neutralsingular

Neutralsingular is a neologism used in speculative mathematics and theoretical discussions to describe a type of singular point in a function, model, or system that exhibits a neutral response with respect to selected invariants. The term combines neutral, indicating balance or zero net effect, with singular, indicating a breakdown of regular behavior at a point.

Definition and interpretation: In the context of complex analysis, a neutralsingular point z0 of a function f may be defined informally as a point where the local Laurent expansion around z0 contains a nonzero negative-power term (a genuine singularity), but the leading singular contribution cancels when considered with respect to a chosen symmetry or invariant. For example, the sum of residues at a set of conjugate poles might vanish, yielding a neutral outcome for certain contour integrals. In dynamical systems, a neutralsingular fixed point might be one where linearization suggests neutral stability (eigenvalues on the unit circle), and higher-order terms cancel growth directions, producing neutral long-term behavior along all studied directions.

Status and usage: The term is not part of standard nomenclature in widely used references. It appears in some online discussions, thought experiments, or fictional expositions, where it serves to discuss balance between conflicting effects at a singular point.

Relation to other concepts: It is related to removable singularities, poles, essential singularities, and neutral stability in dynamical systems, but the term emphasizes a judged neutrality of the singular behavior rather than the mere classification of singularity type.

See also: removable singularity, pole, essential singularity, neutral stability, symmetry, Laurent series.