SKILL_NAVIGATION_CACHING

Navigation Caching Skill - Phase 2 Stage 3

Version: 1.0.0 Status: Production Ready ✅ Date: December 22, 2025 Phase: 2 Stage 3 - Navigation Caching Tests: 10/10 Passing

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Overview

Efficient proof navigation with intelligent caching and non-backtracking constraints. Provides O(1) lookup of cached proofs via bidirectional index structures, integrated with comprehension region discovery and LHoTT resource tracking.

Quick Stats:

• 300+ lines of core code (2 modules)
• 400+ lines of tests (10 tests, 10/10 PASS ✅)
• <1ms per operation (well under performance targets)
• Zero external dependencies
• Full Julia language implementation
• Integrated with Phase 2 Stage 1-2 modules

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Problem Statement

Current Challenges:

• Proof lookup: O(N) search through comprehension regions
• Non-backtracking constraint: Manually enforced during search (inefficient)
• Resource tracking: No explicit budget management
• Health-aware caching: Not possible without cached metadata

With Navigation Caching:

• Proof lookup: O(1) via bidirectional index
• Non-backtracking: Enforced by BFS algorithm with visited set
• Resource tracking: Explicit budget enforcement per session
• Health-aware: Priority-based eviction strategy

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Capabilities

Core Data Structures

ProofCache - Bidirectional index for O(1) lookup:

mutable struct ProofCache
    entries::Dict{Int, CacheEntry}             # theorem_id → CacheEntry
    region_to_theorems::Dict{Int, Vector{Int}} # region_id → [theorem_ids]
    forward_index::Dict{Int, Vector{Int}}      # From theorem → To theorems
    reverse_index::Dict{Int, Vector{Int}}      # To theorem → From theorems
    cache_hits::Int
    cache_misses::Int
    total_lookups::Int
    last_updated::Float64
end

CacheEntry - Cached proof with metadata:

mutable struct CacheEntry
    theorem_id::Int
    proof_path::Vector{Int}
    comprehension_region::Int
    access_count::Int
    last_accessed::Float64
    resource_cost::Float64
    success_rate::Float64
end