Check 1. One unique background article and up to two person-article associations. The background describes a set of articles; the person profiles describe associations with each individual.
Check 2. The forward result is , the transpose is , and is . The returned row is . The combined matrix has rank 24, so it cannot be the 60-dimensional identity.
Check 3. No. Diagonal entries describe individual variances. In the example the off-diagonal entries remain -0.6 after marginal standardization, so the two coordinates remain correlated.
Check 4. Repeating E1 inside the background would weight that reporting more heavily merely because it has two associated people. E1 should nevertheless enter both personal aggregations because each asks about the articles associated with a different person. Deduplicate within a set, not across two different research questions.
Check 5. P1 ranks N3 second: its loading 0.5949 is smaller in magnitude than N1’s 0.7964. N3’s own row ranks P1 ahead of P2 because 0.5949 exceeds 0.3087. The shared entry agrees exactly; the competing entries differ.
Check 6. also projects to and returns as . The two input rows differ only along a discarded direction, so the retained map cannot distinguish them.
Check 7. No. A and B move from cosine 0.0392 to 0.8211, a change of about 0.782. Total variance is an aggregate reconstruction quantity, not a bound on every pairwise angle.
Check 8. Yes. Its comparison background can change because other associated articles enter a cell, or older articles can leave a rolling window. A support threshold can also change which cells remain in the average. These mechanisms do not necessarily describe a change in the person’s activities.
Check 9. No. A smaller topic coordinate can be outweighed by a larger attention share. Calling an article news about a person additionally needs a qualified article-person association and the underlying identity evidence. A ranking product cannot supply that link.
The three later checkpoints distinguish a linear score from a probability, a sourced financing event from its possibly unknown investors, and a coverage neighbor from a documented colleague. Their answers appear where each question is introduced so the required evidence remains next to the proposed inference.