The verified arithmetic register
omnibias.core.verified provides interval arithmetic and specialized enclosure algorithms. These APIs compute bounds under stated assumptions; their guarantees must be read with the particular input representation, rounding model, and algorithm contract.
Represent the input you mean
Interval.point(0.1) represents the exact binary floating-point number supplied to it. It does not automatically enclose the rational number one tenth. Use Interval.from_rational(Fraction(1, 10)) when the intended datum is that exact rational. Constructing Interval(lo, hi) assumes your endpoints already bracket the quantity.
Basic arithmetic uses outward rounding. Reciprocal and division require a denominator interval separated from zero. Interval powers use repeated interval multiplication to account for intermediate rounding. See the full Interval contract.
Choose a representation
| Representation | Useful for | Limitation to inspect |
|---|---|---|
| Intervals | Direct range bounds and arithmetic | Repeated variables can widen bounds |
| Affine arithmetic | Shared dependency information | Nonlinear operations introduce remainder bounds |
| Taylor models | Polynomial structure plus remainder | Domain, truncation order, and remainder enclosure |
| Specialized validated solvers | Specific existence or enclosure questions | The assumptions of that solver and the returned status |
Read evidence at its actual scope
Containment tests are useful regression evidence, but sampled containment alone is not a proof over an entire domain. A numerical certificate must identify the mathematical property, domain, arithmetic assumptions, and any unresolved conditions.
A digest detects changes to a payload; it does not establish that the payload proves a true proposition. Replay and formal checking address separate questions. Consult certificate APIs, replay APIs, and the formal bridge. Application-specific robustness and dynamics tooling belongs to the external ecosystem.
Start with a checkable numerical contract
Read the scope and guarantees before using an enclosure as a downstream decision. Then inspect the interval API, verification package overview, and reference-example instructions. Record the exact input representation and the returned status with the result.