FA-15670 / Numerics / Member archive
Binary field trace: Frobenius orbit initial element · case 05
The exact binary field trace result violates the stated contract at Frobenius orbit initial element.
Case contract
Input [a,irreducible bitmask]; return absolute field trace a+a^2+...+a^(2^(n-1)), an F2 element represented integer 0 or1.
Why this case matters
Exact discrete arithmetic with observable algorithmic state; no floating point approximation is used.
One recorded failure
Sample boundary fixtureThis sample comes from the broken implementation of a controlled reproducer.
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| explicit oracle 0 | 1 | 0 | Failed |
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