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Ghostchars

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
Removed by default
Yes
Governing option
No option needed
Can be load-bearing
No

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

BeforefU+2061(x)
Afterf(x)

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.

Is it an AI watermark?

Used to hide data — 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 textAll characters