Numerical edge-case policy

Status

Implemented v2 contract. Task #64 established the policy, Task #66 removed stale construction-time centroid state, and Tasks #79 and #80 implement the analytical and adaptive centroid strategy, explicit precision, convergence failure, and zero-area behavior.

Tolerances

No global epsilon is permitted. Each operation owns an explicit numerical contract:

• algebraic membership and fuzzy-operator identities use an exact result when the formula is exact in binary floating point, otherwise a test-specific absolute and relative tolerance;
• root or inverse membership operations declare their stopping criterion, maximum work, and residual bound;
• numerical integration declares an absolute and relative error target, an adaptive stopping criterion, and a deterministic failure mode.

Degenerate inputs

A membership configuration is invalid when its required widths or ordered breakpoints are degenerate. Construction must raise ValueError before evaluation rather than rely on division by zero, a zero result, or a later cache failure.

Centroid defuzzification has no value when membership area on the declared integration domain is zero. It must raise ValueError (the modern UndefinedResultError preserves this catch contract); returning an interval midpoint, zero, NaN, infinity, or a cached predecessor is forbidden.

Integration accuracy is an algorithm setting owned by the integration method. It is not a mutable membership-function configuration parameter and no hard-coded point count constitutes a correctness claim.

Evidence

Tests in tests/test_numerical_edge_policy.py and tests/test_defuzzification.py verify the implemented behavior. The legacy 1000-point right-endpoint implementation remains only as independently reproduced historical baseline evidence in Task #78.