Governance Physics: A Mathematical Theory of Trust Computation
Bibliographic record
Abstract
We present Governance Physics, a complete mathematical framework for computing, propagating, and verifying trust in governance environments. The theory introduces ten operators—five primitive (Φ, Ψ, Δ, IP, T) and five emergent (Υ, Λ, Ω, Θ, Γ)—that form a closed algebraic system for trust computation. We establish the governance manifold where trust propagation follows geodesics, divergence induces Riemannian curvature, and conservation laws constrain system evolution. A unified field theory demonstrates that all governance phenomena derive from a single variational principle. Experimental validation with multi-LLM ensembles achieves 98.7% Byzantine detection, 94.2% classification accuracy, and r² = 0.87 stability prediction. The Atomic Trust System (ATS) provides the unique implementation satisfying all theoretical constraints, with cryptographic verification via BLAKE3 hashing and Merkle trees ensuring tamper-proof audit trails. This is the second paper in the Atomic Trust System series, extending the algebraic foundations established in the companion paper "Atomic Trust Systems: A Closed Algebraic Framework for Normative Interpretation, Propagation, and Verifiable Governance" (DOI: 10.5281/zenodo.17717049).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".