Continuous Inverter

# Continuous Inverter

**Category**: Real-Time Monitoring + CI/CD
**Type**: Automated Measurement + Remediation
**Language**: Julia
**Status**: Production Ready
**Version**: 1.0.0
**Date**: December 22, 2025

## Overview

Real-time monitoring and automated remediation for proof system health. Runs on every commit to measure spectral gap across all 6 theorem provers in parallel, generates GitHub Actions CI/CD workflows, and provides automated suggestions when system health degrades.

## Key Data Structures

```julia
struct CommitMetadata
    commit_hash::String
    timestamp::Float64
    author::String
    files_changed::Int
    gap_before::Dict{String, Float64}
    gap_after::Dict{String, Float64}
end

struct CommitAnalysis
    commits::Vector{CommitMetadata}
    trend::String
    violations::Int
    recommendation::String
end
```

## Key Functions

- **`analyze_commit(commit_hash)`**: Measure gap before/after
- **`check_all_provers(files)`**: Parallel analysis across 6 provers
- **`generate_remediation_suggestions(gap_before, gap_after)`**: Automated advice
- **`generate_ci_cd_template()`**: GitHub Actions workflow YAML
- **`generate_monitoring_dashboard()`**: Trend visualization

## Supported Provers

- Dafny
- Lean 4
- Stellogen
- Coq
- Agda
- Idris

## Remediation Strategy

**Alternating Möbius Weights for Resonance Patterns**

When gap declines:
1. Identify which prover degraded
2. Run möbius_filter to find tangled paths
3. Apply safe_rewriting recommendations
4. Re-measure gap across all provers
5. Deploy changes via CI/CD

## Usage

```julia
using ContinuousInversion

# On every commit:
gap_after = compute_prover_gap(proofs)

# If gap < 0.25:
suggestions = suggest_remediation(prover, gap_before, gap_after)

# Generate CI/CD workflow:
yaml = generate_ci_cd_template()
```

## Integration Points

- GitHub Actions continuous deployment
- Per-prover parallel checking
- PR automation with gap status comments
- Artifact upload for compliance tracking

## Performance

- Commit analysis: < 1 second
- Per-prover check: Parallel across 6 provers
- Dashboard generation: < 2 seconds
- Total CI/CD latency: < 5 seconds

## Deployment

```bash
# Save workflow to repo
julia continuous_inversion.jl > .github/workflows/spectral-health-check.yml

# Push to trigger
git add .github/workflows/spectral-health-check.yml
git commit -m "Add spectral health check"
git push
```

## References

- Continuous integration best practices
- Automated remediation workflows
- Möbius inversion for pattern detection