References and source lineage

Komorebi P. Projector-Resolved Large Algebraic Signal Model. Historical 38-page capstone preserved in Komorebi_PR_LASM_2.3.0_Source.zip, paper/Projector_Resolved_Large_Algebraic_Signal_Model.tex. In particular, Sections 2–7 and the categorical-atlas distinction. Historical experimental claims are not used here.

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Komorebi P. Projector-Resolved Seed Calculus VI, corrected presentation in Paper_VI_With_Visual_Appendix.pdf, Section 8, Theorem 8.4 and the adjacent coarsening criterion and one-packet boundary. This supplement restates and proves the finite result it uses. It does not claim a fresh Lean audit of that paper.

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Komorebi P. PR-LASM 2.3.0 Release Audit, 9 October 2026, and the accompanying source. The source inspected includes exact_atlas.py, lasm_packetizer.py, lasm_model.py, docs/RELEASE_GUIDE.md and docs/claim-boundary.md.

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Ronald R. Coifman and Mladen Victor Wickerhauser. “Entropy-based algorithms for best basis selection.” IEEE Transactions on Information Theory 38(2), 713–718, 1992. DOI: 10.1109/18.119732. Source checked: the authors' Washington University research record. The finite additive tree optimization is classical background.

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MIT OpenCourseWare. 6.241J Dynamic Systems and Control, Chapter 24, “Observability,” Spring 2011, especially Section 24.5 on the largest invariant subspace contained in the observation kernel. Source checked: the MIT course notes, PDF page 6. Used to identify the classical control-theoretic antecedent of Proposition 8.

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Michael Woodward, Yifeng Tian, Arvind Mohan, Yen Ting Lin, Christoph Hader, Hermann Fasel, Misha Chertkov and Daniel Livescu. Data-Driven Mori-Zwanzig: Approaching a Reduced Order Model for Hypersonic Boundary Layer Transition, arXiv:2301.07203, version 1, 2023, introduction and description of resolved, memory and unresolved contributions. Cited for the established projection-memory context, not as evidence for PR-LASM's performance or for any application discussed in that paper. Proposition 10 is proved directly by finite linear recurrence expansion here.

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Peter Buchholz. “Exact and ordinary lumpability in finite Markov chains.” Journal of Applied Probability 31(1), 59–75, 1994. DOI: 10.2307/3215235. Source checked: Cambridge University Press publication record. Used for the classical finite Markov aggregation context.

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Michael L. Littman, Richard S. Sutton and Satinder Singh. “Predictive Representations of State.” Advances in Neural Information Processing Systems 14, NIPS 2001. The paper connects state with predictions of future observations conditional on actions. Cited for conceptual lineage, not as a proof of the finite delay theorem or of this implementation. The original paper and proceedings record are the primary sources. The scanned paper carries all three author names.

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Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor and J. Nathan Kutz. “Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.” PLOS ONE 11(2), e0150171, 2016. DOI: 10.1371/journal.pone.0150171. Used for the established role and limitations of finite invariant observable families in nonlinear modeling. No general nonlinear feature-discovery guarantee is imported.

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Daniel Hsu, Sham M. Kakade and Tong Zhang. “A Spectral Algorithm for Learning Hidden Markov Models.” Journal of Computer and System Sciences 78(5), 1460–1480, 2012. Primary author manuscript inspected: hmm-jcss.pdf, hosted by Daniel Hsu at Columbia University, especially its abstract and rank assumptions. The result illustrates observable-operator learning under explicit spectral hypotheses. Its statistical guarantees are not claimed for PR-LASM.

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Stephen Boyd, Laurent El Ghaoui, Eric Feron and Venkataramanan Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM Studies in Applied Mathematics 15, 1994. The authors' Stanford publication page identifies the book and provides the primary text. Used to identify the classical common quadratic Lyapunov and matrix-inequality setting. The discrete contraction implication used in Section 19 is proved directly there.

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Byron Boots, Sajid M. Siddiqi and Geoffrey J. Gordon. “Closing the Learning-Planning Loop with Predictive State Representations.” Robotics: Science and Systems VI, 2010. DOI: 10.15607/RSS.2010.VI.036. Primary eight-page proceedings paper inspected at the authors' Carnegie Mellon host, especially Section II on interventional tests and Section III on observable matrices. A journal version appeared in The International Journal of Robotics Research 30(7), 954–966, 2011. Used for the established PSR lineage, not as an assertion that this supplement implements that paper's complete algorithm or planning guarantees. Source: https://www.cs.cmu.edu/~ggordon/boots-siddiqi-gordon-closing-loop-psrs.pdf.

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Han Zhao and Pascal Poupart. “A Sober Look at Spectral Learning.” ICML 2014 Workshop on Spectral Learning, 2014. Primary author-hosted manuscript inspected, including its discussion of negative probabilities in spectral estimates. Used only to identify that practical failure mode. The cone and packet statements in this supplement are proved independently. Source: https://hanzhaoml.github.io/papers/ICML2014/spectral-main.pdf.

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Wassily Hoeffding. “Probability Inequalities for Sums of Bounded Random Variables.” Journal of the American Statistical Association 58(301), 13–30, 1963. DOI: 10.1080/01621459.1963.10500830. Publisher record checked. Proposition 35 supplies a self-contained Bernoulli moment-generating-function proof for the protocol it uses. Source: https://www.tandfonline.com/doi/abs/10.1080/01621459.1963.10500830.

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Daniel Hsu, Sham M. Kakade and Tong Zhang. “A Spectral Algorithm for Learning Hidden Markov Models.” COLT, 2009. Original conference manuscript inspected at the official Learning Theory proceedings site, particularly Sections 2.3–3.1 on rank, sampling and observable representations. The later journal version is [R7]. No statistical guarantee from either version is imported without its assumptions. Source: https://www.learningtheory.org/colt2009/papers/011.pdf.

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Herbert Jaeger. “Observable operator models for discrete stochastic time series.” Neural Computation 12(6), 1371–1398, 2000. Author-hosted manuscript with the August 2017 erratum. Section 7 gives the polyhedral-cone connection to finite positive realizations and an irrational-rotation obstruction. The controlled rational example in Section 51 is an independently worked adaptation of that established obstruction, not a claim of discovering it. The corrected manuscript and its geometric argument were inspected. Source: https://www.ai.rug.nl/minds/uploads/oom_neco00.pdf.

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Zoltán Horváth, Yunfei Song and Tamás Terlaky. A Novel Unified Approach to Invariance Conditions for a Linear Dynamical System. arXiv:1405.5167, version 2, 5 July 2016. Primary author manuscript, particularly the polyhedral-invariance discussion and use of Farkas' lemma. Used for the classical invariant-cone and optimization setting. The generator and robust-vertex statements used here are proved directly. Source: https://arxiv.org/html/1405.5167v2.

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Marco Fanizza, Josep Lumbreras and Andreas Winter. Quantum theory in finite dimension cannot explain every general process with finite memory. arXiv:2209.11225, version 2, 5 May 2023. Primary manuscript, especially its discussion of finite linear realizations, positive realizations and polyhedral cones. Cited for the distinction between these representation classes. No quantum implementation or quantum advantage is claimed for PR-LASM. The present block uses a real three-dimensional cone construction proved in Section 51. Source: https://arxiv.org/html/2209.11225v2.

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Anna Jenčová. Base norms and discrimination of generalized quantum channels. arXiv:1308.4030, version 1, 19 August 2013. Primary manuscript, Section 1.2, printed page 5, on finite-dimensional proper cones, normalized bases and base norms. That ordered-vector-space definition is used in Section 46. The classical instrument contraction and observation-tree bound needed here are derived in the text, without importing quantum-channel assumptions. Source: https://arxiv.org/pdf/1308.4030.

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John Watrous. The Theory of Quantum Information. Cambridge University Press, 2018. Author-hosted prepublication text, Chapter 2, Theorem 2.22, printed page 82 (PDF page 90), and the trace-preserving characterization in Theorem 2.26. Used for the established Choi and congruence representations of completely positive maps, not to assign quantum physics to the signal model. The relevant theorem page was visually inspected. Source: https://cs.uwaterloo.ca/~watrous/TQI/TQI.pdf. This third-party text is not redistributed in the bundle.

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Pablo A. Parrilo. Algebraic Techniques and Semidefinite Optimization, MIT 6.972, Lecture 10, 14 March 2006. MIT OpenCourseWare notes, pages 10-1 through 10-3, on polynomial Gram matrices, coefficient constraints and interval positivity. Used for the standard sum-of-squares certificate method. Proposition 53 proves only the sufficient matrix-valued certificate used here and does not import scalar completeness as a matrix theorem. The formula pages were visually inspected. Source: https://ocw.mit.edu/courses/6-972-algebraic-techniques-and-semidefinite-optimization-spring-2006/resources/lecture_10/.

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Herbert Jaeger. Modeling and learning continuous-valued stochastic processes with OOMs. GMD technical report, 8 June 2000. Author-hosted report, title and abstract inspected, establishing that continuous-valued observable-operator modeling and learning are prior work. The present polynomial, certificate and binning arguments are proved within this volume. No guarantee from the report is assigned to the reference implementation. Source: https://www.ai.rug.nl/minds/uploads/jaeger.00.tr.contoom.pdf.

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Ulrich Abel, Ana Maria Acu, Margareta Heilmann and Ioan Raşa. A representation for the integral kernel of the composition of multivariate Bernstein–Durrmeyer operators. arXiv:2512.17297v1, 19 December 2025. The authors' primary manuscript, Introduction, gives the classical univariate Bernstein–Durrmeyer kernel used in Section 72. Its composition theorems are not needed or claimed here. Proposition 64 derives the operator-valued positivity and error statements directly. Source: https://arxiv.org/html/2512.17297v1.

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Steven R. Howard, Aaditya Ramdas, Jon McAuliffe and Jasjeet Sekhon. Time-uniform, nonparametric, nonasymptotic confidence sequences. Annals of Statistics 49(2), 1055–1080, 2021. DOI: 10.1214/20-AOS1991. The primary arXiv record and the conditional exponential-supermartingale discussion in the v4 HTML manuscript were inspected. Proposition 66 proves a simpler union-bound confidence sequence, not the paper's sharper rates. Source: https://arxiv.org/abs/1810.08240 and https://arxiv.org/html/1810.08240v4.

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Roland Hildebrand. An LMI description for the cone of Lorentz-positive maps. Author manuscript, 17 January 2006. Primary manuscript inspected, especially the introduction and definitions on pages 1–2. It supplies classical context for Lorentz-positive maps and the existence of convex descriptions. The present margin and semicircle certificate arguments are proved directly and do not claim to implement the manuscript's full matrix-inequality construction. Source: https://optimization-online.org/wp-content/uploads/2005/12/1260.pdf.

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Tareq Hamadneh, Hassan Al-Zoubi, Hamza Alzaareer and Rafael Wisniewski. Optimization and Positivity Certificates of Rational Functions using Bernstein Form. arXiv:1906.11037, 2019. Primary manuscript inspected, including its Bernstein range enclosure discussion on printed pages 3–4. It supplies established positivity-certificate context. Proposition 75 gives its own tensor-product rectangle argument and strict-subdivision proof. Source: https://arxiv.org/abs/1906.11037.

Inherited dependencies. Proposition 52 defines continuous instrument semantics. Proposition 59 supplies the common-domain continuous-law bound. Propositions 62–63 distinguish exact ellipsoid proposals from verification. Proposition 48 supplies repeated confidence-set accounting. The new block restates the specific repair and uncertainty inequalities it uses. The cited earlier results are present in this cumulative volume.

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Yasin Abbasi-Yadkori, David Pál and Csaba Szepesvári. Online Least Squares Estimation with Self-Normalized Processes: An Application to Bandit Problems. arXiv:1102.2670, version 1, 14 February 2011. The primary manuscript's Section 2, Theorem 3, and Section 5 supply the classical martingale-mixture and adaptive-regression context. Proposition 81 includes its own proof, retains conditional noise and design assumptions, and does not claim a new concentration inequality. Source checked: https://arxiv.org/pdf/1102.2670.

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David A. Levin and Yuval Peres, with contributions by Elizabeth L. Wilmer. Markov Chains and Mixing Times, second edition, 2017. Chapters 4 and 5 develop total variation and coupling. The present minorization argument is proved directly and does not import a finite-state assumption into its general kernel statement. The worked reference chain is finite. Source checked: the author-hosted second-edition text, https://pages.uoregon.edu/dlevin/MARKOV/mcmt2e.pdf.

Internal dependencies. Part VII, especially Propositions 71, 73, 75, 76 and 79, supplies the robust checker and predecessor repair comparison. Propositions 59 and 69 supply the continuous and conditional-kernel full-law comparisons. Their mathematical source passages are retained in this cumulative volume; prior archive identifiers remain in the provenance records.

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