Nobles have never been a focus of any of the Traveller gaming sessions I've been part of, either as ref or player. So a lot of my perspective is colored in that regard.
Nobility is assigned through papers through some recognition of service or accomplishment.
Nobility can be hereditary (though not guaranteed).
Nobility is feudal in nature, as is the Imperial interstellar government.
Nobility is required to be recognized in political office.
Nobility affords enfeoffment, usually no more than 100km^2 (though the essay shows a counter example).
Nobility allows a duke to rise from ruling a subsector to a sector, depending on circumstances.
Fiefs, by implication, are assigned for development (emphasis seems to be on economic usage).
Feudal fiefs were parcels granted for farming, rulership and protection, but the inference in the Noble essay very much suggests economic development, and not a "duchy", "barony", nor "county", but an economic holding.
A fief is not an association".
Allegedly there's no Imperial government below the subsector level, meaning worlds (save perhaps the subsector capitol, Duke's predisposition depending).
House Cav is defined in The Spinward Marches campaign.
The point of contention, given Magnus von Thornwood's revelation of "rule your world with pride/honor..." (whatever it was), is that even though lower ranking nobles are not of the peerage, and that the Imperial government begins at the subsector level, then, to me, and this is MY SPECULATION, it seems possible, (your level of likliness may vary) that the term "association" may have some cross-over meaning with the term "rule".
Eh. That is even though the Imperial Government doesn't administer small collections of worlds or single worlds, that a lesser noble, though his letters, possibly rules a world WITHOUT the Imperial bureaucratic apparatus.
I think the point of confusion and contention is what do lesser nobles do with worlds they are "associated" with, if there's no Imperial machine for them to be part of.
If the Imperium is a feudal system, then fiefs MIGHT be more than economic grants (though current material doesn't suggest otherwise, yet doesn't strictly prohibit other "applications").
If the Imperium is a feudal system, then, as per TSMC, house cav can be brought to the theatre of operations, but that OTHER forces are raised as a matter of noble function for the Imperial Government. But, again, private armies (as per many an allusion to mercenary tickets for megacorporations) are not prohibited, and are in fact institutionalized.
If the Imperium is a feudal system, and if there is no Imperial Government or any governance below the subsector level, then a minor noble may perhaps indeed rule an associate world, world government depending.
The thing that "gets me" is that the empire is a feudal system, but has an elaborate bureaucracy; as per Thailand, Spain, Denmark, Saudi Arabia, and any existing nation whose royalty still has a hand in government (note; I intentionally did not include the UK nor Japan, as those families are more figureheads, though I think the Queen of England is allowed some kind of power of ratification on legislation).
Gray Areas;
Do nobles, without the Imperial government, rule worlds?
Do nobles of all ranks raise private forces apart from house cavalry?
Do nobles, not of peerage, have any political or bureaucratic rank apart from the Imperial government, where they can use their title to "gain perks" or exercise powers?
What do Knights do?
What do Baronets do?
What do Counts do?
What do Marquis do?
Back to cleaning.