Certified predicate for exact dyadic geometric inputs

Input: an ordered tuple of exact dyadic points in dimension $d=2$ or $d=3$, with exactly $d+1$ points for an orientation request and exactly $d+2$ points for a raw incircle/insphere or orientation-normalized sphere-side request, and optionally a filter configuration containing a floating format, its exact dyadic unit-roundoff bound, and a verifiable finite range certificate. Output: the requested sign, including zero; for a sphere-side request with zero base orientation, output degenerate-base together with the raw lifted sign. For each required determinant, construct its matrix in Dyadic orientation and lifted sphere determinants exactly using dyadic integer arithmetic.

1. Attempt Outward-bounded floating determinant filter only when the optional filter configuration is present and its format, standard relative model, and finite normal-range certificate satisfy that algorithm's inputs. If it is absent or invalid, skip directly to the exact fallback.
2. If the filter returns a nonzero sign, use that sign. If the filter is unavailable or inconclusive, use Exact dyadic determinant sign by integer clearance. For an orientation or raw lifted request, return this sign.
3. For a requested incircle/insphere side, compute the base orientation and lifted determinant signs by the preceding steps. If the base orientation is zero, return the status degenerate-base together with the raw lifted sign. Otherwise return the sign of their product: positive inside, zero on, negative outside, by The orientation-normalized lifted determinant records the side of a sphere.

The exact fallback is justified by The integer-clearance determinant-sign algorithm is correct and terminates. The exact predicates retain zero. A caller may separately opt into the symbolic tie-break algorithm; it does not alter this procedure.