Circles and Triangles - path to being CTF practitioner
- Leon Como
- Mar 29
- 11 min read
Read the white paper and sign-up or you can sign-up first here: https://www.myhumangpt.com/book-online Executive Summary
The Circles and Triangles Framework (CTF) and it’s modelling tool (Circles and Triangles Model for Everything – Patent Pending) are designed to support discovery, design, orchestration, and implementation across highly varied domains.
In this white paper, CTF is used to refer to both the framework and the modelling tool.
At its most general level, CTF proposes that two fundamental geometric forms — circles and triangles — can be used to represent, structure, and explore any conceivable object, system, or concept. Circles provide bounds, cycles, smoothing, layering, and repetition. Triangles provide structure, tension, complementarity, and foundational relational logic. Used together, they form a practical method for moving from ambiguity toward clarity, from complexity toward workable structure, and from core understanding toward operational edge.
The purpose of this paper is not to fully exhaust the modeling tool or disclose every operational path that can be built from it. Rather, it is to present CTF clearly enough to invite serious collaborators, researchers, designers, builders, institutions, and domain experts to co-develop the most urgent and valuable use cases of our time.
This paper therefore serves four functions at once:
It introduces CTF as a framework and as a universal modeling tool.
It explains why this tool matters now.
It identifies priority use-case domains where co-building is most timely and valuable.
It establishes a collaboration posture: open enough to enable shared progress, disciplined enough to preserve the integrity of the foundational model and the deeper operational pathways required for high-value application.
CTF should be understood as a foundational language for orchestration. It is not limited to one sector, one technical field, or one category of problem. However, the broadness of the model does not diminish the practical value of deeply developed use cases. On the contrary, the most valuable applications are likely to emerge where the framework is most rigorously translated from true core to operational edge.
1. Why This, Why Now
Humanity is increasingly confronted with problems that are not merely complicated, but layered, recursive, fast-moving, and difficult to reconcile within traditional models. Many of today’s most urgent challenges involve simultaneous pressures across people, institutions, technology, nature, economics, and governance. Existing approaches often fragment the problem space, optimize locally, or produce solutions that fail when scaled across interacting layers.
At the same time, new technological capabilities — particularly those associated with generative and inferencing systems — are increasing both the opportunity and the risk. They expand the space of what can be modeled, generated, coordinated, and executed. But they also increase the likelihood of misalignment, fragmentation, abstraction without grounding, and operational drift.
This moment calls for modeling tools that can do more than describe isolated parts. We need tools that can:
identify what is core and what is peripheral,
define minimal and maximal bounds,
preserve productive tension among essential variables,
support layered expansion without losing coherence,
and guide execution from conceptual insight to operational reality.
CTF is offered as one such tool.
2. The Foundational Idea
CTF begins from a simple but expansive premise: circles and triangles can be combined, replicated, layered, expanded, and reconfigured to represent any materially conceivable structure, object, or concept. The usefulness of the framework lies not merely in its visual simplicity, but in the disciplined roles assigned to each form.
2.1 The Role of the Circle
Within CTF, circles primarily represent:
bounds,
cycles,
scope,
inclusion and exclusion,
smoothing,
repetition,
expansion and contraction,
inner and outer limits.
Circles help determine where a system begins and ends, where action is valid, how far influence should extend, what cycles repeat, and what layers surround or constrain a given triangle.
2.2 The Role of the Triangle
Within CTF, triangles primarily represent:
foundational structure,
relational tension,
complementarity,
balancing dynamics,
three-way interaction among essential elements.
The triangle is especially important because any change in one side or corner affects the others. This makes it a strong modeling primitive for situations where variables are interdependent and where action requires navigating tensions rather than eliminating them.
2.3 The Incircle and Circumcircle Logic
A foundational move in CTF is the use of the largest possible circle inside a triangle and the smallest circle that surrounds the same triangle. Repeating this pattern allows the modeler to work with inner and outer bounds, layered expansion, minimal and maximal ranges, and recursive structuring from the core outward.
This makes the framework useful not only for classification, but for:
structured discovery,
scoping,
multi-layer system design,
iterative exploration,
and core-to-edge orchestration.
3. What CTF Is and Is Not
CTF is not merely a diagramming method. Nor is it a claim that geometry alone solves complexity. It is a modeling discipline for finding and structuring essential relationships, bounds, layers, and pathways in complex contexts.
It is not intended to replace domain expertise. Instead, it aims to improve the quality of how expertise is organized, reconciled, and operationalized.
It is not a fixed answer engine. It is a generative and reflective framework that supports discovery, design, clarification, and coordinated execution.
It is not useful only in the abstract. Its greatest value may emerge where the framework is translated rigorously into urgent, high-stakes, high-value use cases.
4. Why Co-Building Matters
A foundational modeling tool becomes truly valuable when it is pressure-tested across real contexts. While CTF can be described in broad terms, its most important future depends on disciplined application and shared development.
No single individual or small team can exhaust the use-case landscape that a general-purpose modeling framework makes possible. Meaningful progress therefore requires co-builders who bring:
domain expertise,
implementation experience,
institutional access,
software capability,
design intelligence,
governance understanding,
operational discipline,
relevant resources
and willingness to work from principle toward execution.
Co-building is especially important because the most valuable use cases are unlikely to emerge from superficial adoption. They will emerge where the framework is understood deeply enough and iterated to preserve coherence from true core to operational edge.
5. Collaboration Posture
This white paper is an invitation to engage and collaborate, not a total disclosure of the deepest operational patterns, implementation pathways, or highest-yield embodiments that may be built using CTF.
The collaboration posture is therefore as follows:
The foundational modeling logic can be examined
Priority use cases can be framed and explored with serious collaborators.
Deeper operational pathways, implementation mechanics, domain translations, and protectable embodiments may be developed through structured collaboration.
The integrity of the framework matters. Use-case development should not dilute the core logic, confuse the bounds, or collapse the distinction between foundational model and operational implementation.
In short: this is an open invitation to co-build, and not a surrender of the foundational or path-dependent value embedded in the framework.
5.1 Proposed Licensing Framework for CTF
To support legitimate adoption while preserving the integrity, attribution, and value of the CTF modeling tool, use of the framework is proposed to follow a licensing structure. The purpose of this structure is not to obstruct good-faith learning or responsible experimentation, but to distinguish between low-friction internal use and higher-value or outward-facing uses that require more explicit alignment and contractual discipline.
The proposed licensing posture is built on a simple principle: low-risk internal use may be licensed through standard terms, while broader, public-facing, commercial, embedded, redistributed, or derivative uses require negotiated agreement.
All licensed use of the CTF modeling tool should preserve attribution and traceability. Any public-facing use, publication, derivative methodology, training material, or implementation explicitly based on or traceable to the CTF modeling tool should include notice of ownership and attribution to the owner, subject to the applicable license terms.
5.2 For the licensing structure, please see appendix of visit the website
6. Criteria for Priority Use Cases
Not every possible application deserves equal attention. The most promising use cases for co-building at this stage are those that meet several of the following criteria:
6.1 Urgency
The use case addresses a current problem where delay imposes significant human, institutional, economic, or ecological cost.
6.2 Structural Complexity
The use case involves interacting layers, conflicting incentives, unclear bounds, or recurring failures of traditional linear approaches.
6.3 High Leverage
A successful implementation would create outsized improvement in clarity, coordination, risk reduction, design quality, or execution effectiveness.
6.4 Need for Core-to-Edge Precision
The use case requires more than broad abstraction. It depends on correctly identifying the true core, preserving coherence through layered expansion, and translating that structure into actionable pathways.
6.5 Reusability
The patterns discovered in one implementation can inform multiple adjacent applications.
6.6 Partnership Readiness
There are credible co-builders, institutions, operators, or communities willing to engage in structured development.
7. Urgent and Valuable Use-Case Domains
The following domains are presented as promising starting points for co-building. They are not exhaustive. They are priority candidates because they combine urgency, complexity, and leverage.
7.1 Organizational / institutional Change and Transformation Orchestration
Many organizations / institutions struggle not because they lack the talents, strategy or technology, but because they cannot reconcile leadership intent, operational reality, stakeholder behavior, system constraints, and adoption dynamics. CTF can help model the true core of current state, of the change, and of the future state, distinguish bounds from sides, map layers of influence, and guide transformation from conceptual direction to operational uptake.
Potential outputs include:
core to edge outlay or mapping
edge to core connections
links to dependencies and dependent entities
decision and escalation models,
stakeholder and governance maps,
change architecture templates,
transformation health indicators,
and systemized pathways from strategy to adoption.
7.2 AI and Inferencing System Orchestration
As generative and inferencing systems become more powerful, there is increasing need for frameworks that can maintain coherence across model core, human orchestration, domain context, bounded deployment, and real-world feedback. CTF is well suited for modeling layered intelligence systems, identifying true core constraints, and structuring paths from abstract capability to useful, safe, and adaptive operational outcomes.
Potential outputs include:
inferencing workflow models,
governance patterns for human-in-the-loop systems,
protocolized decision pathways,
orchestration tools for domain-specific AI use,
and core-to-edge architectures for scalable inferencing ecosystems.
7.3 Governance, Policy, and Multi-Stakeholder Coordination
Many governance failures arise when the parties involved lack a shared model for bounds, incentives, role tensions, and layered consequences. CTF can help map policy spaces, reconcile stakeholder tensions, define operational bounds, and support more coherent interventions where problems span public, private, civic, and technical spheres.
Potential outputs include:
decision models for complex public problems,
governance design templates,
cross-sector reconciliation structures,
layered policy maps,
and practical tools for balancing principles, incentives, and execution.
7.4 Education, Sensemaking, and Human Capability Development
As complexity rises, individuals and institutions need better ways to learn, reason, communicate, and build judgment without being overwhelmed. CTF can serve as both a teaching tool and a practical reasoning scaffold, helping people structure complexity, identify essential tensions, and work more confidently from bounded models.
Potential outputs include:
educational modules,
reasoning and problem-framing tools,
leadership development models,
visual learning systems,
and capability-building platforms.
7.5 Systems Design for Sustainability, Resilience, and Regeneration
Problems involving environmental stewardship, infrastructure resilience, and long-horizon societal design require models that can track tradeoffs, bounds, cycles, and recursive consequences. CTF may help structure such contexts without reducing them to one-dimensional optimization.
Potential outputs include:
resilience and regeneration maps,
scenario structures,
operational boundary tools,
and layered decision models connecting technical, human, and ecological factors.
8. What Serious Co-Builders Should Bring
The most valuable co-builders are not necessarily those with the loudest enthusiasm, but those willing to work rigorously across abstraction and implementation.
Useful collaborator profiles may include:
domain experts facing structurally complex problems,
enterprise leaders with real transformation mandates,
software and systems architects,
product and UX designers,
policy and governance practitioners,
researchers and educators,
operators who understand what breaks at the edge,
and institutions willing to test the framework in live settings.
Ideal co-builders should be prepared to help answer questions such as:
What is the real core in this domain?
What are the correct bounds?
What tensions must be preserved rather than flattened?
What constitutes operational edge in this context?
Where does translation commonly fail?
Which outputs can become reusable artifacts, tools, or methods?
9. A Suggested Co-Building Method
The following staged approach can guide collaboration:
Stage 1: Context Framing
Define the opportunity / problem space, operating environment, stakeholders, usable breakthroughs, current pain points, and why the opportunity / problem matters now.
Stage 2: Core Identification
Use CTF to identify the true core triangle and the relevant circle of bounds. Clarify what is essential, what is peripheral, and what constitutes valid scope.
Stage 3: Layer and Tension Mapping
Map inner and outer circles, adjacent triangles, recurring cycles, and interactions among layers. Surface tensions that need to be managed rather than removed.
Stage 4: Core-to-Edge Path Design
Translate the model into practical pathways, structures, artifacts, workflows, protocols, tools, or interventions that can operate in real environments.
Stage 5: Validation and Iteration
Test whether the model holds under pressure, where it drifts, what needs refinement, and which elements become reusable for adjacent use cases.
This staged approach does not claim to be the only way to co-build with CTF. It is simply one practical path for converting foundational modeling into collaborative development.
10. On Intellectual Integrity and Value Creation
A framework as broad as CTF raises understandable questions about openness, attribution, and protection.
This paper takes the view that both openness and discipline are needed.
Openness matters because foundational tools become stronger when understood, challenged, refined, and applied across domains.
Discipline matters because high-value embodiments often depend on deeper operational understanding, precise translation, and sustained developmental effort. Not all value lies in the broad statement of the model. Much of it lies in the exact path by which the model is applied from true core to operational edge.
Accordingly, this paper invites collaboration while preserving the principle that not every operational layer needs to be publicly exhausted in order for the ecosystem to grow.
11. What Success Would Look Like
If this effort succeeds, CTF will not remain only a conceptual model. It will become:
a practical modeling language,
a catalyst for co-developed use cases,
a bridge from complexity to clarity,
a design and orchestration aid across multiple fields,
and a source of reusable patterns, tools, and implementations that improve real-world outcomes.
Success would mean that the framework helps serious builders:
identify what truly matters,
preserve coherence under complexity,
move from insight to execution,
and develop systems that are more grounded, more adaptive, and more generative of value.
12. Invitation
This is an invitation to individuals, teams, organizations, and institutions who recognize that many of today’s most important opportunities and problems cannot be realized / solved by fragmented models or isolated optimizations.
If you are working on urgent, high-value, structurally complex opportunity / problems and need a better way to model, reconcile, design, and operationalize from core to edge, CTF may be worth building with.
The invitation is especially open to those willing to do the harder work: not just discussing a general model, but helping translate it into practical, rigorous, high-leverage use cases that matter now.
The next step is not to declare that the framework already answers everything. The next step is to co-build the places where it can prove most useful, most urgent, and most valuable.
Appendices
Appendix A: Concise Description of the Foundational Model
The foundational description of CTF presents circles and triangles as the two basic forms needed to model any conceivable structure, object, or concept. Triangles can be replicated, reconfigured, and combined in unlimited ways to form polygons and structural variants. Circles can be expanded, replicated, reconfigured, and combined to model curves, bounds, arcs, layers, and cyclical characteristics. Used together, they create practically limitless modeling possibilities. The method emphasizes circles for bounding, smoothing, and cyclical properties, and triangles for structural interdependence, complementarity, and balancing tension. A key pattern involves the largest possible circle within a triangle and the smallest circle surrounding the same triangle, repeated as needed to manage complexity, establish layering, and define minimal and maximal bounds.
Appendix B: Collaboration Signals
Potential collaborators may find this work aligned if they are interested in any of the following:
building high-value use cases from a general modeling framework,
translating foundational concepts into software, systems, or operational methods,
co-developing tools for orchestration, change, governance, AI, education, or systems design,
and participating in a disciplined collaboration that values both openness and integrity.
Appendix C: Concise Licensing Matrix
The following matrix summarizes the proposed licensing posture for the CTF modeling tool.
The fee range starts from being a registered subscriber of regular COPOP drops to being fully trained and coached on your CTF orchestration dependent on the number of participants and the size of projects in an organization.
License Class | Intended Use | Indicative Fee Range | Key Conditions |
Personal, Nonprofit Internal Use | Internal use by nonprofit, educational, exploratory, or mission-driven organizations | USD 0–500 | Internal only; no sublicensing; no resale; no external commercialization; attribution and owner notice for public-facing outputs |
Commercial Internal Use | Internal use by for-profit organizations | USD 501–10,000 | Internal only; non-transferable; non-sublicensable; no resale of the tool; no client-facing commercialization of CTF as a named method without further agreement; attribution and owner notice for public-facing outputs |
Negotiated License | Any external, embedded, derivative, redistributed, or broader commercial use | Negotiated | Required for co-build, consulting delivery, software embedding, training/certification, derivative methodologies, sublicensing, multi-entity deployment, white-label use, and similar use cases |
Closing Note
This white paper is a starting point. It is intended to make the framework legible enough for meaningful collaboration while preserving the depth and developmental potential of the work still to be built.
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