1. A method of organizing a series of sibling entities for facilitating on-demand production of a ranked parent candidate of the series of sibling entities, each of the sibling entities comprising one or more child possibilities having an associated child confidence, the ranked parent candidate including one or more component elements, each component element consisting of one of the child possibilities selected from one of the sibling entities, the ranked parent candidate having a parent rank representing an aggregate of the child confidences associated with the child possibilities that comprise the component elements of the ranked parent, the method comprising: (a) receiving a series of sibling entities including a first sibling entity and a last sibling entity; (b) establishing a rollup matrix having a matrix height and a matrix width, the rollup matrix including multiple columns spanning the matrix width and multiple rows spanning the matrix height, each row having a row position along the matrix height; and (c) loading the rollup matrix with the series of sibling entities in a predetermined loading sequence starting with a first-loaded column of the rollup matrix and ending with a last-loaded column of the rollup matrix, the loading of the rollup matrix including: i) storing the first sibling entity in the first-loaded column, including storing each child possibility of the first sibling entity in one of the rows, the row position of said row corresponding to the child confidence associated with the child possibility being stored, ii) in an unfilled column of the rollup matrix immediately following a previously-loaded column in the loading sequence, for each loaded row of the previously-loaded column in which a child possibility has been stored, storing in the unfilled column a next one of the sequential sibling entities including storing each of its child possibilities in the matrix rows having row positions equal to the sum of the row position of the loaded row of the previously-loaded column and the child confidence associated with said child possibility being stored, iii) repeating step (ii) until the last one of the sequential sibling entities has been stored in the last-loaded column of data matrix, whereby the row position of each row of the last-loaded column containing one of the child possibilities corresponds to the parent rank of at least one ranked parent candidate that can be generated using said one of the child possibilities.