diff --git a/in2lambda/validation/__init__.py b/in2lambda/validation/__init__.py
new file mode 100644
index 0000000..2cdfba6
--- /dev/null
+++ b/in2lambda/validation/__init__.py
@@ -0,0 +1,37 @@
+"""Pre-flight checks for the ``#``/``##`` markdown that flows through in2lambda.
+
+The markdown produced by the wizard (and hand-written by users) is the shared
+contract between the wizard, the ``Markdown`` filter and Lambda Feedback. These
+checks catch structural mistakes - currently unbalanced/misplaced math
+delimiters - before the markdown is converted.
+"""
+
+from in2lambda.validation.delimiters import MathDelimiterError, math_delimiter_checker
+
+__all__ = ["MathDelimiterError", "math_delimiter_checker", "check_markdown"]
+
+
+def check_markdown(md_content: str) -> list[MathDelimiterError]:
+    """Run every markdown check and return the problems found.
+
+    Args:
+        md_content: The markdown text to validate.
+
+    Returns:
+        A list of :class:`MathDelimiterError` members, one per problem found.
+        An empty list means the markdown passed every check.
+
+    Examples:
+        >>> from in2lambda.validation import check_markdown
+        >>> check_markdown("Inline $x = y$ is fine.")
+        []
+        >>> check_markdown("Unbalanced $x = y")
+        [<MathDelimiterError.MISSING_CLOSING_SINGLE_DOLLAR: 'unclosed inline $ ... $'>]
+    """
+    problems: list[MathDelimiterError] = []
+
+    result = math_delimiter_checker(md_content)
+    if result is not MathDelimiterError.PASSED:
+        problems.append(result)
+
+    return problems
diff --git a/in2lambda/validation/delimiters.py b/in2lambda/validation/delimiters.py
new file mode 100644
index 0000000..6824b99
--- /dev/null
+++ b/in2lambda/validation/delimiters.py
@@ -0,0 +1,119 @@
+"""Checks that ``$ ... $`` and ``$$ ... $$`` math delimiters are balanced and placed correctly.
+
+KaTeX (and Lambda Feedback) expect inline math wrapped in single dollar signs on
+one line, and display math wrapped in ``$$`` that each sit alone on their own
+line. This module scans markdown character by character and reports the first
+delimiter mistake it finds.
+"""
+
+from enum import Enum
+
+
+class MathDelimiterError(Enum):
+    """Outcome of :func:`math_delimiter_checker`.
+
+    ``PASSED`` means no problem was found; every other member describes a
+    specific delimiter mistake. The value is a short human-readable message
+    suitable for showing on the command line.
+    """
+
+    PASSED = "ok"
+    MISSING_NEWLINE_BEFORE_OPENING_DISPLAY = "opening $$ must start its own line"
+    MISSING_NEWLINE_AFTER_OPENING_DISPLAY = "opening $$ must be followed by a newline"
+    DOUBLE_DOLLAR_INSTEAD_OF_CLOSING_SINGLE = "inline $ ... $ closed with $$"
+    MISSING_CLOSING_DOUBLE_INSTEAD_OF_SINGLE = (
+        "display $$ ... $$ closed with a single $"
+    )
+    MISSING_NEWLINE_BEFORE_CLOSING_DISPLAY = "closing $$ must start its own line"
+    MISSING_NEWLINE_AFTER_CLOSING_DISPLAY = "closing $$ must be followed by a newline"
+    INVALID_NEWLINE_INSIDE_INLINE = "newline inside an inline $ ... $ expression"
+    MISSING_CLOSING_SINGLE_DOLLAR = "unclosed inline $ ... $"
+    MISSING_CLOSING_DOUBLE_DOLLAR = "unclosed display $$ ... $$"
+
+
+def math_delimiter_checker(md_content: str) -> MathDelimiterError:
+    r"""Scan markdown for the first math-delimiter mistake.
+
+    ``\$`` is treated as a literal dollar sign, not a delimiter.
+
+    Args:
+        md_content: The markdown text to check.
+
+    Returns:
+        ``MathDelimiterError.PASSED`` if the delimiters are well formed,
+        otherwise the member describing the first problem found.
+
+    Examples:
+        >>> from in2lambda.validation.delimiters import math_delimiter_checker
+        >>> math_delimiter_checker("An inline $x = y$ expression.")
+        <MathDelimiterError.PASSED: 'ok'>
+        >>> math_delimiter_checker("Display:\n$$\nx = y\n$$")
+        <MathDelimiterError.PASSED: 'ok'>
+        >>> math_delimiter_checker("This costs \\$5, no math here.")
+        <MathDelimiterError.PASSED: 'ok'>
+        >>> math_delimiter_checker("Broken $x = y")
+        <MathDelimiterError.MISSING_CLOSING_SINGLE_DOLLAR: 'unclosed inline $ ... $'>
+    """
+    # False once we are inside a math expression and awaiting its closing delimiter.
+    expect_open_delimiter = True
+    # While inside an expression, whether it opened with a single "$" (inline) or "$$" (display).
+    expect_single_dollar = True
+
+    idx = 0
+    while idx < len(md_content):
+        prev_character = md_content[idx - 1] if idx > 0 else None
+        character = md_content[idx]
+        next_character = md_content[idx + 1] if idx + 1 < len(md_content) else None
+
+        if character == "$" and prev_character != "\\":
+            if expect_open_delimiter:
+                expect_open_delimiter = False
+
+                if next_character == "$":
+                    next_next_character = (
+                        md_content[idx + 2] if idx + 2 < len(md_content) else None
+                    )
+                    # "$$" must sit alone on its own line.
+                    if prev_character != "\n" and prev_character is not None:
+                        return MathDelimiterError.MISSING_NEWLINE_BEFORE_OPENING_DISPLAY
+                    if next_next_character != "\n":
+                        return MathDelimiterError.MISSING_NEWLINE_AFTER_OPENING_DISPLAY
+
+                    expect_single_dollar = False
+                    idx += 1  # Skip the second "$"; the loop increments idx again.
+                else:
+                    expect_single_dollar = True
+            else:
+                expect_open_delimiter = True
+
+                if expect_single_dollar and next_character == "$":
+                    return MathDelimiterError.DOUBLE_DOLLAR_INSTEAD_OF_CLOSING_SINGLE
+
+                elif not expect_single_dollar:
+                    if next_character != "$":
+                        return (
+                            MathDelimiterError.MISSING_CLOSING_DOUBLE_INSTEAD_OF_SINGLE
+                        )
+
+                    next_next_character = (
+                        md_content[idx + 2] if idx + 2 < len(md_content) else None
+                    )
+                    if prev_character != "\n" and prev_character is not None:
+                        return MathDelimiterError.MISSING_NEWLINE_BEFORE_CLOSING_DISPLAY
+                    if next_next_character != "\n" and next_next_character is not None:
+                        return MathDelimiterError.MISSING_NEWLINE_AFTER_CLOSING_DISPLAY
+
+                    idx += 1  # Skip the second "$"; the loop increments idx again.
+
+        # A newline may not appear inside an inline "$ ... $" expression.
+        elif character == "\n" and not expect_open_delimiter and expect_single_dollar:
+            return MathDelimiterError.INVALID_NEWLINE_INSIDE_INLINE
+
+        idx += 1
+
+    if expect_open_delimiter:
+        return MathDelimiterError.PASSED
+    elif expect_single_dollar:
+        return MathDelimiterError.MISSING_CLOSING_SINGLE_DOLLAR
+    else:
+        return MathDelimiterError.MISSING_CLOSING_DOUBLE_DOLLAR
diff --git a/tests/test_validation.py b/tests/test_validation.py
new file mode 100644
index 0000000..e624e4a
--- /dev/null
+++ b/tests/test_validation.py
@@ -0,0 +1,88 @@
+"""Tests for the math-delimiter checker.
+
+Ported from ``conversion2025/tools and testing/validator_tests.py`` on the
+``Summer2025`` branch and adapted to the :class:`MathDelimiterError` enum.
+"""
+
+import pytest
+
+from in2lambda.validation import (
+    MathDelimiterError,
+    check_markdown,
+    math_delimiter_checker,
+)
+
+E = MathDelimiterError
+
+VALID = [
+    "This is an inline math expression: $x = y$.",
+    "This is an inline math expression: $x = y$",
+    "$x = y$, this is an inline math expression.",
+    "$x = y$\n",
+    "\n$x = y$",
+    "First expression $x = y$ and second expression $a = b$.",
+    "Expression: $\\alpha + \\beta = \\gamma$.",
+    "This is a display math expression:\n$$\nx = y\n$$",
+    "$$\nx = y\n$$\n, this is a display math expression.",
+    "Display math:\n$$\nx = y\n\na = b\n$$",
+    "Expression:\n$$\n$$",
+    "Inline $x = y$ and display math:\n$$\nx = y\n$$",
+    "First:\n$$\nx = y\n$$\nSecond:\n$$\na = b\n$$",
+    "",
+    "This is just regular text with no math expressions.",
+    "This costs \\$5 and that costs \\$10.",
+    "Price is \\$10 and math is $x = y$.",
+    "Price \\$100:\n$$\nx = y\n$$",
+    "This symbol \\$\\$ is not math.",
+    "\\$100 is expensive.",
+    "It costs \\$",
+    "Price \\$50 for $x + y = z$ calculation.",
+    "Expression: $cost = \\$100$.",
+    "Display:\n$$\ncost = \\$100\n$$",
+]
+
+INVALID = [
+    ("This is an inline math expression: $x = y.", E.MISSING_CLOSING_SINGLE_DOLLAR),
+    ("This is an inline math expression: x = y$.", E.MISSING_CLOSING_SINGLE_DOLLAR),
+    ("This is an inline math expression:$x \n= y$.", E.INVALID_NEWLINE_INSIDE_INLINE),
+    ("This is an inline math expression:$\nx = y$.", E.INVALID_NEWLINE_INSIDE_INLINE),
+    ("This is an inline math expression:$x = y\n$.", E.INVALID_NEWLINE_INSIDE_INLINE),
+    ("Expression $x = y$$.", E.DOUBLE_DOLLAR_INSTEAD_OF_CLOSING_SINGLE),
+    ("Expression $x = y$ and $a = b$ and $c =", E.MISSING_CLOSING_SINGLE_DOLLAR),
+    ("Expression $$$x = y$$$.", E.MISSING_NEWLINE_BEFORE_OPENING_DISPLAY),
+    (
+        "This is a display math expression:\n$$\nx = y\n",
+        E.MISSING_CLOSING_DOUBLE_DOLLAR,
+    ),
+    (
+        "This is a display math expression:\nx = y\n$$",
+        E.MISSING_NEWLINE_AFTER_OPENING_DISPLAY,
+    ),
+    (
+        "This is a display math expression:$$\nx = y\n$$.",
+        E.MISSING_NEWLINE_BEFORE_OPENING_DISPLAY,
+    ),
+    (
+        "This is a display math expression:\n$$\nx = y\n$$.",
+        E.MISSING_NEWLINE_AFTER_CLOSING_DISPLAY,
+    ),
+    ("Expression:\n$$text\nx = y\n$$", E.MISSING_NEWLINE_AFTER_OPENING_DISPLAY),
+    ("Expression:\n$$\nx = y\ntext$$", E.MISSING_NEWLINE_BEFORE_CLOSING_DISPLAY),
+    ("Expression $$x = y$.", E.MISSING_NEWLINE_BEFORE_OPENING_DISPLAY),
+    ("Expression $x = y$$", E.DOUBLE_DOLLAR_INSTEAD_OF_CLOSING_SINGLE),
+    ("Expression $$x = y$", E.MISSING_NEWLINE_BEFORE_OPENING_DISPLAY),
+]
+
+
+@pytest.mark.parametrize("content", VALID)
+def test_valid_markdown_passes(content: str) -> None:
+    assert math_delimiter_checker(content) is E.PASSED
+    assert check_markdown(content) == []
+
+
+@pytest.mark.parametrize("content, expected", INVALID)
+def test_invalid_markdown_is_reported(
+    content: str, expected: MathDelimiterError
+) -> None:
+    assert math_delimiter_checker(content) is expected
+    assert check_markdown(content) == [expected]