Research crosswalk
- Non-Self-Approving AI-Assisted Derivation
- Mathematics Ontology Bible
- Appendix C — math-to-toolkit map
- Foundational ontology literature crosswalk
- Consciousness / sentience / ASI crosswalk
- Assurance-case integrity crosswalk
Appendix C: Cross-Reference to the LLM Governance Toolkit
| Math concept | Toolkit component | Role |
|---|---|---|
| Fixed-point theorems (Tarski, Banach) | fixed_point_governor.py | Detects well-founded vs. ungrounded governance towers |
| Well-founded recursion | fixed_point_governor.py | Ensures governance chains bottom out at human authority |
| Gödel incompleteness | fixed_point_governor.py, governed_decision.py | Motivates WITHHOLD for undecidable scenarios |
| Proxy/truth decoupling (Goodhart) | decoupling_monitor.py, goodhart_auditor.py | Detects when a metric has decoupled from the goal it measures |
| Causal/dependency graph | dependency_graph.py | Traces root causes; ensures well-founded explanations |
| Information theory (entropy) | ground_truth_auditor.py | Measures independence of evidence sources |
| Temporal logic | temporal_governor.py | Enforces tense-to-verifiability mapping |
| Measure theory (probability) | decoupling_monitor.py | Correlation and gap statistics |
| Group theory (symmetry) | capable_agent_cage.py | Symmetry of non-self-approval: no agent self-authorizes |
| Completeness & Compactness | dimensional_governor.py | Checks coverage of multi-dimensional assessments |
| Lattice theory | knowledge_maturity.py | Maturity levels form a lattice with well-defined joins |
| Computability (decidability) | All components | Self-testing = decidable check; WITHHOLD = undecidable |
Document version: 1.0 | August 2026 | Gergely Vámossy / QIERA | gergo@qiera.io License: MIT. All mathematical content is in the public domain.