diff --git a/data_prototype/containers.py b/data_prototype/containers.py
index 4d87446..c278879 100644
--- a/data_prototype/containers.py
+++ b/data_prototype/containers.py
@@ -1,5 +1,15 @@
 from dataclasses import dataclass
-from typing import Protocol, Dict, Tuple, Optional, Any, Union, Callable, MutableMapping
+from typing import (
+    Protocol,
+    Dict,
+    Tuple,
+    Optional,
+    Any,
+    Union,
+    Callable,
+    MutableMapping,
+    TypeAlias,
+)
 import uuid
 
 from cachetools import LFUCache
@@ -16,6 +26,9 @@ def __sub__(self, other) -> "_MatplotlibTransform":
         ...
 
 
+ShapeSpec: TypeAlias = Tuple[Union[str, int], ...]
+
+
 @dataclass(frozen=True)
 class Desc:
     # TODO: sort out how to actually spell this.  We need to know:
@@ -24,12 +37,41 @@ class Desc:
     #   - is this a variable size depending on the query (e.g. N)
     #   - what is the relative size to the other variable values (N vs N+1)
     # We are probably going to have to implement a DSL for this (😞)
-    shape: Tuple[Union[str, int], ...]
+    shape: ShapeSpec
     # TODO: is using a string better?
     dtype: np.dtype
     # TODO: do we want to include this at this level?  "naive" means unit-unaware.
     units: str = "naive"
 
+    @staticmethod
+    def check_shapes(*args: tuple[ShapeSpec, "Desc"], broadcast=False) -> bool:
+        specvars: dict[str, int | tuple[str, int]] = {}
+        for spec, desc in args:
+            if not broadcast:
+                if len(spec) != len(desc.shape):
+                    return False
+            elif len(desc.shape) > len(spec):
+                return False
+            for speccomp, desccomp in zip(spec[::-1], desc.shape[::-1]):
+                if broadcast and desccomp == 1:
+                    continue
+                if isinstance(speccomp, str):
+                    specv, specoff = speccomp[0], int(speccomp[1:] or 0)
+
+                    if isinstance(desccomp, str):
+                        descv, descoff = speccomp[0], int(speccomp[1:] or 0)
+                        entry = (descv, descoff - specoff)
+                    else:
+                        entry = desccomp - specoff
+
+                    if specv in specvars and entry != specvars[specv]:
+                        return False
+
+                    specvars[specv] = entry
+                elif speccomp != desccomp:
+                    return False
+        return True
+
 
 class DataContainer(Protocol):
     def query(