From 7a062a6f5412a3dfd89824045a802f45619e232d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Petr=20Balv=C3=ADn?= <opensource@petrbalvin.org>
Date: Mon, 28 Sep 2026 13:34:52 +0200
Subject: [PATCH] fix(mathml): render a script without a base over an empty
 base

---
 CHANGELOG.md                   | 1 +
 internal/mathml/mathml_test.go | 6 ++++++
 internal/mathml/parse.go       | 6 ++++++
 3 files changed, 13 insertions(+)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index d032510..6364617 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,7 @@ this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.htm
 ### Fixed
 
 - A paragraph that follows a definition list, separated from it by a blank line, is no longer swallowed into the `dl` element: the list ends before it, and terms after the paragraph open a list of their own.
+- A superscript or subscript without a base, the isotope notation of `^3He`, renders over an empty base instead of degrading to an merror.
 
 ### Added
 
diff --git a/internal/mathml/mathml_test.go b/internal/mathml/mathml_test.go
index d0bd2e4..8cbc29e 100644
--- a/internal/mathml/mathml_test.go
+++ b/internal/mathml/mathml_test.go
@@ -37,6 +37,12 @@ var corpus = []struct {
 	{"sqrt", `\sqrt{x}`, `<msqrt><mi>x</mi></msqrt>`},
 	{"root with index", `\sqrt[3]{x}`, `<mroot><mi>x</mi><mn>3</mn></mroot>`},
 	{"sub and sup", `x_1^2`, `<msubsup><mi>x</mi><mn>1</mn><mn>2</mn></msubsup>`},
+	{"baseless sup", `^3\mathrm{He}`,
+		`<msup><mrow></mrow><mn>3</mn></msup><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">e</mi></mrow>`},
+	{"baseless sub", `_1\mathrm{H}`,
+		`<msub><mrow></mrow><mn>1</mn></msub><mi mathvariant="normal">H</mi>`},
+	{"baseless group", `^{-3}`,
+		`<msup><mrow></mrow><mrow><mo>-</mo><mn>3</mn></mrow></msup>`},
 	{"single digit script", `x^10`, `<msup><mi>x</mi><mn>1</mn></msup><mn>0</mn>`},
 	{"group", `{xy}`, `<mrow><mi>x</mi><mi>y</mi></mrow>`},
 	{"left right", `\left( x \right)`,
diff --git a/internal/mathml/parse.go b/internal/mathml/parse.go
index f86e198..29f364e 100644
--- a/internal/mathml/parse.go
+++ b/internal/mathml/parse.go
@@ -128,6 +128,12 @@ func (p *parser) atom() *node {
 			return nil
 		}
 		return p.scripts(n)
+	case tokCaret, tokUnderscore:
+		// A script without a base, the isotope notation of ^3He, takes
+		// an empty base: the script renders over nothing, the way the
+		// notation is printed, and degrading it would refuse notation
+		// the mathematics carries.
+		return p.scripts(el("mrow"))
 	}
 	p.pos++
 	return errorNode(t.text)