             r'no longer "the last n"',
             id='a-named-width-does-not-span-the-summed-axis',
         ),
+        # Before this was refused, it loaded clean and then raised a bare
+        # `AssertionError` out of the typesetter (#62) — on the very rule
+        # `walk.py` reads a named offset as always-backward *because of*.
+        pytest.param(
+            "shift(p, over=snapshot, offset=-spinup, edge='wrap')",
+            r'negates a named offset',
+            id='a-named-offset-is-not-negated-at-the-call',
+        ),
+        pytest.param(
+            'sum_back(p, over=snapshot, within=-spinup)',
+            r'which way a window reaches is the operator',
+            id='a-named-width-has-no-direction-to-negate',
+        ),
+        pytest.param(
+            "shift(p, over=snapshot, offset=bus_lead, edge='wrap')",
+            r"varies over \['bus'\], which that coordinate does not carry",
+            id='a-named-offset-is-read-where-the-expression-has-a-coordinate',
+        ),
     ],
 )
 def test_an_ill_dimensioned_expression_is_rejected(expr, match):