here's abstract for current monograph: "We develop effective...

Prompt

here's abstract for current monograph: "We develop effective causal descent as a section-theoretic account of decision-making under partial observation. The basic constraint is observational uniformity: an interface cannot support different responses to worlds it does not distinguish. From this arise four presentation-relative diagnostics: local validity, compatibility of a declared diagram, effective realisability, and bounded realisability. The labels are not invariants of bare capability predicates; they record where success first fails in a chosen local-to-global presentation. The static kernel is a fibrewise selector lemma. Compactness,Helly, join-tree, parity, support-contextuality, source-integration, and Bell-coupling results provide finite certificate and gluing tools. The obstruction datum records objectwise local success and the nested spaces \(\Gamma_{\mathrm{set}}\supseteq\Gamma_{\mathrm{eff}}\supseteq \Gamma_{\mathcal B}\); terminal compression preserves the nested global spaces while erasing precisely the \(\mathsf D\)-gap. The monograph develops the companion morphism theory: global-family functoriality, diagnostic and certificate morphisms, terminal compression as an idempotent functor,support-packaging functoriality, distributed/one-shot groupoid equivalence,arena patch-sheaf functoriality, and composition laws for constraints, static compilations, sequential composition, parallel composition, and guarded feedback. Computability examples yield the binary DNR \(\Pi^0_1\) class, the PA oracle spectrum, \(\mathsf{WKL}\) Weihrauch degrees, and a \(\Sigma^0_3\)-complete primitive-recursive capability index set. The causal tier proves backward induction, active-sensing presentation relativity, confluent causal-poset execution, global-recall action-recall redundancy, and a height-two causal DNR/PA transfer. The Bell module adds local-causal interpretation, Farkas certificates, finite-sample testing, and repair profiles." develop a separate algorithmic paper. ensuring algorithmic results meet the bar for "Journal of Applied and Computational Mechanics": Algorithms and Certificates for Finite Effective Causal Descent with finite complexity classifications, width-based tractability, and certificate extraction.