1. A computer-implemented system for providing multi-core topic indexing in electronically-stored social indexes, comprising: a storage device comprising: a corpus of articles each comprised of online textual materials and a topics; a finite state pattern for each topic, each finite state pattern defining a fine-grained topic model that is used to identify the articles that are potentially on-topic; and on-topic training examples and off-topic training examples from the articles for each topic; one or more of distinct core meanings for the topic by assigning at least one of the on-topic training examples and the off-topic training examples; a set of average on-topic articles, comprising: a training module configured to provide a set of random training examples from the corpus; a match module configured to match the set of random training examples to the finite state pattern for the topic; an off-topic elimination module configured to eliminate an article that is similar to the off-topic training examples; and an on-topic addition module configured to add the on-topic training examples into the set of the random training examples; and an average on-topic core meaning based on the set of the average on-topic articles; a social indexing system, comprising: a characteristic words selector configured to specify characteristic words for each of the on-topic training examples, the off-topic training examples, and the set of average on-topic articles, and to assign scores to the characteristic words that were specified for the on-topic training examples, off-topic training examples, and the set of average on-topic articles; a characteristic words organizer configured to specify on-topic characteristic word term vectors, each on-topic characteristic word term vector comprising the scores of the characteristic words that were specified for each topic for each of the on-topic training examples; a characteristic words scorer configured to specify off-topic characteristic word term vectors, each off-topic characteristic word term vector comprising the scores of the characteristic words that were specified for each topic for each of the off-topic training examples; a characteristic words specifier configured to specify average on-topic characteristic word term vectors, each average on-topic characteristic word term vector comprising the scores of the characteristic words that were specified for each topic for the set of average on-topic articles; an information collector configured to obtain a new article; a finite state pattern matcher configured to match the new article to the finite state pattern of each of the topics to designate the new article as a candidate article for each topic to which the finite state pattern was matched; a candidate article characteristic words selector configured to specify characteristic words extracted from the candidate article; a candidate article characteristic words scorer configured to assign candidate article scores to the characteristic words of the candidate article; a topic comparer configured to compare the candidate article scores to the off-topic characteristic word term vectors of each topic and to form an off-topic score for each topic, and to discard the candidate article as off-topic for each topic in which the off-topic score for that topic exceeds an off-topic threshold; and a similarity score comparer configured to compare the candidate article scores to the on-topic characteristic word term vectors and the average on-topic characteristic word term vectors of each topic and to form an on-topic score for each topic and configured to select only the candidate articles as candidate on-topic articles which the on-topic score for that topic exceeds an on-topic threshold; and a display configured to present the candidate on-topic articles.