ora-0188
16.8 Progress without a single task score
An ORACLE learner can now report a structural progress vector:
\[ \begin{gathered} (\text{separating probes},\ \text{settled quotient}, \text{universal witnesses},\\ \text{repair coverage},\ \text{transport span}, \text{utility profile}). \end{gathered} \]
No single coordinate is sufficient. A learner may improve prediction while shrinking its transport span, or accumulate many constructions whose utility profiles overlap completely. Lifelong progress means expanding the admitted factorization capacity of the storehouse while preserving or explicitly repairing its settled core.
Guiding question.
Which compactness or accessibility assumptions guarantee that a nested sequence of nonempty finite-horizon persistence cores has a nonempty infinite-horizon core?