Zero-width and invisible
FUNCTION APPLICATION (U+2061)
An invisible mathematical operator meaning "apply this function to this argument": the silent operator between f and (x).
- Codepoint
U+2061- Also written as
u2061\u2061⁡- Category
- Zero-width and invisible
- Removed by default
- Yes
- Governing option
- No option needed
- Can be load-bearing
- No
Copy and paste U+2061
To copy and paste FUNCTION APPLICATION (U+2061), press the button: the character itself goes to your clipboard, and Ctrl+V (Cmd+V on a Mac) pastes it anywhere you can type.
Where it comes from
MathML and equation editors emit it so that a formula can be read aloud and evaluated correctly. It leaks into prose when an equation is copied out of a document and pasted as plain text.
Why it matters
In prose it is an invisible character with no meaning, and it is one of four adjacent codepoints that hidden-payload tools use as a ready-made alphabet.
Before and after
Copied out of an equation editor, the invisible operator comes with it.
The character is shown as a labelled chip so you can see where it sits. In your text it draws nothing at all.
When it is legitimate
Inside real MathML, where semantics matter. Plain text has no formula tree for it to describe.
How to remove it
The default pass removes it, wherever it appears. There is no context in plain text where an invisible operator is doing a job.
Working in a file rather than a paste? The document report for .docx, .odt and .html finds it inside the file, together with hidden runs and tracked changes, without you having to open it. If the question is what the rest of the writing does rather than what this one character does, measure sentence-length variation and see where each habit sits, with no score and no claim about who wrote the text.
Is it an AI watermark?
Used to hide data, but is not a watermark
No. It is a maths markup character. Its appeal to payload tools is that four invisible operators sit next to each other, which makes a compact alphabet. That is a property of Unicode, not of any model.
A known carrier for deliberately hidden payloads. Someone put it there on purpose, which is a different question from who wrote the words.
Questions
Will removing it break my equations?
Not in plain text. In real MathML the operator carries semantics, so clean the exported text rather than the source document.
What are the other three?
U+2062 INVISIBLE TIMES, U+2063 INVISIBLE SEPARATOR and U+2064 INVISIBLE PLUS. All four are removed by the default pass.
Check your own text
Paste anything into the cleaner to see every hidden character it contains, with position, codepoint and what happens to each one. Nothing is uploaded.
Check your own textClean it in Chrome as you pasteClean it on your Mac with one keystrokeAll characters