No web page or browser extension can redraw what the address bar shows, in any browser, on any site. The bar is drawn by the browser itself, outside the page, specifically so a fake page can never wear a real address. Docognito changes how a tab looks inside that boundary and never past it.
What the address bar actually shows
The address bar is not part of the web page loaded inside it. A browser draws that strip itself, above the page, in a region no page script can reach. Whatever a tab contains, and however that content is styled, the bar keeps reporting the address the browser actually requested, claude.ai, chatgpt.com, your bank, or anything else. A page can rewrite every pixel inside its own frame. It has no channel to the strip sitting outside that frame, in any browser, on any device.
Why no page can reach outside its own frame
Every mainstream browser keeps a page and its own interface in separate compartments on purpose. Chrome, Firefox and Safari each implement this differently under the hood, but the boundary itself is not a Chrome habit or a Docognito limit. It is the security model the entire web runs on. A page gets a sandbox: its own document, its own script, its own styling, and nothing outside it. The address bar sits in the browser chrome, a separate layer the page's own JavaScript was never handed access to. No permission an extension can request changes that, because the browser does not expose an interface for it at all. The only thing that legitimately changes what the bar shows is the browser itself navigating to a new address, which is a real page load, not a disguise applied on top of one.
The reason the boundary exists
This is not an accidental gap somebody could patch. If a page could draw its own address bar, a fake bank login page could show a real bank's address while the underlying content sat on a completely different server, and a visitor would have no way to tell the two apart by looking. Preventing exactly that is why browsers reserve the strip and refuse every page, and every extension acting on a page's behalf, a way to write to it. The address bar is one of the few pieces of a browser interface whose entire value depends on the page never being able to touch it.
A disguise that could rewrite the bar would not be a better disguise
It would be the same weakness phishing has always relied on, aimed at a different target. The reason no legitimate extension does this is not caution. It is that the browser does not offer a way to do it at all.
The same boundary protects tabs, cookies and typed data
The address bar is not a special case carved out for this one problem. The same separation is why a page cannot read the cookies a different site set, cannot reach into a tab that is not its own, and cannot see what is typed into a banking site open two tabs over. A disguise running on claude.ai or chatgpt.com operates inside the same sandbox every other web page runs in, with the same restrictions applying everywhere else on the web. Nothing about a page pretending to be a document editor changes that. The address bar being out of reach is not a rule written for this one product. It is the general rule, holding here exactly the way it holds on every other site you visit.
What this means for a page disguise
Docognito changes the page, the tab title and the favicon, all of it inside the boundary a page is actually allowed to touch. the address bar, which still reads claude.ai or chatgpt.com, and it always will, because the alternative is the exact hole browsers exist to close. An earlier version of Docognito tried rewriting the visible path anyway, and the story of what that broke, and why the attempt was pulled, is covered on the page about hiding the address bar.
Judge the disguise by the tab, not the bar
A sceptical read of this page should end here. No browser will ever let a page, or an extension acting inside a page, draw its own address bar, because the entire anti-phishing model depends on that bar being trustworthy. Judge any disguise, this one included, by what it changes inside the tab, not by any claim about the bar above it. If a product ever tells you it hid the address bar itself, on any site, in any browser, that claim does not survive how browsers are built.