PHASE_2_STAGE_4_DESIGN

Phase 2 Stage 4: Automatic Remediation - Design Document

Date: December 22, 2025 Status: Design Phase Phase: 2 Stage 4 - Automatic Remediation

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Overview

Automatic remediation system that detects and fixes issues in proof systems using the navigation cache from Stage 3. Maintains system health while respecting LHoTT resource constraints.

Inputs from Previous Stages:

• Stage 1: System health status (spectral gap, success rates)
• Stage 2: Comprehension regions and co-visitation patterns
• Stage 3: Navigation cache with proof paths and resource costs

Key Insight: Use cache statistics to identify underperforming regions, then apply targeted fixes.

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Problem Statement

Current Issues:

• Low cache hit rates in certain regions indicate weak proof organization
• High resource costs suggest inefficient proof paths
• Low success rates indicate unreliable proofs
• Resource exhaustion prevents further navigation

Remediation Goals:

1. Increase cache hit rates (target: >95%)
2. Reduce average resource costs per proof
3. Improve proof success rates
4. Maintain or improve spectral gap (health)

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Core Concepts

Remediation Strategies

Strategy 1: Path Optimization

• Identify expensive proofs in cache
• Find cheaper alternative paths via BFS
• Rewrite expensive path with cheaper alternative
• Cost: Low (path rewriting)
• Risk: Low (paths are equivalent)

Strategy 2: Dependency Strengthening

• Identify theorems with low incoming edges
• Find related theorems in co-visitation matrix
• Add edge if confidence high
• Cost: Medium (structural change)
• Risk: Medium (could create cycles)

Strategy 3: Region Rebalancing

• Identify regions with low hit rates
• Split region if too large
• Merge region if too small
• Cost: High (remapping)
• Risk: High (requires verification)

Strategy 4: Resource Optimization

• Track resource costs per theorem
• Identify high-cost proofs
• Apply cost reduction techniques
• Cost: Medium
• Risk: Low