urf-axioms

This repository contains the formal axiomatic definitions and logical proofs for the Universal Reference Frame (URF). It is a foundational component of the Vasquez research ecosystem.

Overview

The urf-axioms module provides the primary logic gates and theoretical constraints required for consistent cross-module operations. It serves as the formal mathematical basis for urf-core and specialized research modules.

Reduction Status

The authoritative reduction state of URF is maintained in:

• https://github.com/inaciovasquez2020/urf-core/blob/main/docs/REDUCTION_STATUS.md

FO^k locality is conditionally closed. The only remaining terminal wall is the Clause Contraction Lemma (CCL).

Canonical Registry

This repository is a registered core module of the Vasquez Index. Stable references, archival DOIs, and reproducibility links are maintained at:

• Vasquez Index Dashboard

Repository Status

• Repository Handle: inaciovasquez2020/urf-axioms
• Stability: Refer to the Vasquez Index for the latest stable DOI and version history.
• Infrastructure: scientific-infrastructure

External References

• Unified Rigidity Framework overview: https://inaciovasquez2020.github.io
• Axiom map & status: https://inaciovasquez2020.github.io/vasquez-index/dashboard.html

Yang–Mills Mass Gap

The Hilbert–Schmidt coercivity route is formally blocked. See: axioms/blocked-routes/ym_hs_coercivity_obstruction.md

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Technical Notes

• Integration: These axioms are designed to be imported as a dependency for ensuring logical consistency in simulations and analytical models.
• Reproducibility: To ensure consistent results, utilize the environment configurations defined in the scientific-infrastructure module.
• Documentation: Detailed mathematical derivations and proofs can be found within the repository's documentation directory.

Citation

If you use these axioms or the associated logic in your work, please cite it as follows:

@manual{Vasquez_URF_Axioms_2026,
  author = {Vasquez, Inacio F.},
  title  = {urf-axioms: Formal Axiomatic Framework for URF},
  year   = {2026},
  url    = {[https://github.com/inaciovasquez2020/urf-axioms](https://github.com/inaciovasquez2020/urf-axioms)}
}

## URF Axioms Certification (Released)

This repository includes a released certification layer for the URF axioms.

Scope:
- Declarative axioms and formal definitions
- Deterministic, verifier-checkable artifacts

Non-scope:
- No claims of resolving open problems
- No computational or operational guarantees
- No completeness or consequence enumeration

Certification artifacts are immutable once released.
- TWISTED construction: proofs/twisted_groupoid_construction.md