CMA rank-mu covariance update

⚠️ Curated Limitations & Negative Results

• This record is restricted to the 2003 equal-weight selected-step moment and nonnegative path/moment blend. Arbitrary unequal or negative weights, active covariance updates, later safeguards, restart schemes, limited-memory variants and modern implementations are not established by this source scope. The alpha=1 endpoint recovers the source’s reviewed host rule without making the new component identical to the whole maintained 2001 CMA-ES algorithm.
• The source’s rank=min(mu,n) wording requires a generic full-span qualification. Degenerate supplied steps or finite precision can reduce rank. Positive-semidefinite arithmetic and a retained positive old-covariance coefficient do not guarantee good conditioning, stable eigendecompositions or an admissible numerical implementation. The boundary c_cov=1 requires adequate positive span; the ordinary positive-definite domain cannot be assumed there.
• The neutral-model expectation argument on PDF pp. 6–7 / printed pp. 5–6 does not establish conditional martingale behavior or stationarity throughout an adaptive optimization run. The zero-path first-step calculation is curator hand algebra under fixed C and independent neutral steps, not an author-issued erratum or a claim to have disproved the separate Hansen 1998 argument cited by the paper. That thesis proof was not acquired or audited here.
• The new term uses old-mean normalized individual steps. Replacing it by covariance around the selected mean, by an outer product of the selected mean step or by a generic elite maximum-likelihood covariance changes the rule. Connections to IGO or natural-gradient search require their own distribution, utility and finite-update assumptions; neither a first-order resemblance nor a shared Gaussian family makes these methods exact aliases.
• Equation 12 is an empirically selected rate, not a universal optimum. Reported time-complexity results count generations in the stated parallel experiments; they do not establish linear dense-matrix arithmetic, a universal speedup or a convergence guarantee. No numerical performance result or benchmark replication is imported.
• Section 7, PDF pp. 18–19 / printed pp. 17–18, reports excessive shrinkage of overall variance and difficulties with global step-size control for large populations and rates. Smaller covariance rates and covariance renormalization are discussed as possible responses, not silently added to this component as mandatory safeguards. Positive-definite covariance alone does not prevent these problems.
• The acquired article has 19 PDF pages including a courtesy cover; printed pages 1–18 therefore occur at PDF pages 2–19. Core formulas were inspected visually because native formula extraction is garbled. The author’s separately retained errata correct test-function separability and a summation index, not Equations 10–11. The full empirical table/figure analysis and cited theoretical dependencies were not audited; no general historical-priority claim is made.
• The primary publication year and author-hosted copy are retained without inferring a publication day from file metadata. Initial sandbox DNS failures and separate successful acquisition retries remain in the source provenance. Historical research assessed 733 native and 442 pinned AIO records and associated this component with existing frontier owner 200. That dated scope is not a claim of current frontier absence. No author code, calculator, optimizer or benchmark was executed in that research.