Governance Physics: Empirical Foundations and Physical Grounding

This paper provides the empirical foundations and physical grounding for Governance Physics (GP), extending the axiomatic framework established in two prior works: Atomic Trust Systems (DOI: 10.5281/zenodo.17717049) and Governance Physics v2.1 (DOI: 10.5281/zenodo.18063583).

Key contributions:

1. Physical grounding of the Conservation Law in Landauer's principle and the Byzantine Bound in the Lamport-Shostak-Pease theorem
2. First-principles derivation of the D·I bound (κ = 0.534 predicted, 0.535 observed, <0.2% error)
3. Cross-domain empirical validation across five domains with >1M data points: blockchain DAO governance (n=12,341, AUC=0.87), social media bot detection (n=1,023,847, AUC=0.912), organizational health prediction (n=200, r=0.43), FlashAPCE neural verification (100% detection), and the Velado Limit phase transition (96.1% accuracy)
4. Stochastic extensions including Ornstein-Uhlenbeck dynamics for Byzantine index evolution and first passage time calculations
5. Topological extensions with network-dependent Byzantine bounds and scale-free vulnerability analysis
6. Three extended operators (resilience ρ, influence I, coherence Ξ) with formal axioms

Together with the prior papers, this completes Governance Physics as a mathematical theory of trust dynamics with substrate-independent validity.

One physics. Multiple substrates. Predictable invariants.