Hello Vladimir,
The title of your essay 'Crisis in fundamentality' is well chosen and timely. You only have to read the essays of other contestants to confirm that the notion of fundamentality in science is not generally as fundamental as one might expect.
You have demonstrated that consideration of some of the best thoughts of some of the best minds in the field of consciousness is a very direct and rewarding place to focus one's own mind.
A theory of everything is a fine goal but identifying a goal is just the beginning of something much more worthy: an understanding of the process. To that end there is no better teacher than nature. Science is in the forefront of that endeavour, and physicists curious participants.
If we were to build a tree of fundamentality we would likely start by recognising that existence is a prerequisite for any and all other entities. The highest branches appear to be few but not as clearly independent as one might expect: time, space, energy and matter.
Below these we have a tangle of intertwining branches each claiming in their own special ways entitlements to be recognised as fundamental, i.e. essential, for further developments to ensue.
As Karl Popper noted; "Science does not rest on a rock". A stream of products of evolution have emerged that Popper usefully consolidates into "three worlds".
Cognizance is the foundation of mankind's special claim to an imperative status by virtue of our perceptions, however cloudy, of a totality that extends far beyond our comprehension. However, we cannot deny our dependence upon prior products (i.e. higher branches of the tree) of evolution.
While we accept the notion of 'laws of nature', a more supple term would be 'principles' by which deviations from statistical norms can be admitted, subject to correction when they extend too far from the median condition.
Yuri Vladimirov's contention that "The main goal of theoretical physicists is to build a physical picture of the world on the basis of a single generalizing category" is commendable but in order to accommodate the dynamics of change any such 'picture' would necessarily require to be a continuously changing 'movie'. The principle function of a 'goal' is to establish direction in which to proceed. Goals change as determined by priorities, but processes continue.
The notions of 'the systemic approach' and 'intuition' are utilities that afford assistance in an otherwise chaotic world of unfathomable complexity. Proof in the absolute sense is absolutely unnecessary. We need to identify what we need in the short and longer terms as individuals, collectively, and in support of the greater establishment - and to proceed accordingly.
Yu A. Neretin's comment that "the situation in mathematics and mathematical physics ... is quickly becoming more sinister" echoes Einstein's earlier conviction that 'As far as the mathematical theorems refer to reality, they are not sure, and as far as they are sure, they do not refer to reality.' We are thus inevitably drawn to accept Lee Smolin's conclusion that "The loss of certainty" in mathematics caused "the loss of certainty" in fundamental physics.
Finally, It is important for all specialists to communicate with the public in non-specialist language in order to enhance the degree of understanding and acceptance of ideas.
It was a pleasure to become acquainted with your thoughts.
Good luck,
Gary.