In the Kharkiv-Northern Donetsk-Western Luhansk direction the Russians are still clinging to Lyman. Here's
Andrew Perpetua's map. Most other OSINT maps are quite similar.
If one were to zoom out a little, it would be immediately apparent why the Russians want to hold Lyman.
The Ukrainians want to liberate Svatove to gain control of transport routes, outflank Russian positions to the south around Severodonetsk, and as another step on the way to Starobilsk. Starobilsk's liberation would in turn cut the last Russian rail route from the north - which runs from Valyuki down through Starobilsk to the Siverskyi Donets near Luhansk. Additionally, Svatove and Starobilsk are both in north-south valleys flanked by escarpments, those escarpments, like most of those in eastern Ukraine, having the steep side to the east. These would make ideal positions for a Ukrainian defensive line to secure the liberated territory.
But the Ukrainians can't advance on Svatove safely yet. If they were to do so, it would leave Lyman on their flank, threatening the flank of such an advance. However, much as the Russians
want to hold Lyman, the question remains as to whether or not they can hold Lyman. There's been various reports of troops being partially encircled, with Ukrainian fire control over their GLOCs.
The Ukrainians aren't so far from reaching the Zherebets river (highlighted in cyan on this map) to the north of Lyman. If they were able to also reach Zarichne, that would limit Russian lines of retreat to those over the Zherebets. The Zherebets may not be the most formidable obstacle, and several crossings are marked, however, retreating by these crossings would still funnel the Russians into corridors within range of the Ukrainian artillery. After the Russian treachery at Illovaisk, I can imagine the Ukrainians would quite like to shell some retreating invaders.
It's quite possible we may see another Balakliya-Kupyans'k-Izyum type rout here, should the encirclement succeed or appear about to succeed, where the Russians, rather than risking the above scenario of retreat under fire, steal civilian vehicles and abandon their equipment*.
I AM NOT SAYING THIS WILL HAPPEN. I'm saying it
could happen.
Meanwhile in the south, the eternal question of the war - What Airdefence Doing? - continues to plague the Russian.
Here, a pair of Su-24 "Fencers" conduct a low level bombing run with parachute retarded bombs. Usual warnings about combat footage apply. The attack definitely struck a Russian tank, but it's likely there were more vehicles there or Ukraine wouldn't have sent a pair of Fencers. This is something MANPADS struggle with. Those Sukhois came through low, and very fast. The Igla does not lock on instantly, and has a short range. Finally, both planes released flares during the attack.
Nonetheless, from a Russian perspective, attacks like that oughtn't be possible. However, their air defence is probably more degraded west of the Dnipro than it is anywhere else on the front. They may have tried to reinforce air defences in this area, as there are claims that three Pantsirs were destroyed trying to cross the Dnipro on a barge, though I can't verify this claim.
*
Russian losses round Izyum are still being documented, and Russian losses round Kupyans'k apparently haven't even been largely recorded yet. What's recorded so far, though, is the loss of hundreds of tanks and infantry fighting vehicles and significant quantities of artillery and ammunition, such that the Ukrainians captured rather more functional materiel than they lost in that offensive.