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The Cambridge-based company, which designs chips for devices from smartphones to game consoles, plans to list on New York's Nasdaq in September.
Arm did not reveal the number of shares for sale or the price, but its proposed initial public offering (IPO) could be the biggest listing this year.
Reports in January said Prime Minister Rishi Sunak had restarted talks with Arm's owner about listing on the London Stock Exchange.
But Arm's chief executive Rene Haas has said the company will keep its material intellectual property, headquarters and operations in the UK.
The latest filing shows further intent that Softbank is pushing ahead with the multi-billion dollar sale despite difficult conditions in the global financial markets.
Arm's sales declined to $2.68bn in the year ended 31 March, hurt by a slump in global smartphone shipments.