deliver the coherent, top-down, bird's eye view, grand pictu...

Prompt

deliver the coherent, top-down, bird's eye view, grand picture that emerges from unifying the following works, a through h: a) decision-making under partial observation — the setting in which an agent cannot choose different actions in worlds its sensors do not distinguish. The first volume develops the mathematical foundations; the second turns the same framework into a proof-producing, artifact-backed synthesis pipeline for sensor-limited mechanical control. Each book is fully self-contained with shared notation and non-load-bearing cross-references; read together they form a theory–algorithms duplex. 1. Effective Causal Descent: Uniform Selection, Contextual Gluing, and Causal Histories (~100 printed pages) From a single constraint — observational uniformity — the book derives four presentation-relative diagnostics for when local-to-global assembly of policies fails (local validity, compatibility, effective realisability, bounded realisability), an obstruction datum recording exactly where failure first occurs, and a complete morphism theory (functoriality, sequential and parallel composition, guarded feedback). Classical selection tools — compactness, Helly, join-trees — are recast as finite certificate and gluing tools, and the framework is interfaced with four literatures usually treated separately: constraint satisfaction and sheaf contextuality; Bell nonlocality (Farkas certificates, finite-sample tests, repair profiles); computable analysis (Weihrauch degrees, DNR classes); and extensive-form games and causal protocols. 2. Algorithms and Certificates for Finite Effective Causal Descent: Width-Based Synthesis for Sensor-Limited Mechanical Control The algorithmic companion. A certificate-producing dynamic program over tree decompositions, with ordinary and weighted-width bounds, emits typed, independently checkable certificates: policies, refutations, optimum costs, fibre conflicts, sensor repairs, finite-element rows, and sparsification ladders. A mechanics front end converts declared truss and mass–spring models into certified exact influence rows and brackets the true policy space in an inner/outer sandwich; width-adaptive sparsification provides monotone certified refinement. A recorded computational study benchmarks the pipeline against SAT, CP-SAT, and MILP solvers under strict cross-checking of every answer, is version-exactly replicable via the accompanying public software artifact, and the design side of the problem is completely classified (NP-completeness, W[2]-hardness, logarithmic-approximation barriers under P ≠ NP, and ETH-tight limits). Audience. Graduate students and researchers in theoretical computer science (constraint satisfaction, parameterized complexity, certifying algorithms), AI and decision theory, formal methods and verified numerical computing, quantum contextuality, and control and mechatronics engineering. b) The Rate–Distortion Theory of Bounded Sequential Transduction: A Comparative Syntax for Finite-State Approximation. Research area: Theoretical computer science, at the interface with information theory and operator theory — a rate–distortion theory for finite-state automata and transducers, with lower bounds obtained via AAK/Nehari-type Hankel-operator approximation. The work establishes several principal theorems — a rate–distortion characterization of bounded sequential transduction, a determination-index calculus, and multiletter AAK-type lower bounds and requires substantial background spanning automata theory, information theory, and Hankel operators c) 10.6084/m9.figshare.33926710 d)10.6084/m9.figshare.33954649 e)https://zenodo.org/records/21895686 f)https://zenodo.org/records/21808587 g)https://zenodo.org/records/21792637 h)https://zenodo.org/records/21795780 DOIs:10.5281/zenodo.21789865, 10.5281/zenodo.21808029, 10.5281/zenodo.21804123, 10.5281/zenodo.21791191,