Local freedom and capacity barriers in quadratic trace reconstruction
A completely multiplicative sign function is determined by its values on $n^2+1$, $n^2+2$, and $n^2-2$, but exact determination does not quantify how many readings detect a negative prime sign. We distinguish three losses of information: partial compatibility tests, geometric restrictions on certificates, and fractional relaxation of signed constraints. After fixing a prime head, we describe the exact fibre of a window and the parity constraints joining two windows. For any fixed head and any sequence $H_N=N^{o(1)}$, one table with $o(N)$ negative entries passes every $H_N$-window test and…
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