The claim sits in the day's headline. Al Jazeera titled its Tuesday liveblog on the war "Trump claims the strait is open, seeks Iranian compensation" [1]. Tuesday's checkable record is narrower and stranger than the headline: a diplomatic signal that talks are advancing, a US military helicopter firing on the rudder of a container ship, six written Iranian conditions that have not moved, and no public transit numbers by which anyone could test the word open. This piece takes the items one at a time.
The diplomatic signal is real and specific. Majed al-Ansari, spokesman for Qatar's Ministry of Foreign Affairs, said that "negotiations between Oman and Iran on the future of shipping in the Strait of Hormuz have reached an advanced stage" [1]. Oil traded on the mood. TradingEconomics' commentary Tuesday read: "Brent crude oil fell toward $87 per barrel on Tuesday after Pakistan signaled that the US and Iran could be close to an arrangement aimed at easing tensions and potentially reopening the Strait of Hormuz" [6]. In that account, Pakistan's defence minister put the two sides "close to some sort of arrangement," with conditions "moving in favor of peace" [6]. That is market commentary relaying a third country's characterization, not confirmation from either principal, and it belongs in the record with that label attached.
Iran's price has not moved since this desk reported it Sunday. Supreme National Security Council Secretary Mohammad Bagher Zolghadr delivered the conditions Saturday, and Iran's NourNews published them in full [3][4]. Verbatim, the six points are: first, "Never threatening Iran, under any circumstances or in any language, and refraining from insulting the sacred beliefs of the Iranian nation"; second, "Permanently ending the war and aggression against Iran and Iran's allies in Lebanon, Palestine, Yemen and Iraq"; third, "Lifting the maritime blockade and withdrawing its military forces (naval and air forces) from around Iran"; fourth, "Fully compensating Iran for the damages caused by the two wars of aggression imposed on it, without any reduction"; fifth, "Lifting the unjust and illegal sanctions imposed against the Iranian people"; sixth, "Unconditionally releasing the frozen and seized assets of the Iranian people" [4]. NourNews framed the list as demands "the Iranian people have expressed loudly during 160 days" [4]. IRGC spokesman Hossein Mohebbi, quoted by the Tasnim news agency, stated the mechanism plainly: "Whenever the United States accepts Iran's conditions, the Strait of Hormuz will certainly be reopened." [3]
Washington's posture, on the record across Monday, sits at a distance from both the demands list and the advanced-stage signal. At 2:54 AM Monday, President Trump wrote: "We are only semi-negotiating with them. We are just watching Iran with its huge inflation and the fact they have no money." [5] At 1:11 PM came the compensation demand this desk reported Monday, "I am likewise demanding compensation from Iran, for all of the people that they have killed and gravely wounded with their roadside bombs and many conflicts," invoking the families of the 17 sailors killed aboard the USS Cole in 2000 [5]. At 4:16 PM he described the waterway itself: "We control the strait 100%. Now, can they make trouble? Yeah, they can make trouble, but they're broke, they have no money." [5]
The strait those statements describe produced its own datum on Tuesday. At 3:55 pm, The Times of Israel's liveblog, citing the Wall Street Journal, reported that "A US military helicopter has fired at the rudder of a Panama-flagged ship after its crew ignored warnings from personnel working to enforce a naval blockade on Iranian ports" [2]. The vessel is the container ship Vela Nova. There were no immediate reports of casualties, and after the strike the ship appeared to be trying to transfer its crew to another civilian vessel [2]. A waterway in which the blockading force is firing on a merchant ship's rudder, and that ship's crew is climbing onto another vessel, is not open in the sense a shipowner, a charterer or an insurer uses the word.
Here is what this piece cannot tell you: how many tankers transited Hormuz on Tuesday, or this week. No transit count appears in any source fetched for this piece, and the one traffic figure circulating sits behind a source we could not access. That number is the test of the word open, and it is not publicly available.
While the principals posture, one measurable bill has been published next door. Kurdistan Regional Government Prime Minister Masrour Barzani said "The regional conflict and the security repercussions led to a 70 percent decrease in trade across the Kurdish region" [7]. KRG spokesman Peshawa Hawramani put the region's losses through April at 1.5 trillion Iraqi dinars, $1.14bn, a figure submitted to the Iraqi government [7]. Aland Kareem Salih, an economy researcher at the Vision Foundation for Strategic Studies, said oil production has fallen from an agreed 200,000 barrels a day to "only 30,000," and non-oil revenues by around 70 percent [7].
As this desk reported Monday, both capitals spent the start of the week raising the price of reopening rather than lowering it. Tuesday adds an advanced-stage signal worth watching and a fired-on container ship worth remembering. The demands list has not moved, the traffic data is not public, and the strait's status remains what it has been for months: a claim, priced daily in Brent, billed locally in Erbil, and enforced by helicopter.