To answer your question about her level of culpability for the war breaking out, I'd like to ask you to further expand on the question. Do you mean to say she caused the Arab invasion in some way? Or that she made the war possible? What precisely are you asking about there?

As for the unpreparedness, it is fair to say Meir holds a fair amount of culpability. Israel's voters certainly thought so, and Israel elected its first non-Labour government in its history since 1948 not long after the war, in 1977.

The biggest reason she shares culpability is because she was part of what has been referred to as a "feedback loop" reinforcing prejudices, namely the belief by Israeli political and intelligence leaders that the Arab world would not dare attack given Israel's decisive victory in 1967 and its strength since.

The intelligence community ignored all of the signs, despite getting advance warning, and so did Golda Meir, who received a warning of sorts from Jordan. It's worth noting that the United States was also fooled; they likewise did not believe that a concerted war was possible, and Kissinger's office even sent a CIA cable to Israel on September 30 saying that a limited attack was the most they foresaw, saying that Syria would not act without Egyptian assistance. The Egyptians, Israel believed, were not planning an attack, and were just carrying out military exercises, so it was a round failure to realize what was going on, as the Americans deferred to the Israelis on this point.

Many books also make reference to "the Source", the Egyptian who was Mossad's greatest source of information. However, the Source had also made false claims that war was coming in the past. In a "boy cries wolf" scenario, the Source had already called for war twice before, and the third time was when it actually came.

As the days got closer, Meir met with most of Israel's military chiefs, as well as the famous hero of 1967, Moshe Dayan. They all, with varying levels of certainty, agreed that the Arab states would not attack. Their response to the massing of troops was to send a small amount to reinforce the Golan (which may have saved it from the Syrians, apparently) and to transmit a message through the US that Israel had no hostile intentions, but would be prepared if the Arabs attacked. They hoped this could keep the situation calm. And here is where the feedback loop becomes most apparent, with one of the people who typically gets the most blame (far more than Meir) for the war. Moshe Dayan saw these events happening, and as Minister of Defense and a famous general, could have seen the Arab actions for what they were. Instead, Dayan argued that the Egyptian armies set up a high level of alert not because they were planning an attack, but because they feared an Israeli one, and if Israel just said they weren't going to attack, nothing would occur in his views. In short, he was justifying their actions tautologically: "they went on alert before us, but that's because they're afraid of our going on alert, so they went on alert". But given that all of Israel's intelligence agreed that they would not attack and couldn't possibly hope to win if they did, the threat was overlooked.

Meir holds responsibility for making the wrong choices, but for what it's worth, she seems to have been more aware of what was going on than her own military officials. She noted that Arab press was writing the same types of things about Israeli troops massing (falsely) as they wrote on the eve of the 1967 war. She also noted that the Syrians seemed particularly and unusually eager with their troop deployments. She even said, "Maybe this should tell us something", and her instincts told her something bad was on the horizon. Still, she did not act, because she didn't know about military strategy personally and had no way of knowing what was to come better than all of her military chiefs.

So it is absolutely true that, as Prime Minister and part of this feedback loop, she bears responsibility for the intelligence failure. Even so, she likely bears less responsibility than her military and intelligence chiefs, from Moshe Dayan to one of the most ardent believers that no war was coming, the head of Israel's military intelligence (AMAN), Gen. Eli Zeira. Zeira insisted ardently and in every meeting that there was simply no way an attack would be launched. Zeira was the least prepared for the possibility of war, and even the head of the Mossad, Zvi Zamir, was more aware that war might be coming. It was his transmission of the Source's warning that helped start the process of preparation on Yom Kippur before the attack began, though it was far too late to make a difference in the early hours. He decided not to mention the previous false alarms from the Source in his message. Upon receipt of the message, Gen. David Elazar, chief of staff of the IDF, launched into action. He finally saw war as the likeliest option...and it was the day of the war. So he decided to begin asking for a mobilization and a pre-emptive strike. And here is why Dayan is one of the most blamed people here; in response to these requests, Dayan slowed Elazar. He asked what the hurry was. He was adamantly opposed to any pre-emptive strike, and said "We don't order full mobilization on the basis of a report by Zvika [Zamir]". He noted false warnings from the Source in the past, and said the political situation wouldn't allow a preemptive strike, because the world would view it as aggression far worse than in 1967, where the world saw it (mostly, and particularly in the West) as a justified preemptive strike. Elazar's proposal for an almost full mobilization of 200,000+ men was also shot down. Dayan only authorized 20,000 to 30,000 men, not wanting to mobilize on a scale that would be perceived as an act of war, in his telling. Elazar argued Dayan up to agreeing to 50,000 to 60,000, which was what Elazar said would be needed for defense alone, but he insisted on a full mobilization anyways.

Now the decision went to Golda Meir. A pre-emptive strike was now off the table, due to poor weather conditions in the Golan, meaning a strike could only target bases and runways. That required refitting the planes with the correct armaments, which took more time. Elazar was getting ready to meet with Meir, but first met with his generals, telling them to prepare for war and saying he would mobilize whatever he could. At 8:05AM on the day the war began, Meir met with Dayan and Elazar (these arguments had been happening early, due to the warning). Dayan said that children in the Golan settlements would be evacuated in the late afternoon, to give the excuse that they had field trips and outings. Meir overruled him, ordering that they be evacuated immediately (another good instinct on her part). Dayan and Elazar then presented their cases for/against pre-emption and mobilization. One author notes the bizarre situation, saying it "was admittedly bizarre to have two generals, veteran warhorses at the pinnacle of Israel's military establishment, bringing their differences over vital military matters to a seventy-five-year-old grandmother". She smoked heavily, and the smoke filled the room, as Elazar compromised, saying he could accept a mobilization of 100,000 to 120,000. Before the decision was even made, he sent out his aide to start making the calls necessary for such a mobilization, knowing Meir seemed to be leaning that way.

After both argued their piece, Meir made another consequential pair of decisions: she decided against a pre-emptive strike. It's actually unclear how this might've turned out had she authorized such a strike, but the decision to mobilize Elazar's compromise amount was also consequential. And, as you can imagine, despite her failure to be prepared up to this point, she did make a relatively good decision here, despite the loss of three hours to make it because of the argument. That there is why Dayan is, as I mentioned, one of the figures who was most "fallen" from heroic status following the war. Meir's decisions here were sound, logically and instinctively, at a critical juncture. And while, again, the pre-emptive strike debate can never be settled, her assurance to the US that no such strike was forthcoming may have helped ensure that the eventual US support would be forthcoming (an implicit nuclear threat may also have helped here, though).