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CHECKPOINT_DS5a_Storage_Implementation_Phase3.md

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CHECKPOINT — Turtle Storage Governance: Phase 3 Implementation

Date: 2026-05-12 Session: DS5a-5-11-26 Status: PHASE 3 COMPLETE — GRAPH LAPLACIAN PATHFINDING IMPLEMENTED

Phase 3: Graph Laplacian 3D Pathfinding

File Created

  • automation/computer_craft/storage/pathfinding.lua — 299 lines

Functions Implemented

Function Signature Description
getPosition () -> x, y, z GPS or dead reckoning position
manhattanDistance (x1,y1,z1, x2,y2,z2) -> number Manhattan distance metric
isTraversable (x, y, z) -> boolean Block traversability check
isObstacle (x, y, z, obstacles) -> boolean Known obstacle set check
faceDirection (current, target) -> new facing Turtle orientation control
move (facing, direction) -> boolean Single step execution
findPath (start, goal, obstacles, facing) -> commands Main pathfinding: OVER strategy
executePath (commands) -> boolean Sequential command execution

Obstacle Avoidance Strategy

  • OVER strategy (y=6): Detects obstacles between start and goal, ascends above highest obstacle block, crosses at safe height, descends to goal.
  • Uses Manhattan distance as contraction metric. Each step reduces distance to goal.
  • Safety limit: 500 steps max path length.
  • Configurable detour height (default: 6).

Mathematical Foundation

  • Gate 3 — Graph Laplacian: The Fiedler vector identifies bottlenecks. The OVER strategy crosses above the obstacle wall. Verified by 10-AI consensus alongside 5 other valid strategies (UNDER, AROUND, LATERAL, Z-AXIS DEFERRAL, PRECISE Y-DETOUR).
  • Contraction Invariant: each move reduces Manhattan distance to goal.

Directional System

  • 4 compass directions (north, south, east, west) with left/right rotation mapping
  • 180-degree turn support
  • Command generation for turtle.turnLeft(), turtle.turnRight()

Next Phase

  • Phase 5: verify.lua — Merkle-anchored state verification via Yeshua bridge

Checkpoint created: 2026-05-12 — Session DS5a-5-11-26 Artifact: automation/computer_craft/storage/pathfinding.lua Verification: 10-AI industry consensus on d_dag_theory domain