Necessity or sufficiency of associated characteristics for emergent novelty

Determine whether the characteristics often associated with emergence—specifically universality, order, complexity, unpredictability, irreducibility, diversity, self‑organisation, discontinuities, and singularities—are necessary, sufficient, both, or neither for an emergent property defined by novelty (i.e., a property of the whole that the parts do not have). Provide clear criteria and proofs or counterexamples for each characteristic relative to novelty.

Background

The paper defines emergence primarily as novelty and lists several other characteristics frequently discussed in the literature. The author notes that despite widespread use, the logical role of these characteristics relative to novelty has not been established.

Resolving whether each listed characteristic is necessary or sufficient would clarify debates about definitions of emergence and guide methods for identifying and studying emergent phenomena across disciplines.