Relatum

A relation-first reasoning system exploring autonomous abstraction from minimal primitives.

Versions

v1/ — archived (tag v1.0)

Relational closure engine with axiom instantiation.

• Algebraic discovery (inductive). From exhaustive enumeration of the 19,683 binary operations on a 3-element carrier, the engine partitions the model space by axiom class and identifies the abelian group region through dual-signal alignment of rarity and closure richness.
• Set-theoretic derivation (deductive). With variable-variable unification, ZFC axioms produce universally quantified consequences directly.
• Phase 1–9 exhaustive verification across 935 models / 10 axiom classes.
• DSL playground at v1/www/ (deployed to GitHub Pages).
• Essay: v1/docs/essay/main.tex.

Frozen. No further development except critical fixes.

v2/ — active

Rebuild from a single ontological commitment: R(x, y) as the only primitive. Self-driven abstraction over R instances. No frontend.

See v2/docs/constitution.md for the five non-negotiable commitments that define v2.

Why the split

v1 proved that relational closure can discover and derive. It does not, however, construct new relations from intrinsic drive. v2 is a rebuild from the stance that cognition is continuous abstraction — the system's ongoing activity is the generation of new relations, not the closure of given ones.

v1 remains as the benchmark; v2 is the current direction.