Simulation Governance

Computational Governance Doctrine, Error Allocation & Reproducibility Standards

Spine Position

Mathematics Root · Simulation Governance · Computational Standards

Status Boundary

This work is part of the authorial PHYSICA / Science of Fabric Reality corpus. It is presented as a research framework, formalization target, computational model, or theoretical synthesis unless explicitly marked otherwise. It is not presented as accepted physics, external consensus, or experimentally confirmed science.

1. Computational Governance Doctrine

Simulation models within /04-mathematics/simulations/ and /04-mathematics/simulation-atlas operate under strict computational governance rules. Because numerical simulation can easily introduce discretization artifacts or numerical drift, empirical verification runs must adhere to machine-verified mathematical invariants.

Governance Rules for Simulation Models

1. Source Traceability: Every simulation target must map directly to an authoritative mathematical proposition or invariant registered in the Axioms Register or provenance/equation-provenance-ledger-v5.json.
2. Bounded Error Allocation: Numerical simulations of continuous topological fields must declare their spatial and temporal discretization steps, ensuring that conserved quantities are preserved within explicit tolerance bounds (${ϵ}_{\text{drift}}\le {10}^{-6}$).
3. Reproducible Diagnostic Traces: Any simulation trace cited in public documentation represents a deterministic diagnostic run executed under GILC CodexStation standards ($p_{\text{null}}=0.62$).

---

2. Epistemic Demarcation

┌─────────────────────────────────────────────────────────────────────────────┐
│                    SIMULATION GOVERNANCE PRINCIPLES                         │
│  1. Invariant Preservation: Simplicial boundary nullity (∂² = 0) holds      │
│  2. Error Bound Declaration: Explicit spatial-temporal Δx, Δt bounds        │
│  3. Null Permutation Verification: Standardized null benchmark (p = 0.62)   │
│  4. Non-Equivalence Law: Simulation belongs strictly on the C-axis (C0–C5); it is NEVER proof    │
└─────────────────────────────────────────────────────────────────────────────┘

---

3. Canonical Continuations

Direction	Target Resource	Purpose
Simulation Lab	Canonical Simulation Atlas Hub	15-point typed simulation contract, solver families, and $p_{\text{null}}=0.62$ benchmark
Simulation Bridge	Formalization ↔ Simulation Bridge	Diagnostic mapping between Lean 4 proofs and discrete numerical solvers
Proof Governance	Proof Governance & Verification Scale	Orthogonal status coordinates $S=(F,C,P,R,V)$ and verification scale
Proof Gateway	Lean 4 Formalization Roadmap	35 machine-verified theorem records and lemma dependency DAGs

EXTERNAL REFERENCE