Uniqueness in multivariate curve resolution, re-tuned

There are many misunderstandings about the term and interpretation of uniqueness in multivariate curve resolution tasks. In CAC2026 Tarragona, it turned out that even mathematicians do not properly construe Manne’s theorems. So we decided to provide this re-tuned summary, using several original quotes, their explanations, and newly created illustrative figures to get the points across. This contribution then explicitly offers the following: (i) a unified interpretation of Manne’s conditions, DBU, GRU, minimal constrained duality, and particular-solution-based criteria; (ii) newly constructed visual illustrations, including a counterexample; and (iii) a practical workflow for diagnosing uniqueness in nonnegative bilinear MCR.