Explore the connections
Every page and idea on this site, and where each one leads
DCT is one argument, not a list of topics. Every object on this site leads somewhere: deeper into the mathematics, out to a laboratory or a case, into practice through DCT Helix, or back to plain words. Choose any point and follow it as far as you like.
Points are arranged by DCT’s moves, from Represent on the left to Adapt on the right. Pages and parts that serve every move sit in the frame around them.
Choose a point to see where it leads and what leads to it.
Every point, by kind
DCT moves 7
Map objects 34
- A · Problem to instance; static methods
- AC · Enterprise Capital Architecture
- AP · Enterprise Performance Architecture
- AR · Risk, Resilience, Robustness
- AS · Enterprise State Architecture
- AT · Enterprise Transformation Architecture
- Architectural Jacobian
- B · Dynamic methods
- C · Uncertainty methods
- Capital allocation and risk-adjusted strategy
- Certificates, audits, and readiness gates
- Certified decisions and case studies
- D · Multi-criteria and decomposition
- Digital twin execution and the AXIOM laboratory
- Dynamic enterprise systems
- E · Intelligence layer
- Enterprise as open adaptive system
- Enterprise state
- Environment and disturbance
- F · Digital twin and autonomy
- Feasible region
- GEOP · General Enterprise Optimization Problem
- Limits of existing frameworks
- Management controls
- Mathematical language
- Modeling principles
- Need for state, dynamics, control, optimization
- Neumann multiplier
- Roadmaps and policy design
- Stochastic enterprise dynamics
- The transformation question
- Transformation operator
- UE · Unified Enterprise Transformation Architecture
- Viability kernel
The mathematical stack 10
Chapters 32
- Vol. I, Ch. 1: Introduction to Dynamic Corporate Transformation
- Vol. I, Ch. 10: Enterprise Capital Architecture
- Vol. I, Ch. 11: Enterprise Performance Architecture
- Vol. I, Ch. 12: Enterprise Risk, Resilience, and Robustness Architecture
- Vol. I, Ch. 13: Unified Enterprise Transformation Architecture
- Vol. I, Ch. 14: Mathematical Analysis of the Unified Enterprise Transformation Architecture
- Vol. I, Ch. 15: Mathematical Formulation of Enterprise Optimization
- Vol. I, Ch. 16: Synthesis, Future Directions, and Transition to Volume II
- Vol. I, Ch. 2: Enterprise Systems and Transformation
- Vol. I, Ch. 3: Mathematical Foundations
- Vol. I, Ch. 4: Enterprise Modeling Principles
- Vol. I, Ch. 5: Enterprise State Representation
- Vol. I, Ch. 6: Enterprise Transformation Operators
- Vol. I, Ch. 7: Dynamic Enterprise Systems
- Vol. I, Ch. 8: Stochastic Enterprise Dynamics
- Vol. I, Ch. 9: Enterprise State Architecture
- Vol. II, Ch. 1: Introduction to Enterprise Optimization
- Vol. II, Ch. 10: Neuro-Fuzzy Robust Enterprise Optimization
- Vol. II, Ch. 11: Distributionally Robust Enterprise Optimization
- Vol. II, Ch. 12: Multi-Objective Enterprise Optimization
- Vol. II, Ch. 13: Machine Learning for Enterprise Transformation
- Vol. II, Ch. 14: Artificial Intelligence for Enterprise Optimization
- Vol. II, Ch. 15: Enterprise Digital Twins and Autonomous Enterprise Transformation
- Vol. II, Ch. 16: Enterprise Applications and Integrated Transformation Case Studies
- Vol. II, Ch. 2: The General Enterprise Optimization Problem Revisited
- Vol. II, Ch. 3: Convex Enterprise Optimization
- Vol. II, Ch. 4: Nonlinear and Mixed-Integer Enterprise Optimization
- Vol. II, Ch. 5: Dynamic Enterprise Optimization
- Vol. II, Ch. 6: Optimal Control of Enterprise Systems
- Vol. II, Ch. 7: Dynamic Programming for Enterprise Systems
- Vol. II, Ch. 8: Hamilton–Jacobi–Bellman Enterprise Framework
- Vol. II, Ch. 9: Stochastic Enterprise Optimization
Laboratories 32
- Lab I.1: Introduction to Dynamic Corporate Transformation
- Lab I.10: Enterprise Capital Architecture
- Lab I.11: Enterprise Performance Architecture
- Lab I.12: Enterprise Risk, Resilience, and Robustness Architecture
- Lab I.13: Unified Enterprise Transformation Architecture
- Lab I.14: Mathematical Analysis of the Unified Enterprise Transformation Architecture
- Lab I.15: Mathematical Formulation of Enterprise Optimization
- Lab I.16: Synthesis, Future Directions, and Transition to Volume II
- Lab I.2: Enterprise Systems and Transformation
- Lab I.3: Mathematical Foundations
- Lab I.4: Enterprise Modeling Principles
- Lab I.5: Enterprise State Representation
- Lab I.6: Enterprise Transformation Operators
- Lab I.7: Dynamic Enterprise Systems
- Lab I.8: Stochastic Enterprise Dynamics
- Lab I.9: Enterprise State Architecture
- Lab II.1: Introduction to Enterprise Optimization
- Lab II.10: Neuro-Fuzzy Robust Enterprise Optimization
- Lab II.11: Distributionally Robust Enterprise Optimization
- Lab II.12: Multi-Objective Enterprise Optimization
- Lab II.13: Machine Learning for Enterprise Transformation
- Lab II.14: Artificial Intelligence for Enterprise Optimization
- Lab II.15: Enterprise Digital Twins and Autonomous Enterprise Transformation
- Lab II.16: Enterprise Applications and Integrated Transformation Case Studies
- Lab II.2: The General Enterprise Optimization Problem Revisited
- Lab II.3: Convex Enterprise Optimization
- Lab II.4: Nonlinear and Mixed-Integer Enterprise Optimization
- Lab II.5: Dynamic Enterprise Optimization
- Lab II.6: Optimal Control of Enterprise Systems
- Lab II.7: Dynamic Programming for Enterprise Systems
- Lab II.8: Hamilton–Jacobi–Bellman Enterprise Framework
- Lab II.9: Stochastic Enterprise Optimization
In Practice cases 16
- American Airlines: $1.4 billion over three years, by American's estimate
- Ford: 408 very-high-impact sites among 4,534 examined
- Google: About 30 percent cooling savings under direct control, by Google's account
- Institutional brokers: An impact model estimated from 29,509 orders
- Kellogg: An estimated $4.5 million saved in 1995
- Large banks: A supervisory expectation since 2008
- MISO: $2.1–3.0 billion saved in 2007–2010, by MISO's estimate
- Netflix: A 10.06 percent improvement, after almost three years
- NFL: More than 80,000 feasible schedules analyzed for 2021
- Northern Prawn Fishery: Maximum economic yield, the target since 2003
- NS: A record 87 percent punctuality in 2007
- ONS · CCEE: The model chain sets Brazil's official spot price
- Reclamation · Basin States: Futures with Lake Mead below 1,000 feet cut from about 19 to 3 percent
- Rolls-Royce: 75 percent of potential in-flight events mitigated in 2008, by its account
- UPS: $320 million saved by December 2015
- Zara: Clearance revenue up about 6 percent in a controlled pilot
The integrated case 1
Retrospective readings 4
- Danaher’s improvement engine compounds, and every acquisition runs through it.
- DBS laid its platforms first, then let each business step on its own clock.
- Ford secured financing early, ran one plan and made the truth visible every week.
- Microsoft let each business move on its own clock and made culture the shared rung.
Overview stages 12
- Stage 1: The model of the enterprise is usually the problem
- Stage 10: Watch the conditions that would void the plan
- Stage 11: A shock tests the certificates, not the nerve
- Stage 12: Re-plan on triggers declared in advance, with fresh certificates
- Stage 2: Describe the enterprise as a state, not a dashboard
- Stage 3: Say what “better” means before the analysis
- Stage 4: Write down what cannot be breached
- Stage 5: Treat programmes as moves with a cost, a duration and a dip
- Stage 6: Check that the commitments can hold together
- Stage 7: Feasible today is not viable tomorrow
- Stage 8: Order and money are decisions, and the model prices them
- Stage 9: Departments step on their own clocks, around shared platforms
Principles 10
- Autonomy only inside a declared envelope.
- Certify before you optimize.
- Every constraint has a price.
- Feasible today is not viable tomorrow.
- Order is a decision: transformations don't commute.
- Policies respond to the state; re-planning responds to changed assumptions, on triggers declared in advance.
- Represent before you optimize: a dashboard is not a state.
- Silos are the integrated problem with extra constraints.
- The path is graded, not just the destination.
- Uncertainty belongs inside the decision, not after it.
Lexicon terms 110
- A · architectural Jacobian
- A · Problem to instance; static methods
- AS, AT, AC, AP, AR, UE · architecture objects
- AC · Enterprise Capital Architecture
- AP · Enterprise Performance Architecture
- AR · Risk, Resilience, Robustness
- Architectural Jacobian
- AS · Enterprise State Architecture
- AT · Enterprise Transformation Architecture
- Autonomy envelope
- AXIOM
- B · Dynamic methods
- Banach / Hilbert spaces
- Best-practice transfer
- C · Uncertainty methods
- Capital allocation and risk-adjusted strategy
- Certificate
- Certificates, audits, and readiness gates
- Certified decisions and case studies
- Change management
- Continuous improvement
- Control
- Coupling register
- Customer experience
- D · Multi-criteria and decomposition
- Data and AI platform
- Digital twin execution and the AXIOM laboratory
- Dynamic enterprise systems
- E · Intelligence layer
- End-to-end processes
- Enterprise as open adaptive system
- Enterprise state
- Enterprise state
- Enterprise step
- Environment and disturbance
- ERP and core systems
- F · Digital twin and autonomy
- Feasible region
- Feasible region
- Finance
- Financial discipline
- Focused step
- Foundation first
- G1 Baseline certified
- G2 Diagnosis certified
- G3 Step certified
- G4 Design certified
- G5 Benefits banked
- G6 New equilibrium certified
- G7 Renewal decision
- General Enterprise Optimization Problem
- GEOP · General Enterprise Optimization Problem
- Hard
- Hausdorff spaces
- J[u] · objective functional
- Leadership and culture
- Learning and adaptation
- Limits of existing frameworks
- M&A integration
- Management controls
- Manifolds
- Mathematical language
- Measure, probability
- Metric spaces
- Modeling principles
- Need for state, dynamics, control, optimization
- Neumann multiplier
- Neumann multiplier
- Non-commuting operators
- Normed spaces
- Operating equilibrium
- Operating model and organization
- Operational excellence
- Operations and supply chain
- Optimization, control
- Orchestrated multi-strand step
- Orchestrator
- People (HR)
- Procurement
- Product and innovation
- Risk and compliance
- Risk and resilience
- Roadmaps and policy design
- S · Neumann multiplier, long-run impact
- Set theory
- Shadow price (multiplier, costate)
- Soft
- Spectral radius
- Stochastic enterprise dynamics
- Stochastic processes
- T · transformation operator
- Target state
- Technology and data
- The transformation question
- Topological spaces
- Transformation operator
- Transformation operator
- U · admissible control space
- u(t) · management controls and decisions
- UE · Unified Enterprise Transformation Architecture
- V · value function
- Value
- Viab(Ω) · viability kernel
- Viability kernel
- Viability kernel
- W · disturbance space
- w(t) · environment and disturbance
- X · state space
- x(t) · enterprise state vector
- λ, p · multipliers and costates
Open questions 12
- How can architectural coupling be estimated empirically?
- How can DCT be compared empirically with conventional transformation methodologies?
- How can leadership capability be measured without false cardinal precision?
- How do transformation operators behave when the organization learns?
- How much transient amplification do real organizations show?
- How should AI agents enter the enterprise state and the transformation architecture?
- How should behavioural and political organizational constraints be represented?
- How should latent capabilities be estimated?
- How should organizational culture be represented within the enterprise state?
- How should time-consistency be kept when boards use risk measures?
- How stable are optimal transformation policies under model misspecification?
- When is an enterprise state representation sufficient?
Audience pages 4
DCT Helix sections 6
DCT Helix moves 7
- DCT Helix, Adapt: Embed, learn and renew
- DCT Helix, Analyze: Understand the dynamics
- DCT Helix, Certify: Size and certify the step
- DCT Helix, Execute: Mobilize and deliver
- DCT Helix, Monitor: Measure, sense and steer
- DCT Helix, Optimize: Design the target and the path
- DCT Helix, Represent: Diagnose the enterprise
Strands 8
Rungs 6
Engines 7
One loop, three layers 31
- Adapt in AXIOM: Planning, Strategy
- Adapt in DCT Helix: gate G7, Renewal decision
- Adapt in DCT: Re-estimate, re-certify, re-solve on declared triggers
- Adapt: one move, three layers
- Analyze in AXIOM: Profitability, Feedback
- Analyze in DCT Helix: gate G2, Diagnosis certified
- Analyze in DCT: Five architectures and the coupling register M
- Analyze: one move, three layers
- Certify in AXIOM: Optimization
- Certify in DCT Helix: gate G3, Step certified
- Certify in DCT: Consistency, ρ(A) < 1, x₀ in the viability kernel
- Certify: one move, three layers
- Execute in AXIOM: PMO, Execution
- Execute in DCT Helix: gate G5, Benefits banked
- Execute in DCT: Sequence by operator order and allocate by costates
- Execute: one move, three layers
- Monitor in AXIOM: Dashboard, Execution
- Monitor in DCT Helix: gate G6, New equilibrium certified
- Monitor in DCT: Estimate the state; watch the certificate conditions
- Monitor: one move, three layers
- Optimize in AXIOM: Strategy, Planning, Financing
- Optimize in DCT Helix: gate G4, Design certified
- Optimize in DCT: Solve the GEOP: policy π*, multipliers, costates
- Optimize: one move, three layers
- Represent in AXIOM: Structure, Dashboard
- Represent in DCT Helix: gate G1, Baseline certified
- Represent in DCT: Declare state, controls, disturbances, dynamics
- Represent: one move, three layers
- The AXIOM layer: the instrument
- The DCT Helix layer: the practice
- The DCT layer: the discipline
Pages 36
- About the author
- AXIOM
- Board Transformation Checklist
- Book an Executive Discovery Conversation
- Case studies
- Cases and evidence
- Chapters
- Computational validation standard
- DCT Advisory
- DCT Diagnostic
- DCT for the Boardroom
- DCT Helix
- DCT Lexicon
- DCT principles
- Endorsements
- ERP and enterprise systems
- Explore the connections
- Four transformations, read through the Helix lens
- Home
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- How DCT, DCT Helix and AXIOM fit
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- Privacy
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- Schedule
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- What is DCT
- Why DCT?