Floor loading of hearth / stove

I will be installing a 700 lb. Woodstock Progress Hybrid on a hearth I built over an existing floor. My house was built in 1958 and has 2x10 solid pine floor joists with 3/4" solid pine subfloor and 3/4" solid oak flooring, all with no known or suspected deficiencies. I built the hearth on top of the oak flooring as it would have been a shame to remove it, plus I expect the 3/4" oak is adding considerable strength and/or rigidity to the entire installation. What I am not fully certain of is if the combined structure needs to be braced in any way. This area is over a basement and the 2x10 joists are spanning a little over 12' to 2x4 load bearing walls'. The stove & hearth is installed in the middle of this span and the hearth is 60" along the joist spans and 44" across the joist spans (so directly bearing on 3 of the 12' span joists). The hearth consists of 2 layers of 3/4" underlayment plywood screwed together in a 1 foot grid pattern for rigidity, 2 layers of 1/2" concrete backerboard for R value, and 1 layer of 1/4" ceramic tile The hearth is secured to the existing oak flooring / pine sublfoor with #10 deck screws at 9 evenly distributed locations. I expect the oak flooring and pine subflooring are further distributing this load but I am not an engineer. Does anyone have any education/training based feedback on whether this install is structurally acceptable without any additional joist support? With all due respect, I am not seeking any un-educated "I'd do this just to be safe" speculative recommendations. I could easily over-engineer additional bracing myself.

Thanks all for the feedback. To answer a few of your questions: The basement ceiling is finished but I believe it is acoustical tiles directly on the joists so probably no contribution to the structure. The joists are on 16" centers and are braced. The only ink stamps I can see look to read "82 PIB CONST", the PIB is questionable as the letters are crammed together in a ball shape. I don't know if that's a grade marking or simply a mill marking, however, the joists are very straight grained and to me appear to be choice old-growth lumber (was anything else available in 1958?).

There are 3 load-bearing walls in the basement which, along with a basement wall, form this central room. This central room is surrounded on 3 sides by additional rooms & utility areas beyond the load-bearing stud walls. All of the surrounding rooms are along the perimeter of the basement wall.

The stove is now installed and it does appear there may be a very slight deflection as a hairline crack has appeared in the grout joint between the hearth surface tile and the wall tile. Not the least bit alarming to me.

By the way, this old shack had a good shaking from the Oklahoma earthquakes last year. It creaked and groaned some but no cracks appeared anywhere. I never expected to feel an earthquake in this part of the world. The wife and I were sitting on the couch surfin when it sounded like strong wind gusts hit the house from all directions at the same time, then it just kept shaking for 15 or 20 seconds. Very interesting experience. The house is well-built, I have no question of that.