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/ — paused (2026-05-29)

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.

Paused, not frozen — the closure / theory runtime is mature through ADR 0083 and stable on the long-horizon OQ#1 (tick 2400). Work resumes when v3 reaches M5 (the bridge milestone).

v3/ — active

World-model substrate. Primitive shifts from R(x, y) to state(node, t) / transition(node, t → t+1); R(x, y) becomes a derived layer recovered from anonymous state sequences.

Working proposition: recover de-named relation structure from anonymous state sequences. n-ary primitives are allowed natively, with mandatory binary projection + irreducibility test.

See v3/docs/constitution.md for the changed primitive, the changed arity, and the v3-specific augmented commitments (A1–A4).

Why the split

v1 proved that relational closure can discover and derive. v2 added self-driven abstraction over given R. v3 attacks the layer underneath: recovering R from state dynamics, with anonymization as the test bench.

v1 is the benchmark; v2 is the closure / theory runtime; v3 is the world-model substrate. The three coexist by design — v3 has no Cargo dependency on v2 and vice versa.