When Does Memory Orchestration Help a Strong LLM? An Efficiency Law and Certified Representation Levers for Long-Term Memory

We ask when adding a memory-orchestration layer around a strong LLM actually helps, and when it does not. Across controlled multi-vendor experiments we derive an efficiency law separating the regimes in which orchestration pays from those in which it is neutral or harmful, and we certify four representation-level levers that survive the stricter regime: date-anchored rendering, consolidation memoranda, cheap consolidation that outperforms full re-processing across vendors, and a value-of-information gate. Negative and null results are reported in full: several intuitively appealing configurations do not compose. The contribution is a decision rule for practitioners — orchestrate here, do not orchestrate there — grounded in measured effect sizes rather than architectural preference. Changelog v2 (2026-08-19) — correction release. Four text corrections; no changes to data, methods, results, or references. (1) Section 2 (related work): a quoted attribution to Du et al. (2023) is replaced by a factual statement of the same point — the quoted phrase does not occur in the cited work. (2) Section 2: a pointer to an internal repository file is removed. (3) Appendix A: a repository path is removed from the provenance sentence. (4) Section 2: a line-break-induced stray space in one compound term is fixed. Page count, figures, tables and the bibliography are unchanged (11 pp). This record also contains main.pdf.ots, the OpenTimestamps proof for main.pdf, anchored in Bitcoin block 963199.