Simulation Candidates Registry

Candidate Computational Models, Discrete State Machines & Invariant Stress Testing

Spine Position

Mathematics Root · Simulation Telemetry · Candidate Models

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 Simulation Pathway

The computational simulation pathway ($C2$–$C3$) provides numerical stress-testing and empirical falsification testbeds on the computational axis ($C$) for mathematical assertions across the Science of Fabric Reality. Alongside formal interactive theorem proving in Lean 4 (35 machine-verified proofs across 11 modules), candidate propositions are translated into executable discrete state machines (e.g. cellular automata, lattice field solvers, and operator resolvent packages) to validate structural invariants and numerical stability.

Primary Candidate Classes

• Recursive Observer Knots: Topologically validating that ${\mathcal{K}}_{n+1}$ can be constructed from ${\mathcal{K}}_n$ under localized projection constraints.
• Trace Reciprocity Flow: Numerically validating bilinear trace pairing rules and dual involution through discrete state transitions.
• KP Field Propagation: Finite-difference solvers checking wave propagation and energy conservation across elliptic-hyperbolic grids.
• Recursive Intelligence Networks: Multi-agent graph diffusion testing convergence to invariant equilibrium states.

TIP

Target Architecture: Language-agnostic (Motoko / Rust / Python CA prototypes) mapped to deterministic validation receipts.

---

2. Interactive Runtime & Candidates Table

---

3. Prototype Traces & Benchmarks

Auditable computational traces and invariant stress-test results:

• Closure Field Dynamics — Field closure convergence and boundary conditions.
• KP Field Propagation — High-order wave propagation and dispersion bounds.
• Invariant Preservation Check — Algorithmic checks for discrete 1-cycle conservation.
• Recursive Intelligence Network — Graph consensus and information preservation.

Note: Simulation traces record diagnostic verification runs; they do not constitute physical experiment data or ungrounded proof claims (ACTIVE_P4_SEALS = 0).

---

4. 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 Gateway	Lean 4 Formalization Roadmap	35 machine-verified theorem records and lemma dependency DAGs
Falsifiability Map	Falsifiability Index & Negative Theorems	Quantitative failure criteria and singular Fisher information bounds

EXTERNAL REFERENCE