Resource-preserving reductions and operational profiles of stochastic memories

Which internal distinctions in a stochastic memory matter for the resources of its future changes? This preprint studies memories F = AB with nonnegative row-stochastic factors, protected response rows and peak available component width as the resource. For connected cubic bipartite graphs without four-cycles, an aggregate own-flow condition permits a continuous preparation to a canonical realization at the original available width, without increasing the initial error of any protected row. Components within a group may have heterogeneous prototypes. The criterion survives exact splitting into arbitrarily small copies, while all slots remain counted. A protected preparation preserves the minimum peak for every common terminal task in the specified family that permits preparation. On the Fano incidence memory at width nine and maximum-row L1 tolerance at most 0.001, an observable binary statistic of the full labeled population pair law identifies exactly two protected reachability classes and the entire permitted resource profile. All 128 named atomic subtasks are classified: in one class all have peak nine; in the other, 36 have peak nine and 92 have peak ten. An exact-response reduction is also given when the actual positive response support has no four-cycle. The general group-flow condition is structural, not an established observable test from J. The results use a fixed shared protection budget, known readout and population laws. They do not assert universal sufficiency of temporal observations, finite-sample identification, a learning algorithm, or a general law of memory. Version 0.2; preprint, not peer-reviewed. This is a separate development of Temporal prediction and the reserve cost of safe memory reconfiguration (DOI 10.5281/zenodo.23455109), not a replacement of that record. Full proofs, LaTeX source and deterministic finite-control materials are supplied. Finite checks verify identities and path implementations; the general theorems rest on analytical proofs. Text, LaTeX, PDF and documentation: CC BY 4.0; original code and recorded results: MIT. AI systems assisted analysis, coding, checking and drafting; the human author is responsible for the released content.