Even though the circus has come to town in Singapore this week with performers Donald Trump and Kim Jong Un and various supporting actors, it can distract from the serious business of Korea after World War 2. Since governments present themselves through documents claiming to authorize their creation, and more papers are said to establish laws, departments, organizations, decrees, and orders that people are expected to follow, the documents about Korea after Japan officially lost it as a colony following the Second World War are important. However, they are hard to find .
The U.S. Government Printing Office, now called the publishing office, no longer prints treaties and agreements, and from what I have been able to find out, does not publish them in digital form. I think the reason is that Congress did not give the printing/publishing office money to do so. The State Department is now supposed to publish them, but only more recent ones, starting in 1996; some of them amend earlier treaties. The Library of Congress is trying to get all treaties also published in digital form, but is still working on the period from 1950-1984 and has not yet finished .
Although not emphasized to the public in the past, Congress did not declare war to start the U.S. involvement in the Korean War (there was a United Nations resolution), and no treaty was signed to conclude it. As a technical legal matter, the Korean War has not ended. There was an "agreement concerning a military armistice in Korea, with annex," and a "temporary agreement supplementary to the armistice agreement in Korea," signed at Panmunjom on 27 July 1953.
Citations to treaties and agreements regarding Korea are usually done in the form of: [number] UST [number], and TIAS [number]. UST refers to the "United States Treaties and Other International Agreements", which is a bound volume made up of the individual documents. TIAS refers to "Texts of International Agreements" and "Treaties and Other International Acts Series", and is the individual treaty or agreement published as a separate item, which would then became part of the bound volume, the UST.
Here is a list of documents from my brief research I think are relevant to the time frame of the Korean conflict.
1. Agreement concerning interim military and security matters during the transitional period. Signed at Seoul August 24, 1948. Entered into force August 24, 1948. 62 Stat. 3817; TIAS 1918; 9 Bevans 477; 79 UNTS 57.
2. Mutual defense assistance agreement. Signed at Seoul January 26, 1950. Entered into force January 26, 1950. 1 UST 137; TIAS 2019; 80 UNTS 205.
3. United Nations resolutions 82 of 25 June 1950, 83 of 27 June 1950, and 84 of 7 July 1950, which were used to justify or support military action in Korea by the U.S. and others against North Korea, under the unified command of the U.S.; there was no declaration of war by Congress–
4. Agreement relating to the assurances required by the Mutual Security Act of 1951. Exchange of notes at Pusan January 4 and 7, 1952. Entered into force January 7, 1952. 3 UST 4619; TIAS 2612; 179 UNTS 105.
5. Agreement concerning a military armistice in Korea, with annex. Signed at Panmunjom July 27, 1953, by the Commander-in-Chief, United Nations Command; the Supreme Commander of the Korean People’s Army; and the Commander of the Chinese People’s Volunteers; entered into force July 27, 1953. 4 UST 234; TIAS 2782.
Notice that South Korea (the Republic of Korea) did not sign the armistice.
6. Temporary agreement supplementary to the armistice agreement in Korea. Signed at Panmunjom July 27, 1953, by the Commander-in-Chief, United Nations Command; the Supreme Commander of the Korean People’s Army; and the Commander of the Chinese People’s Volunteers; entered into force July 27, 1953. 4 UST 346; TIAS 2782.
7. Mutual defense treaty. Signed at Washington October 1, 1953. Entered into force November 17, 1954. 5 UST 2368; TIAS 3097; 238 UNTS 199–
The date a war ends can vary, depending on the activity being looked at and when it is concluded. Although the Korean armistice was signed on 27 July 1953, the U.S. government describes the conflict as starting on 27 June 1950 and ending on 31 January 1955. This is the time period for determining Veterans' pension and disability benefits and concerning the Department of Veterans Affairs. Here is a useful paper from 2017 by the Congressional Research Service with time periods of U.S. conflicts starting with the Indian Wars beginning in 1817 to the murky military action regarding ISIS/Islamic State, which is continuing–
UPDATE: Although the publicized focus of the summit is about North Korea and nuclear weapons, there are other issues that from North Korea's perspective would need to be settled. Each year the State Department puts out a publication called "Treaties in Force". This year it lists treaties and agreements in effect as of 1 January 2018, and is 595 pages long. The list is divided into agreements with one other country (bilateral) and with more than one (multilateral). The bilateral section is presented by countries and then the subjects of the agreements for each country. For South Korea, the list is seven and a half pages, and treaties and agreements still in effect run from 1948 to 2017. There are five relating to atomic energy and 48 about defense. The Korea agreements are on pdf pages 273-280.
Whether or not Trump realizes it, the multi-faceted Korea issue is not just another New York City real estate transaction or licensing his name to a building that someone else constructs and shoulders the financing and risk.
The foolish Senator Lindsey Graham of South Carolina said on the ABC "This Week" television program of yesterday (10 June) that: "there are ultimately three possible outcomes to President Trump's negotiations with North Korea's Kim Jong Un: 'Peace, where we have a win-win solution; military force where they — we devastate the North Korean regime and stop their program by force; or to capitulate like we've done in the past.' He said that Trump was not going to capitulate. Graham, of course, was an Air Force JAG lawyer operating in the structured and quite comfortable legal system, and is ignorant of actual combat with no personal experience in the violence and destruction of war–
 State Department general information about treaties and agreements–
 The Library of Congress page about treaties–