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

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

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

# 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