bibkey: baake2011peanobaker authors: Michael Baake; Ulrike Schlaegel year: 2011 title: The Peano-Baker series doi: 10.1134/S0081543811080098 claim: The time-ordered Peano-Baker series converges on compact intervals and gives the unique solution of continuous finite-dimensional linear systems. strata_touched:

• D5/S3/Quantum/Transport/MatrixUnitDyson license: citation-only triage: anchor

Ordered series for continuous matrix paths

Proceedings of the Steklov Institute of Mathematics 275 (2011), 167-171. DOI: https://doi.org/10.1134/S0081543811080098 Public author version: https://arxiv.org/abs/1011.1775 Readable version: https://arxiv.org/html/1011.1775v3

Section 2, equations (3)-(5), gives the actual Volterra equation, ordered integral series, and recursive terms with the latest matrix acting on the left. Lemma 1 establishes the derivative of a recursive term. Theorem 1 proves compact convergence by a factorial majorant using a compatible matrix norm. Section 3 identifies the series with the unique fundamental solution. These are classical antecedents of the generic branch of constructive_transport.

The repository declaration realizes these mechanisms using Bochner integrals, an independent closed-simplex integral with a noncommutative List.prod, and the Euclidean operator norm. It covers nonnegative horizons, within derivatives at both endpoints, and a finite physical index type that may be empty. It then applies the repository’s computed matrix-unit generator to obtain unitarity and transport of every logical matrix unit. This note does not attribute that full combined telescope or the matrix-unit averaging formula to this paper, and does not claim mathematical priority for the series method.

Verified locator

Verified DOI: https://doi.org/10.1134/S0081543811080098

The arXiv abstract identifies the title, both authors and journal reference. The readable author version contains equations (3)-(5), Lemma 1, Theorem 1, and the uniqueness discussion in Section 3. Crossref identifies the journal DOI and title above. The citation does not supply a Lean proof dependency.