The first glimmers of progress surfaced Tuesday in Harrisburg, exactly three weeks after the July 1 deadline for Gov. Tom Wolf and the Republican-dominated General Assembly to adopt a state budget.

They’re right on schedule, too — not the official schedule of course, but rather the unofficial, rules-be-damned, “it’s the way we’ve always done things” schedule of their own keeping.

“We have . . . a better understanding of why the things that separate us separate us,” said Wolf, a first-year Democrat, emerging from four hours of budget talks with Republican House leaders.

House Speaker Mike Turzai, R-Allegheny, chimed in: “We want to get to an agreement, “but we realize there are some significant differences, but we had to get into the details and we did that today.”

What? Three weeks past deadline, and we’re just now getting into the details?

Apparently so. But there’s time left for that in Harrisburg, where rules don’t matter and deadlines are ignored.

Officially, the budget dance began March 3 when Wolf proposed $33.8 billion plan that beefed up education spending and cut local property taxes — two of Wolf’s campaign pledges. His budget was laden with tax increases and a few new taxes, most notably a 5 percent severance tax on Marcellus Shale gas wells.

Republicans rejected Wolf’s budget and, on the eve of the July 1 deadline they handed Wolf a budget of their own design — a zero-tax-increase, $30.1 billion budget.

The Republican plan had 401 line-item expenditures, including 274 that were equal to or greater than those in the governor’s budget. They sent along two companion bills, one to sell off the state liquor monopoly and the other to reform public pensions.

Wolf vetoed it all,

Tuesday’s meeting focused on the 127 budget items that Wolf wants to increase, said House Appropriations Chairman Bill Adolph, R-Delaware County.

The governor said the review and discussion gave him insight into the legislators’ priorities.

“There are still gulfs out there and we’re going to have to work through that, but . . . we have to come up with a budget that is good for the people who elected us, and we’re going to do that,” Wolf said.

Wolf declined to “even guess” how much longer the budget stalemate will go on.

The meeting focused on spending, the sort of process that historically has been done by staff, not by the governor and the leaders in person.

Wolf said the parties agreed to meet again soon. Maybe then the talk can turn from spending to revenue — the governor’s proposed $4.6 billion net tax increase.

In the end, Wolf won’t get all of that spending increase, but he will get some of it. The Republicans’ zero-increase budget is equally unrealistic, and they’ll have to make concessions, too.

That’s how budget negotiations work.

They’ll ultimately work that way in Harrisburg, too — just not on anybody’s official timetable.