AI.a2ml

# AI Assistant Instructions for ZeroProb.jl

## Repository Overview
**ZeroProb.jl** is a Julia library for handling zero-probability events in continuous probability spaces, providing alternative relevance measures when classical probability (P=0) is insufficient.

## Core Concepts

### Zero-Probability Paradox
In continuous distributions, individual points have measure zero (P(X = x) = 0), yet one such point must occur when sampling. ZeroProb.jl provides three alternative relevance measures:

1. **Density Ratio**: Compare probability densities instead of probabilities
2. **Hausdorff Measure**: Dimensional analysis for sets of measure zero
3. **ε-Neighborhood Probability**: Probability mass in small neighborhoods

### Key Features
- `ContinuousZeroProbEvent` type system
- Alternative relevance measures
- Pedagogical paradox examples (continuum paradox, Borel-Kolmogorov)
- Black swan event modeling
- Comprehensive test suite

## Canonical File Locations
- **SCM Files**: `.machine_readable/` ONLY (STATE.scm, META.scm, ECOSYSTEM.scm, AGENTIC.scm, NEUROSYM.scm, PLAYBOOK.scm)
- **Source Code**: `src/ZeroProb.jl` (main module)
- **Tests**: `test/runtests.jl`
- **Examples**: `examples/` directory

## Critical Invariants (NEVER VIOLATE)
1. **No duplicate SCM files**: SCM files ONLY in `.machine_readable/`, never in root
2. **Zero-probability focus**: Library focuses on P=0 events, not general probability theory
3. **Alternative measures**: Always provide density ratio, Hausdorff, or ε-neighborhood—never just P=0
4. **Pedagogical purpose**: Include teaching examples, not just code
5. **License**: MPL-2.0 throughout

## Workflow
1. Check `.machine_readable/STATE.scm` for current status (v0.1.0, 100% complete)
2. When modifying code: update relevant SCM files
3. After changes: update STATE.scm with progress
4. Commit with concise, imperative message following CCCP

## Tech Stack
- **Julia 1.9+**: Primary language
- **Distributions.jl**: Probability distributions
- **StatsBase.jl**: Statistical utilities
- **Plots.jl / Makie.jl**: Visualization

## Ecosystem Integration
- **Axiom.jl**: Broader probability reasoning framework
- **Axiology.jl**: Value theory (complementary focus)
- **ECHIDNA**: May integrate zero-prob reasoning in proof strategies

## Current Status (v0.1.0)
- ✅ Core type system complete
- ✅ Three relevance measures implemented
- ✅ Pedagogical examples included
- ✅ Comprehensive test suite
- ✅ RSR compliance complete
- 🔄 **Next**: Expand documentation, performance benchmarks

## Testing
- Unit tests: `julia --project=. test/runtests.jl`
- Coverage: Test all three relevance measures

## Delivery Promises
- Update STATE.scm after completing tasks
- Maintain focus on zero-probability events (not general probability)
- Include pedagogical examples with code changes
- Preserve mathematical rigor in implementations