The roots of the kavkem organisation Dynash (from dynas, meaning 'to destroy') lie in no particular mythology and generally avoid mingling spiritual and practical concerns. They are the closest to what humans would consider an actual terrorist organisation - their goals are to do as much damage to Nayabaru society as they can get away with.
WARNING: The following material has not yet had a chance to become canonical.
Like Shy͡ilun, Dynash enjoys scattered membership on most of Nekenalos - although with the exception of Sefusa and Tabraan (true even after the Tabraan pushback in A Thread Between The Stars). Further like Shy͡ilun, the brunt of Dynash's numbers are on Asheenagiji.
However, while some number just shy of 20% of kavkema are members of Shy͡ilun, Dynash hovers under 10% adoption. Despite these low numbers, it tends to be more memetically viral - groups of kavkema are usually Dynash, rather than individuals.
Dynash has no meta-structure between its groups. Instead, it can be understood as a set of oaths and rituals that groups of kavkema ascribe themselves to. While Dynash itself is strictly secular (indeed, owing much of its adoption to its complete neutrality in regards to mythology), its practises are almost cult-like in manifestation.
Within the Dynash framework, groups are encouraged to decide on their own structure.
Dynash lives for its methodology - indeed, it is not much more than its methodology, by definition.
Pure Dynash is a long cycle of action. The cycle begins with the decision to pick a particular target - a Nayabaru settlement - on the map. The whole group will then enter the vicinity of the target and spend several nights with increasingly bold intelligence gathering in groups of two or three. Important and/or weak infrastructure is made a note of. The means to attack or destroy this infrastructure is acquired (poisons, fire, explosives). In a single run, as simultaneously as possible, the infrastructure is attacked, and the Dynash group scatters. They recoalesce as a group in a previously agreed-upon place. Then the cycle begins anew.
This general modus operandi leaves Dynash especially vulnerable to losing information to the Nayabaru about where they will gather next - if even one of their members is captured, they will be able to identify where the group will next meet for the Nayabaru.
To combat that, some members of Dynash (those choosing to strike deepest into the heart of the target) are known to voluntarily destroy their body's vocal apparatus, leaving them literally unable to speak to betray their brethren. This procedure kills some of them, but as Dynash are known to consist of kavkema that are especially willing to truly die for the cause, this has rarely given anyone much pause.
While pure Dynash is this cycle, repeated until the wheel is broken by death or captivity, there are further axioms to the 'organisation' that make it more than that. Dynash members vow to assist their fellow kavkema if asked to help. Of course, their help tends to preferentially be rather destructive in nature, but one should not underestimate their flexibility - Dynashgades̈a are known to be good allies to Shy͡ilungades̈a, and the organisations tend to view each others' standard approaches as 'helpfully complementary' rather than 'dangerously different'.
Almost all members of Dynash can be said to be fervently loyal to their cause (which ultimately is an end to kavkem suffering), obsessed with making a difference. They are exceptionally good at and least hesitant to embrace qasai and members of Dynash die to cleverly concealed poisons in the early stage of captivity more often than the members of any other organisation, despite Nayabaru experience and efforts to prevent it.
Arguably, Dynash has done the most damage to the Nayabaru out of all kavkem efforts otherwise combined. That said, damage tends to be all it is, given that damage is what Dynash is optimised for. If Dynash rescue someone, it is a happy accident; rescue is never their goal. They manage to kill captive kavkema more often than rescue them and even the killing is fairly rare.
As such, Dynash effectively grows by memes only, usually acquiring new members when the story of a particularly successful Dynash cycle spreads. Paired with the gradual loss of members to captivity, it maintains fairly steady membership numbers.