URF Axioms — formal axiomatization of the Unified Rigidity Framework, defining primitives, admissibility conditions, and base invariants.

Biological Friction Framework — structural limits on biological dynamics from capacity, dissipation, and rigidity, with executable consistency checks.

URF Counterexamples — certified counterexamples and boundary cases for the Unified Rigidity Framework, clarifying limits and failure modes.

URC Minimal Blockchain — minimal, auditable blockchain core illustrating capacity, locality, and rigidity constraints with deterministic verification.

Description Radiative Rigidity — structural rank-1 constraints on long-distance electroweak radiative corrections with executable consistency tests.

Rank Dichotomy Theorem for CAT(0) Cube Complexes (canonical)

Cycle-Local Rigidity — locality-based rigidity from cycle structure; executable witnesses and proofs of local-to-global obstruction.

URF Prefab System — canonical prefab constructions and normal forms for the Unified Rigidity Framework, enabling reproducible instantiation of certified rigidity results.

Chronos–EntropyDepth — information-theoretic limits on refinement and computation; entropy depth bounds, certificates, and executable witnesses.

Exchange Force Framework — structural exchange-force model unifying interaction, capacity, and rigidity constraints with executable consistency checks.

Chronos–URF RR — reference implementation of Chronos entropy-depth bounds and rigidity results within the Unified Rigidity Framework.

Final Wall (FOᵏ Locality) — terminal obstruction results for FOᵏ locality, proving rigidity walls and limits of refinement-based computation.

URF Core — foundational axioms, definitions, and theorems of the Unified Rigidity Framework, serving as the minimal trusted base.

URF Spine — canonical spine of the Unified Rigidity Framework: normal forms, invariants, and formally verified core constructions.