Under "Born Secret" doctrine, the answer is different. In those cases, the government does not designate information as classified; the information is classified without any action being taken by the government. But it's too narrow to be applied to just any information that could be classified. As originally enacted (the statute has been moved to somewhere else in the U.S. Code, and I can't find it), the Atomic Energy Act of 1946's Born Secret provisions only apply to disclosures of:

• "data concerning the manufacture or utilization of atomic weapons, the production of fissionable material, or the use of fissionable material in the production of power";
• made "with intent to injure the United States or with intent to secure an advantage to any foreign nation" or with knowledge that another will use the information with such an intent.

So if an inventor revealed the existence of the atomic weapon she invented, but not data concerning its manufacture, that shouldn't implicate Born Secret. Or if the inventor revealed data concerning the manufacture of the invention, but did reasonably believed that the data would not be used to injure the United States or secure an advantage with a foreign nation, that should also be permissible.

Of course, all of this assumes that Born Secret or the Invention Secrecy Act can withstand a First Amendment analysis, which is hardly certain. Under Bartnicki v. Vopper, 532 U.S. 514, 527 (2001) "state action to punish the publication of truthful information seldom can satisfy constitutional standards." There's obviously a strong argument to be made that an atomic bomb how-to would be a good exception. This was the subject of United States v. Progressive, which was never resolved.

Both restrictions also implicate the Fifth Amendment's Takings Clause, though the Invention Secrecy Act makes some provisions for compensation to the inventor.

Born Secret
Under "Born Secret" doctrine, the answer is different. In those cases, the government does not designate information as classified; the information is effectively classified without any action being taken by the government. But it's too narrow to be applied to just any information that could be classified.

Here's how it works:

1. First, it applies only to "restricted data," defined as "all data concerning (1) design, manufacture, or utilization of atomic weapons; (2) the production of special nuclear material; or (3) the use of special nuclear material in the production of energy." 42 USC § 2014.
2. Then it imposes restrictions on anyone "having possession of, access to, control over, or being entrusted with any document, writing, sketch, photograph, plan, model, instrument, appliance, note, or information involving or incorporating Restricted Data." Under 42 USC § 2274, it is a felony if that person:

• "communicates, transmits, or discloses the same ... with intent to injure the United States or with intent to secure an advantage to any foreign nation" or
• "communicates, transmits, or discloses the same ... with reason to believe such data will be utilized to injure the United States or to secure an advantage to any foreign nation."

1. It also includes a broader provision prohibiting the disclosure of restricted data regardless of purpose, but it only applies to federal employees, contractors, and the like. 42 USC § 2277.

So the law applies to anyone with "possession of ... any ... instrument ... or information involving or incorporating Restricted Data," and restricted data is "data concerning ... manufacture ... of atomic weapons." If our inventor had developed a 3-D atomic bomb printer, she would have possession of an instrument and information involving data concerning the manufacture of atomic weapons. She would therefore be covered under the law.

That means that she would be prohibited from disclosing any restricted data, but only if:she made the disclosure because she was trying to injure the United States or to help a foreign nation, or if she knew that disclosing the data would have that information.

Selling the data to North Korea would obviously be a problem in that case, but it sounds as though a simple announcement of the fact that she had successfully built the device would not violate the Act, as that would not actually be disclosure of "data" concerning the manufacture of atomic weapons.

Even the disclosure of the data itself would not necessarily violate the law. If she shared it with someone to facilitate a collaboration on improvements to the device, that shouldn't be a problem unless she knew that the collaborator was trying to injure the United States or help a foreign nation. On the other hand, simply taking all the data and posting it to the Internet probably would be a violation, as anyone doing so would know that it would then be used by foreign nations to their own advantage.

Constitutional limitations
Of course, all of this assumes that Born Secret or the Invention Secrecy Act can withstand a First Amendment analysis, which is hardly certain. Under Bartnicki v. Vopper, 532 U.S. 514, 527 (2001) "state action to punish the publication of truthful information seldom can satisfy constitutional standards." There's obviously a strong argument to be made that an atomic bomb how-to would be a good exception. This was the subject of United States v. Progressive, which was never fully resolved.

Both restrictions also implicate the Fifth Amendment's Takings Clause, though the Invention Secrecy Act makes some provisions for compensation to the inventor.