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That’s roughly Schmidhubers compression progress hypothesis. I think the staircase is lower bounded by accumulation of incompressibles. Like collecting prime numbers as you count. My own current tack is to interpret the process as time experience.
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"accumulation of incompressibles" (nice) and not-yet-and-maybe-never-compressibles Very Schmidhuberian. I want something more neural or winner-take-all mass flow and more phenomenological and more (deep refactorable) ontological and less bitstringy and computationy. But yeah.
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Way back in like 2002, I tried a different modeling approach, using phase transitions in computational complexity of graph problems. It was a popular topic in the 90s. It gets the suddenness of transitions right but is neurophysiologically very shaky even as an allegory.
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It’s easy to find cartoon math models that rhyme in “space” or “time” with felt subjective experiences, but ultimately mapping to brain (which is where it gets interesting) runs into too much complexity so I gave up and turned to stuff I was actually being paid to think about