Euclid's axiomatic method applied through compass and straightedge to agent governance. The four-layer architecture that SwiftVector inherits directly from the Elements.
Euclid didn't discover geometry. He organized it. Book I of the Elements begins with 23 definitions, 5 postulates, and 5 common notions. From these, 48 propositions follow — each one derived from what came before, never from intuition, never from authority.
This is not ancient history. This is the architectural pattern that governs SwiftVector. Type definitions. Common axioms. Constitutional laws. Evaluation decisions. The same four layers, the same derivation chain, 2,300 years apart.
The first proposition in the Elements. Given a finite straight line, construct an equilateral triangle upon it. Seven steps. Each step cites a definition, postulate, or common notion. No step can skip a step.
Explore the proof interactively below. Hover over each step to see the construction animate.
SwiftVector's constitutional governance layer is Euclid's structure applied to agent behavior: a small set of declared laws, from which every permitted action is derived, and through which every evaluation is traceable.
Both systems share the same structural requirement: primitives declared, everything derived, no step skipping a step.
A Euclidean construction tool built for the web. Compass and straightedge only — no rulers, no protractors, no measurement. Every operation invokes a named postulate. Every step is logged with its Euclidean citation.
In the tradition of Geometer's Sketchpad (Jackiw, 1991) — which never made the Silicon transition. Construkt is deterministic, citation-tracked, and built on the same formal principles that govern SwiftVector.
Both Euclid and SwiftVector follow the same derivation structure. Definitions ground the vocabulary. Axioms establish domain-independent truths. Postulates define what operations are permitted. Propositions are derived — never assumed.
Point. Line. Circle. What each term means, stated precisely.
23 definitionsDomain-independent axioms about equality. Shared across all reasoning.
5 common notionsWhat you are permitted to do: draw a line, describe a circle.
5 postulatesEverything derived. Each cites definitions, postulates, or prior propositions.
48 propositions (Book I)ResourceType. ActionType. Principal. The primitive action surface.
Compiler-enforcedSession deny overrides action allow. Composition accumulates monotonically.
Core invariantsBoundary, resource, authority law. The fail-closed constitutional layer.
Declared · auditableEvery ALLOW, DENY, ESCALATE derived from layers above. Full trace required.
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