Hallo!
I think the proof is both simpler and found *by being simpler*. Then you can flesh out the academic layering on top.
The Wiki version of the chart is a nice place to start.
https://en.wikipedia...s_hierarchy_of_needsIn the spirit of not using buzz words, let's skip "actualize" and go to the subset words. Morality, Creativity, Problem Solving, Dispelling Predjudice, Accepting (Emotionally Difficult) Facts.
It seems easy to prove that people embark on qualitatively higher morality, social action reform, etc that certainly doesn't fit the lower categories.
If I were constructing a formal proof, I'd use one of the indirect proofs when that need is missing, and make it (I think the word is longitudinal) when an "actualizing" moment is identified, report/study it. You found an important partial proof fragment that you can't just "Game Show" someone into that top couple of levels. (In fact, there are famous esteem traps if the needs are met too fast!) And of course it's not nearly as airtight as the diagram hints, tons of poor people follow spiritual recommendations and "Actualize First, fulfill basic needs later".
I think the heart of "proofs" would come from when those missing top categories, which is how the theory developed in the first place. You'd start in a couple of categories. You pick someone running ragged, just ground down by life, say a factory worker whose plant just closed, and next week he'll get evicted because he has no savings.
"Hi. I talked to your landlord. You have 3 months free rent. Here's your new job. Start Tuesday, so you can sleep in Monday. Here's a $500 supermarket gift voucher and a $50 certificate to a nice restaurant. Here's a Gas card with $1000 on it. Have a nice day!"
So after the shock wears off, you go find him in 3 months. Tiers 1 and 2 are all set. Tier 3 could be fuzzy, let's say he used the gift card to take a buddy out to Fish & Chips and Beer to watch the Superbowl on TV. There's his friend.
It turns out his new boss is better than the old one, so he gets some nice OJT to learn a newer computerized machine and becomes Quality Supervisor Level 1. There's your Esteem boost. Maybe he gets his girl back because he's not being a jerk from stress.
So then he's just hanging out, but he's missing that top tier.
Then he hears about SOPA.
Boom - something clicks - he gets involved and schedules a vacation to visit Washington and visit his congressman. Actualization!