Intelligence and Computation Regime Companion — From Representation to Recursive Agency Joshua K. Cliff, 2026 294 pages · 32 chapters · 9 appendices · 113 formal results · CC BY 4.0 Overview This volume is the intelligence and computation regime companion to the Principal Dynamics foundation monograph (10.5281/zenodo.19334803). It proves that the monograph's abstract framework — coherence, gating, projection, and coarsening — admits a concrete realization on the class of intelligence and computation systems: systems that represent, learn, predict, plan, and govern their own operation. The central result is full quantitative cognitive closure: on the declared admissible class and canonical completion branch, every benchmark-facing quantity is determined, with no free continuous moduli within the declared benchmark-facing inventory, by a single normalized datum λ*. Every theorem is either a direct specialization of a monograph result or a consequence of such specializations composed with explicitly stated regime closure laws satisfying the Extension Charter (EC1–EC8). Direct Reductions (Part I) Five direct-reduction layers are constructed from the monograph foundation: dynamics (corrected representation domain, gate margin, update susceptibility), memory (attractor landscape, basin geometry, interference index), semantics (semantic functor, compositional structure), learning (learning-as-coarsening, generalization law), and world-modeling (predictive bridge, calibration). These reductions use only the monograph foundation and standard mathematics, without regime closure laws. Structural Closure (Part II) Six structural closure targets are closed: universality (A) — the low-order infrared structure of admissible intelligence systems is universal; canonical capture (B) — the intelligence-regime analogue of Lorentz emergence; bridge uniqueness (C) — the semantic functor is uniquely determined; learning-as-coarsening (D) — learning is a coarsening semigroup; world-model bridge (E) — the predictive bridge is constructive; and governance/safe-recursion (F) — the governance architecture and recursive-improvement ceiling are forced by the gate structure. Quantitative Closure (Part III) On the canonical branch, all sector parameters — capacity, generalization defect, hallucination threshold, adversarial margin, planning regret, governance risk, and recursive-improvement ceiling — are uniquely determined as branch functionals of λ*. The forcing proceeds through finite-moduli, common-source, sector-rigidity, ceiling, normalization, and endpoint arguments, culminating in full closure with zero free continuous moduli. Deeper Sectors and Predictions (Parts IV–V) Part IV extends the closed regime to multi-agent systems (institutional completion, coordination labels), scientific discovery (discovery-as-coarsening), and alternative architectures (alternative-branch exclusion). Part V states the benchmark protocol and the explicit claim boundary. What Is Not Claimed No executed benchmark packet is claimed in this volume. No concordance verdict is rendered. The execution architecture is a specification; actual execution of the benchmark sheet remains external to this volume and pending evaluation. Full empirical adequacy is not established. If the normalized branch fails any blocking row of the benchmark sheet, the regime is falsified on that domain. Branch universality holds on the declared comparison neighborhood; universality across all conceivable admissible classes is not asserted. All quantitative results are branch-qualified: they hold on the declared admissible class and canonical completion branch. This volume does not claim that Principal Dynamics is the unique correct theory of intelligence. It claims that PD provides a mathematically consistent, internally closed, and empirically falsifiable framework for the intelligence regime. Related Volumes Foundation Monograph: 10.5281/zenodo.19334803 Physics Regime Companion: 10.5281/zenodo.19334816 Keywords: Principal Dynamics, intelligence regime, computation, representation, learning, governance, quantitative closure, branch functional, AI safety, hallucination threshold, benchmark, recursive improvement