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State Root Chain Approach for ZK Games

An analysis of using cryptographic state root chains for zero-knowledge game verification.

The Approach

Instead of proving facts about a game after it ends, prove each state transition as it happens:

Traditional ZK Game:

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ZK Tic-Tac-Toe Implementations Comparison

A survey of zero-knowledge proof implementations for tic-tac-toe games.

Implementations Overview

Implementation	Framework	Year	Language	Live Demo
andreysobol/tic-tac-toe-snark	ZoKrates	2019	JavaScript/Java	No
Aleo Leo Examples	Leo/Aleo	2022+	Leo	Playground

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Purging jsdelivr CDN Cache

When using cdn.jsdelivr.net/gh/{owner}/{repo}@latest/..., the @latest tag resolves to the latest GitHub Release (not just a git tag).

Common issue

You push a new tag but @latest still serves the old version because:

1. The tag has no corresponding GitHub Release

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Generics in Petri-Pilot Generated Code

Petri-pilot generates Go code that leverages generics from go-pflow for type-safe event sourcing.

1. Type-Safe Aggregate State Machine

Every generated aggregate uses eventsource.StateMachine[State] for compile-time type safety:

// generated/erc20token/aggregate.go

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# Petri Net Lemmas

Formal properties of arcnet's Petri net object model.

## Definitions

**Model** = (P, T, A) where:
- P = set of places
- T = set of transitions
- A = set of arcs ⊆ (P × T) ∪ (T × P)

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Dual State Engine Architecture

A template for building deterministic, verifiable systems with parallel Go/JavaScript implementations.

Core Concept

Build complex stateful systems where state is a function of events:

State(t) = fold(apply, initialState, events[0..t])

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Petri Net ODE Simulation Results

Simulation Parameters

• Time Span: 0 to 10
• Initial Step: 0.01
• Absolute Tolerance: 0.000001
• Relative Tolerance: 0.001

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