On the quintessential issue of Israeli settlements on the West Bank, exactly what was Prime Minister Menachem Begin's commitment to Jimmy Carter on the final night of the Camp David negotiations in September 1978?

That question has bedeviled every discussion of the Arab-Israeli "peace process" ever since. It has cropped up with every expansion of the Israeli presence on the West Bank by the "thickening" or addition of existing settlements.

Is Begin right in his claim that this proliferation of new settlements is no violation of his understanding with Carter? If so, that presents one sort of problem for Ronald Reagan's "initiative" to press on with the Camp David formula-- one that could conceivably be dealt with by some tighter understanding with Ronald Reagan. The exploitation of an honest misunderstanding is one thing.

But suppose Begin played fast and loose with Carter? If he never meant to clamp a moratorium on new settlements until the West Bank's "autonomy" had been settled by negotiation, then the futility of the Reagan Mideast "initiative"-- or any further effort to negotiate the West Bank's future--becomes inescapable.

So it is worth examining the new evidence available in the memoirs ("Hard Choices") of former Secretary of State Cyrus Vance, who was one of the five people in the room throughout that fateful, five-hour Saturday-night meeting. Vance's account offers solid reinforcement to the Carter version of what transpired--and a flat challenge to the official Israeli line.

The Israeli position has been that Begin never committed himself to anything more than a settlement freeze for the duration of a euphoric three-month timetable agreed to by Israel and Egypt for reaching agreement on their peace treaty (the second half of the Camp David accords). Jimmy Carter's recollection is diametrically different: In his memoirs ("Keeping Faith"), Carter insists that "my notes are clear--that the settlement freeze would continue until all negotiations were completed." By this he plainly meant negotiations not only on the Egyptian-Israeli peace treaty but on the first half of the Accords--the interim, five-year "full autonomy" for the West Bank.

The late Moshe Dayan, a third participant, concedes in his memoirs ("Breakthrough") that Carter did request "settlement be stopped during the peace negotiations," but concedes only that Begin agreed to "give it thought." He insists that the notes of another Israeli in the room, Aharon Barak, support his recollection.

Enter the fifth participant, Vance. He recalls that Begin was unwilling to sign an agreement with Egypt's President Anwar Sadat that tied Israel's hands on West Bank settlements. But, Vance writes, "Begin said he was finally willing to give President Carter a separate letter stating that Israel would establish no new settlements until the autonomy negotiations were completed. On that basis we agreed to drop from the draft comprehensive Accord our proposed language on a settlement moratorium."

This "side letter" technique was adopted in an effort to fudge a number of the more sensitive issues, such as the future state of Jerusalem. On Sunday night, Sept. 17, 1978, on live television in a dramatic White House ceremony, the Camp David Accords were signed. But by Monday, as Carter was preparing to report his triumph to a joint session of Congress, Begin's "side letter" on the West Bank settlements was the only one that still had not been received. When a U.S. negotiator inquired about the missing letter, he was told Begin was "redrafting it," Vance writes, adding:

"When the redrafted letter arrived Monday afternoon, it referred to a moratorium during the negotiations for a peace treaty between Egypt and Israel, i.e., three months. It was not until then--after the Accords had been signed and announced--that we realized that the prime minister was not going to carry through on the understanding we had reached with him the previous Saturday night. . . .

For its part, let it be noted, the Carter administration did little thereafter to press the point. But neither has Ronald Reagan pressed his insistence of last September on a settlement freeze. If Begin's game has the look of duplicity, the inability of two successive American administrations to prevail in a matter judged by both to be in the U.S. national interest has the look of impotency.