Not quite right, Uncle Milt

Definition of 'Permanent Income Hypothesis'

A theory of consumer spending which states that people will spend money at a level consistent with their expected long term average income. The level of expected long term income then becomes thought of as the level of "permanent" income that can be safely spent. A worker will save only if his or her current income is higher than the anticipated level of permanent income, in order to guard against future declines in income. Investopedia

Let me rewrite and correct:

People save according to the value of the permanent purchases they want to make. The value of car they desire and most likely wait time. How big the house down payment They have finite choices, they prefer to target the one of a few rather than count out the intermediate value of a non-existent good.

And that, Uncle Milt, is why your pluck theorem is correct.

THe consumer has inventory, a portfolio of finite dimension.  Food, leisure,clothes, car, house. The consumer is finite bound on choices he can select for his porfolio. His housing, for example, might be move from college, grab an apartment for five years, then buy with a down.  The consumer is sampling a particular transaction rate and transaction size from all the available housing, over multiple purchase. The consumer is operating a particular Shannon recoding of the broad consumer market, as a stream of previously encoded transactions. When his current income seems stuck and out of balance, the consumer rebalances his entire portfolio, creating a different, and sometimes rank reduced, 'recoding' tree.