Arithmetic reconstruction and error recovery from three quadratic traces
We study completely multiplicative sign functions $h$ through their values at positive integers of the forms $n^2+1$, $n^2+2$ and $n^2-2$, with observed indices $1\le n\le N$. First occurrences of prime factors give a canonical information set and a complete, prefix-compatible family of parity relations, each involving at most $\lfloor\log_2N\rfloor+3$ readings. These relations yield exact bounded-distance repair, including corrupted information coordinates, in time $N^{O(1)}(4+\lfloor\log_2N\rfloor)^t$ for $t$ errors; erasures enter through an explicit rank parameter. We then construct…
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