Increasingly it appears that the most intriguing aspect of the new Gorbachev disarmament proposal is its approach to verification. The phrasing is broad and the fine print is a long way from being negotiated. But the suggested provisions appear to move toward meeting some part of the American concern about Soviet cheating. The effect could be to ease some of the general American hesitation to consider Moscow's substantive terms -- a development that will please some in the administration and trouble others.

General Secretary Mikhail Gorbachev did not do the usual Soviet thing on Jan. 15. He did not go through the motions of dismissing American complaints of Soviet noncompliance with past arms control agreements. He did not contend that American toughness on verification amounts either to spying or to torpedoing otherwise reachable agreements. Nor did he stand pat on the Kremlin's stingy past formulas and on its tendency to dole out verification as a reward of sorts only for progress toward full disarmament.

Instead, Gorbachev, extending earlier initiatives, put his stamp on an approach to verification going well beyond the "national technical means" -- the electronic eyes and ears with which each side spies on the other -- that are the standard Soviet prescription.

He offered on-site inspections and "any other additional verification measures" to police the destruction and limitation of strategic arms; on-site inspections "whenever necessary" to police a full test ban; on-site inspections to ban chemical weapons and their industrial base, and "permanent verification posts" for European troop cuts. Earlier, he had offered to open Soviet labs to verify a ban on space-based weapons; this followed a Reagan open-labs offer meant to show that his Strategic Defense Initiative is no threat to Moscow.

On-site inspection: If in the Soviet mind this is the synonym for intrusiveness, in the American mind it is the standard of good-faith dealing. The experts know its limitations: Michael Krepon points out that even if the Russians met the administration's ambitious reach for "anytime, any place" inspections, other verification measures -- some yet more intrusive -- may still be required. So the "other additional measures" that Gorbachev alluded to may turn out to be more important, and harder to negotiate, than on-site inspections.

At worst, what Gorbachev says is propaganda. At best, it is a sign that Moscow recognizes the reality if not the legitimacy of the American preoccupation with compliance and verification and that it is going to try to meet it in some measure. The difference between worst and best may lie as much in the American response as in Gorbachev's intent, whatever that may be. A stiff, scoffing response could diminish his offer; a skeptical but respectful hearing could firm it up.

In the past the Soviets have resisted verification; their custom and culture encourage secrecy and suspicion in dealing with foreigners, and their policy has contained a bent for deception. Now the question is whether Gorbachev perceives verification as the central element that the American political culture and the current American political scene make it out to be.

If he does, then the already-tense arms control deliberations of the Reagan administration may become tenser. For the more reasonable Gorbachev is on verification, the harder it will be to keep the image of Soviet cheating as an obstacle to serious negotiation.

The hard-liners, their eye on the slipperiness of the slope, are right: Just by starting down the summit path, Reagan undercut his earlier view that the Soviets are an unworthy negotiating partner. As he has gotten a bit of the arms control bug, it has become more difficult to argue that the Soviet compliance record on old agreements is reason to fend off Soviet proposals for new ones. Hard-liners resist steering compliance complaints into the available negotiating forum, and keep trying to raise American verification demands beyond Soviet reach, but in the post-Geneva atmosphere of expectation, there is a limit to those tactics, too.

Soviet violations matter. They may not matter much militarily at least for now, or so most conservatives and military people appear to believe, but they sure do matter politically by feeding distrust and fear. They impose on any Soviet leader who is interested in an agreement a stern requirement for openness. If Gorbachev recognizes he has to meet it, that's to the good.