What are the possibilities for “paranormal” influences that would not be detected by science?

Inspirations that could be attributed to human unpredictability,
“Anecdotal” anomalies, because they cannot be repeated and reproduced, they are always changing,
Incalculable complexities, because they can only be assumed to be calculable.
Additional quantum fluctuations with distribution of complementarities within statistical bandwidths,
Statistical outliers that are averaged away,
Long time periods,
Deliberately ignored anomalies, such as UFOs, OBEs, Astrology, Gemstone Therapy, because they do not fit into the prevailing world view,
Infinitely sensitive tipping points within chaos theory.

Is there a way to verify or falsify the central thesis of my theory?

Yes, an AI must be constructed so that it comes as close as possible to an ideal infinitesimality-structured state, and also so that this state can be brought about continuously. The continuous transition is necessary in order to be able to calculate an expected distribution of outcomes from the i-structured state from the statistical distribution of outcomes from the non-i-structured state in the event that consciousness does not occur. If the expectation occurs, the theory is falsified. If, on the other hand, “anomalies” occur, they support consciousness in the sense of the theory.