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

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Document version: 1.0 | August 2026 | Gergely Vámossy / QIERA | gergo@qiera.io License: MIT. All mathematical content is in the public domain.