Recently it has been affirmed here (again) that the quantity called "interval (also 'spacetime interval' or 'invariant interval')" is referring to two (in general distinct) events as arguments, such as $\varepsilon_A$ and $\varepsilon_B$, and is denoted (as shorthand) by $$ \Delta s^2.$$
Consequently, writing out the concrete arguments explicitly, the "interval between" (also called "interval of") events $\varepsilon_A$ and $\varepsilon_B$ is denoted as $$ \Delta s^2[~\varepsilon_A, \varepsilon_B~],$$
where by definition $$ \Delta s^2[~\varepsilon_A, \varepsilon_B~] \equiv \Delta s^2[~\varepsilon_B, \varepsilon_A~].$$
If two events are "timelike separated" (such as events $\varepsilon_{(\mathsf P \mathsf H )}$ and $\varepsilon_{(\mathsf P \mathsf J )}$ where participant $\mathsf P$ took part in both, having met and passed participant $\mathsf H$, and separately met and passed participant $\mathsf J$) then the "interval between" these two events is of opposite sign than the "interval between" any two events which are "spacelike separated".
Following the convention set out in Wikipedia (even though it is just inverse from the convention adopted in the answer referred to above) therefore explicitly: $$\Delta s^2[~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf J )}~] \lt 0.$$
With this convention, considering three events which are (pairwise) "timelike separated" from each other (such as events $\varepsilon_{(\mathsf P \mathsf H )}$, $\varepsilon_{(\mathsf P \mathsf J )}$, and $\varepsilon_{(\mathsf P \mathsf K )}$, where participant $\mathsf P$'s meeting/passing of participant $\mathsf J$ had been between participant $\mathsf P$'s meetings/passings of participants $\mathsf H$ and $\mathsf K$, respectively) therefore holds
$$ \Delta s^2[~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf K )}~] \lt \Delta s^2[~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf J )}~],$$
$$ \Delta s^2[~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf K )}~] \lt \Delta s^2[~\varepsilon_{(\mathsf P \mathsf J )}, \varepsilon_{(\mathsf P \mathsf K )}~],$$
and the "inverse triangle inequality":
$$\sqrt{-\Delta s^2[~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf J )}~]} + \sqrt{-\Delta s^2[~\varepsilon_{(\mathsf P \mathsf J )}, \varepsilon_{(\mathsf P \mathsf K )}~]} \le \sqrt{-\Delta s^2[~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf K )}~]}.$$
Note the square roots, "$\sqrt ~$", operating on each term of the latter inequality. Correspondingly, the (any) "interval, $\Delta s^2$", is considered a "squared quantity" (and appropriately its name involves an exponent: "$~^2$").
My question:
Is there a name for the corresponding linear quantity "$\Delta \overline s$" ?,
for which (written in shorthand) $$ \text{sgn}[~\Delta \overline s~] \equiv \text{sgn}[~\Delta s^2~]$$
and
$$\Delta \overline s \equiv \text{sgn}[~\Delta s^2~] \times \sqrt{ \text{sgn}[~\Delta s^2~] \times \Delta s^2~]},$$
and therefore in turn
$$ \Delta s^2 \equiv \text{sgn}[~\Delta \overline s~] \times \Delta \overline s \times \Delta \overline s,$$
and such that (again following the sign convention of Wikipedia) the "inverse triangle inequality" relating three pairwise "timelike separated" events is (simply, linearly)
$$\overline s [~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf K )}~] \le \overline s [~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf J )}~] + \overline s [~\varepsilon_{(\mathsf P \mathsf J )}, \varepsilon_{(\mathsf P \mathsf K )}~], $$
provided
$$\overline s [~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf K )}~] \lt \overline s [~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf J )}~] \lt 0$$
and
$$\overline s [~\varepsilon_{(\mathsf P \mathsf H )}, \varepsilon_{(\mathsf P \mathsf K )}~] \lt \overline s [~\varepsilon_{(\mathsf P \mathsf J )}, \varepsilon_{(\mathsf P \mathsf K )}~] \lt 0.$$
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