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using-simulation-foundations

@tachyon-beep/skillpacks
5
25

Router for simulation math - ODEs, state-space, stability, control, numerics, chaos, stochastic

Install Skill

Shared

Installs to .agents/skills, used by Codex, Amp, Warp, Cursor, OpenCode, and more.

CodexAmp
WarpCursorOpenCode
ClineGemini CLI
GitHub Copilot
Personal

Available across projects.

$npx skills-installer add @tachyon-beep/skillpacks/using-simulation-foundations --client shared
Project

Writes to .agents/skills.

$npx skills-installer add @tachyon-beep/skillpacks/using-simulation-foundations -p --client shared
Note: Review the skill instructions before using it.

SKILL.md

name using-simulation-foundations
description Use when a simulation needs numerical-model, integration, stability, control, stochastic or determinism checks.

Simulation Foundations

Use this contract for the concrete task. Apply a short relevant check for a small change; expand investigation when the failure, risk or requested artifact warrants it. Resolve facts from the repository and runtime before imposing a process. Delegation is optional and should answer a bounded unresolved question.

Mathematical and numerical contract

Identify state, units, transitions/rates, time scale, boundaries and the behavior the simulation must preserve. Choose continuous, discrete-event or hybrid modeling from the quantities and workload; an ODE is not mandatory for every game system.

  • State conservation, positivity, boundedness, equilibrium and event-order invariants relevant to the model.
  • Select an integrator using stiffness, step size, error/energy behavior and runtime budget. A locally accurate method may drift or destabilize over the required horizon.
  • Distinguish continuous-model stability from discrete-update stability. Linearization/eigenvalues have local assumptions and inconclusive cases; they do not prove all nonlinear trajectories safe.
  • Test boundaries, large time steps, long horizons and sensitivity to parameters/initial state. Mathematical predictions and empirical traces should agree within the declared tolerance.
  • Define determinism scope: same process, platform or cross-machine. Control RNG streams and arithmetic/order as required; fixed timestep or shared seed alone does not prove replay equivalence.
  • For controllers, record target, delay, saturation and disturbance assumptions. Validate overshoot, windup and response under actual update timing.
  • For random systems, distinguish the intended distribution from player-perceived fairness constraints such as pity bounds. Test both statistical behavior and deterministic replay where required.

Evidence and output

Produce the model and assumptions, selected method/step policy, invariant/error budget and validation traces. State what is analytically established, locally approximated or observed. Do not promise zero desyncs, no extinction or no overshoot from reading a recipe.

Fault-specific references

  • Rates/continuous behavior: differential-equations-for-games.md.
  • State/reachability: state-space-modeling.md.
  • Explosions or equilibrium questions: stability-analysis.md, with numerical-methods.md for discrete updates.
  • Tracking/delay/oscillation: feedback-control-theory.md.
  • Model mismatch: continuous-vs-discrete.md.
  • Sensitivity/desync or random-process behavior: chaos/stochastic sheets below.

Game-engine implementation and fidelity/LOD decisions belong to simulation tactics; system replay architecture belongs to determinism/replay. Load derivations only when needed to establish the task's proof or explain a concept.

Optional references

All sheets below are in this directory. Choose a sheet because its checks or examples help the task; there is no requirement to read the catalog in sequence. Verify time-sensitive APIs and numerical/performance claims before relying on examples.