In the spirit of the What is a Word™/Phrase™ series started by JLee, a special brand of Phrase™ and Word™ puzzles.

If a word conforms to a special rule, I call it a Coalescent Word™.
Use the examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ Coalescent }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\ \def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words }^™\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2017.02.04}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ AGHAST }&\text{ UNSURPRISED }\\ \hline \text{ ALABAMA }&\text{ MISSISSIPPI }\\ \hline \text{ BASS }&\text{ TREBLE }\\ \hline \text{ BLACK }&\text{ WHITE }\\ \hline \text{ JUSTIFIED }&\text{ UNWARRANTED }\\ \hline \text{ MADAME }&\text{ MONSIEUR }\\ \hline \text{ PROCESSED }&\text{ NATURAL }\\ \hline \text{ RUST }&\text{ OXIDIZE }\\ \hline \text{ STONED }&\text{ SOBER }\\ \hline \text{ SUPPORT }&\text{ SABOTAGE }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

Coalescent Words™,Not Coalescent Words™

The puzzle satisfies the series' inbuilt assumption, that each word can be tested for whether it is a Coalescent Word™ without relying on the other words. These are not the only examples of Coalescent Words™.

What is the special rule these words conform to?


Coalescent words satisfy the property that

Each letter in the word is either repeated in the word or the word contains one of its alphabetical neighbours.


If we sort the letters of JUSTIFIED we get DEFIIJSTU which has three groups of neighbouring letters, (DEF)(IIJ)(STU), and no letter is alphabetically isolated.

On the other hand if we sort the letters of UNWARRANTED we get AADENNRRTUW in which 'W' is not repeated and does not have an alphabetical neighbour within the word.

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