The length-restricted antipalindrome sum conjecture

An antipalindrome is a natural number whose canonical base-$2$ expansion is an antipalindromic word, meaning that the word equals the complement of its reversal. An even integer has an even least significant bit. For an odd integer length $n\geq 9$, consider even integers whose canonical base-$2$ expansions have length $n$.

The length-restricted antipalindrome sum conjecture. Every even integer of length $n$, for $n$ odd and $n\geq 9$, is the sum of at most $10$ antipalindromes of length $n-3$.

The conjecture is intended to be proved using nondeterministic pushdown automata, but the authors' computations were incomplete because their program ran out of space. They hoped to establish it as a theorem in a future version; its truth would imply that every even natural number is the sum of at most $13$ antipalindromes.