DCT for academics and students
The formal route through Dynamic Corporate Transformation: what is proved, what is computed, and what is still open.
What is proved?
Every object on the DCT Map carries its formal statement, the theory it rests on and its canonical sources. The mathematical stack beneath the Map names the results that carry the weight, from measurable selection and Berge's maximum theorem to the Banach fixed point and the viability theorem.
What is computed?
Every number in the book's Worked Examples and AXIOM Labs is regenerated by an executed notebook, with an Excel mirror, and checked against the book. The validation standard reports the checkpoints and states plainly what they do and do not show.
What is still open?
The research programme sets out open questions, from representing culture in the enterprise state to comparing DCT empirically with conventional methods, each with the Map objects it touches and candidate methods.
Eight stops from the question to the certified decision. Each opens the Map at that object; its drawer gives the formal statement, the theory and the sources.
- 1 The transformation question
What a transformation is: a controlled trajectory, graded on the whole path.
- 2 Enterprise state
The state: sufficient, structured, and chosen for identifiability.
- 3 Transformation operator
Operators that compose but do not commute: sequencing and irreversibility.
- 4 UE · Unified Enterprise Transformation Architecture
Five architectures, one law of motion, one coupling register.
- 5 Viability kernel
Feasible today is not viable tomorrow: the kernel.
- 6 GEOP · General Enterprise Optimization Problem
The General Enterprise Optimization Problem: Volume I poses it.
- 7 B · Dynamic methods
Dynamic methods: Pontryagin, Bellman and Hamilton–Jacobi–Bellman.
- 8 Certified decisions and case studies
The certified decision: policy, certificate chain and sensitivity.
What every object on the Map is built out of. Each layer is used by a named later result.
- Set theory
Sets, relations, mappings and correspondences: the vocabulary in which a state space, an admissible control set and a transformation operator can be defined at all.
- Topological spaces
Neighbourhoods, open sets, continuity and convergence: what it means for a transformation operator to be continuous, for a trajectory to converge, and for a feasible set to be closed.
- Hausdorff spaces
Separation axioms.
- Metric spaces
Distance between enterprise states: how far x(t) is from a target x*, whether it is getting closer, and at what rate.
- Normed spaces
Norms give magnitude: the size of a state change, the effort in a control, the deviation from plan.
- Banach / Hilbert spaces
Completeness makes limits of approximating sequences exist; the inner product makes projection, orthogonality and least squares available.
- Manifolds
Local coordinates on a curved state space, for the case where constraints make X something other than a flat vector space: simplices of shares, positive-definite covariance blocks, ratio and rotation constraints.
- Measure, probability
Measure-theoretic probability and filtrations: the only precise way to say what the enterprise knows and when.
- Stochastic processes
Brownian motion, Poisson and jump processes, Lévy drivers and Markov chains: the concrete disturbance models the enterprise dynamics are driven by, each with a generator that determines the form of the optimality equation.
- Optimization, control
Objectives, constraints, multipliers and policies: the apparatus that turns the unified dynamics into a solvable problem.
Two volumes, thirty-two chapters, a fourteen-week course and a laboratory for every chapter.
Endorsements
…drawing on his outstanding background, exceptional experience, and unique pedagogical skills.
Affiliations are listed for identification only.